TSTP Solution File: SWW222+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW222+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 12:22:08 EDT 2023
% Result : Theorem 25.12s 6.40s
% Output : Refutation 26.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1363
% Syntax : Number of formulae : 2616 ( 844 unt; 112 typ; 0 def)
% Number of atoms : 6447 (1721 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 32489 ( 371 ~; 120 |; 699 &;28175 @)
% ( 277 <=>;2847 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 122 ( 122 >; 0 *; 0 +; 0 <<)
% Number of symbols : 114 ( 112 usr; 15 con; 0-3 aty)
% Number of variables : 4913 ( 0 ^;4840 !; 73 ?;4913 :)
% 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(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(v_p_type,type,
v_p: $i ).
thf(v_wa_____type,type,
v_wa____: $i ).
thf(v_z_____type,type,
v_z____: $i ).
thf(c_Rings_Oinverse__class_Odivide_type,type,
c_Rings_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: $i > $i > $i ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(v_s_____type,type,
v_s____: $i ).
thf(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
thf(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
thf(c_Int_OPls_type,type,
c_Int_OPls: $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
thf(class_Groups_Ogroup__add_type,type,
class_Groups_Ogroup__add: $i > $o ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(class_Rings_Oordered__cancel__semiring_type,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_Transcendental_Otan_type,type,
c_Transcendental_Otan: $i > $i ).
thf(c_Transcendental_Opi_type,type,
c_Transcendental_Opi: $i ).
thf(class_Rings_Oordered__semiring_type,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_type,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__comm__semiring__strict_type,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(class_Rings_Odivision__ring_type,type,
class_Rings_Odivision__ring: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Groups_Omonoid__add_type,type,
class_Groups_Omonoid__add: $i > $o ).
thf(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_type,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
thf(class_Rings_Osemiring_type,type,
class_Rings_Osemiring: $i > $o ).
thf(class_Groups_Oordered__ab__group__add_type,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(class_Rings_Omult__zero_type,type,
class_Rings_Omult__zero: $i > $o ).
thf(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(class_Rings_Ocomm__ring__1_type,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(class_Fields_Olinordered__field_type,type,
class_Fields_Olinordered__field: $i > $o ).
thf(class_Groups_Oordered__ab__group__add__abs_type,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
thf(class_Groups_Oab__group__add_type,type,
class_Groups_Oab__group__add: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_type,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Rings_Oordered__comm__semiring_type,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_type,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Fields_Ofield__inverse__zero_type,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(class_Int_Onumber_type,type,
class_Int_Onumber: $i > $o ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_RealDef_Oreal_type,type,
c_RealDef_Oreal: $i > $i > $i ).
thf(class_Rings_Olinordered__semiring__strict_type,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Rings_Ocomm__semiring_type,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(c_RComplete_Onatceiling_type,type,
c_RComplete_Onatceiling: $i > $i ).
thf(class_RealVector_Oreal__normed__div__algebra_type,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(c_Groups_Osgn__class_Osgn_type,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(class_Groups_Oab__semigroup__add_type,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__ring__strict_type,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(class_Rings_Odivision__ring__inverse__zero_type,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(class_Rings_Olinordered__ring_type,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_RealVector_Oreal__normed__field_type,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(c_Transcendental_Oarctan_type,type,
c_Transcendental_Oarctan: $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Rings_Ocomm__ring_type,type,
class_Rings_Ocomm__ring: $i > $o ).
thf(class_Rings_Olinordered__semiring__1_type,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_Rings_Oordered__ring__abs_type,type,
class_Rings_Oordered__ring__abs: $i > $o ).
thf(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
thf(class_Fields_Olinordered__field__inverse__zero_type,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(class_Rings_Olinordered__semiring__1__strict_type,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
thf(class_Rings_Oring__1__no__zero__divisors_type,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(class_Groups_Oabs__if_type,type,
class_Groups_Oabs__if: $i > $o ).
thf(class_Groups_Ocancel__comm__monoid__add_type,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
thf(class_Rings_Oordered__ring_type,type,
class_Rings_Oordered__ring: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_type,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(class_Rings_Oring__1_type,type,
class_Rings_Oring__1: $i > $o ).
thf(class_Rings_Osemiring__1_type,type,
class_Rings_Osemiring__1: $i > $o ).
thf(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Fields_Ofield_type,type,
class_Fields_Ofield: $i > $o ).
thf(c_Transcendental_Ocos_type,type,
c_Transcendental_Ocos: $i > $i ).
thf(class_Rings_Olinordered__semiring_type,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(v_r_type,type,
v_r: $i ).
thf(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(c_Int_Oiszero_type,type,
c_Int_Oiszero: $i > $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_type,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(class_Groups_Osgn__if_type,type,
class_Groups_Osgn__if: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_type,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(c_SEQ_Osubseq_type,type,
c_SEQ_Osubseq: $i > $o ).
thf(v_f_____type,type,
v_f____: $i ).
thf(class_Rings_Ono__zero__divisors_type,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra__1_type,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).
thf(class_Groups_Oone_type,type,
class_Groups_Oone: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_type,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(c_Polynomial_Oorder_type,type,
c_Polynomial_Oorder: $i > $i > $i > $i ).
thf(class_RealVector_Oreal__field_type,type,
class_RealVector_Oreal__field: $i > $o ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(v_g_____type,type,
v_g____: $i > $i ).
thf(v_d_____type,type,
v_d____: $i ).
thf(v_w_____type,type,
v_w____: $i ).
thf(268,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
thf(2163,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(29,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(1322,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)],[29]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( 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(2094,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(117,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(1633,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)],[117]) ).
thf(1151,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).
thf(4899,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(370,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__eq) ).
thf(2480,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(836,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(3927,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)],[836]) ).
thf(303,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
thf(2280,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( 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(2630,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(813,axiom,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
thf(3873,plain,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(910,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(4188,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)],[910]) ).
thf(1039,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
thf(4560,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(1002,axiom,
class_Fields_Ofield @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
thf(4447,plain,
class_Fields_Ofield @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(147,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
thf(1718,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(819,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).
thf(3883,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1214,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OPls @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).
thf(5116,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OPls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(1207,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(5088,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)],[1207]) ).
thf(44,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(1369,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)],[44]) ).
thf(498,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(2889,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)],[498]) ).
thf(310,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(2295,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)],[310]) ).
thf(1041,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ 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 @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).
thf(4571,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ 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 @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(883,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 @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
thf(4101,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 @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(326,axiom,
class_Int_Onumber__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
thf(2336,plain,
class_Int_Onumber__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(537,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(3008,plain,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(259,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(2131,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ B ) ) ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ B ) ) )
=> ( ( D != C )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1153,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(4909,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)],[1153]) ).
thf(251,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(2109,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)],[251]) ).
thf(1127,axiom,
class_Rings_Oring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
thf(4824,plain,
class_Rings_Oring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ D @ ( 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(3661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(868,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(4062,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)],[868]) ).
thf(1093,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(4729,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)],[1093]) ).
thf(855,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ B ) @ ( c_Transcendental_Oarctan @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__monotone) ).
thf(4022,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ B ) @ ( c_Transcendental_Oarctan @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(948,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(4290,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)],[948]) ).
thf(748,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
thf(3698,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(656,axiom,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(3397,plain,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(192,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 ) @ ( 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(1899,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 ) @ ( 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)],[192]) ).
thf(26,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(1315,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)],[26]) ).
thf(792,axiom,
class_Groups_Oone @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
thf(3830,plain,
class_Groups_Oone @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(408,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
thf(2595,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(1188,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(5028,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)],[1188]) ).
thf(1092,axiom,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
thf(4728,plain,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( 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(1950,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( 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 ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1218,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).
thf(5131,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(96,axiom,
! [A: $i] :
( ( c_Transcendental_Otan @ ( c_Transcendental_Oarctan @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__arctan) ).
thf(1549,plain,
! [A: $i] :
( ( c_Transcendental_Otan @ ( c_Transcendental_Oarctan @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
<=> ( ( ( B
= ( c_Nat_OSuc @ ( 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_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(3534,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
=> ( ( ( B
= ( c_Nat_OSuc @ ( 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_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( c_Nat_OSuc @ ( 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_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( c_Nat_OSuc @ ( 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)],[697]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
thf(1750,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(859,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(4037,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)],[859]) ).
thf(285,axiom,
class_Groups_Oab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
thf(2210,plain,
class_Groups_Oab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(923,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__pi__half__less__zero) ).
thf(4226,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( 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)],[923]) ).
thf(874,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_Ominus__class_Ominus @ 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_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
thf(4075,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_Ominus__class_Ominus @ 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_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(827,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).
thf(3905,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(375,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 @ B @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(2495,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 @ B @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(688,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( 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(3509,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( 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)],[688]) ).
thf(406,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
thf(2590,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(830,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(3912,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)],[830]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(4960,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(482,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 @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(2837,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 @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( 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(1305,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( 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)],[22]) ).
thf(1098,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(4747,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)],[1098]) ).
thf(1011,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
<=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
thf(4479,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(253,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
thf(2117,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(514,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(2940,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)],[514]) ).
thf(105,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(1596,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)],[105]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
thf(2231,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(414,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(2622,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)],[414]) ).
thf(807,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(3858,plain,
class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(64,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(1443,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)],[64]) ).
thf(464,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(2776,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ) )
& ( ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(428,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
= ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
thf(2659,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
= ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) )
& ( ( B
= ( 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)],[428]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( 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(2527,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(549,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(3040,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)],[549]) ).
thf(56,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(1422,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(297,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 ) )
=> ( ( 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(2248,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 ) )
=> ( ( 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 ) )
=> ( ( 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)],[297]) ).
thf(94,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
thf(1544,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( ( 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(2676,plain,
! [A: $i,B: $i] :
( ( ( ( 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 ) ) )
=> ( ( 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)],[432]) ).
thf(1088,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
thf(4711,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(1053,axiom,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
thf(4603,plain,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(2099,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(304,axiom,
class_Rings_Osemiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(2282,plain,
class_Rings_Osemiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(170,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Osemiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__1) ).
thf(1793,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Rings_Osemiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(659,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(3402,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)],[659]) ).
thf(487,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(2854,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)],[487]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
thf(1692,plain,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(1062,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(4623,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(1176,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).
thf(4973,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(780,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(3794,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)],[780]) ).
thf(433,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(2686,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)],[433]) ).
thf(363,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 @ ( 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 @ ( 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(2448,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[363]) ).
thf(724,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(3616,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)],[724]) ).
thf(1140,axiom,
! [A: $i] :
( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
thf(4856,plain,
! [A: $i] :
( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
thf(2459,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(703,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(3562,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)],[703]) ).
thf(1233,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(5178,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)],[1233]) ).
thf(708,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(3577,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)],[708]) ).
thf(263,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(2146,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)],[263]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).
thf(3895,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
thf(1426,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(3530,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( B = A )
<=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
thf(3049,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(1097,axiom,
! [A: $i] :
? [B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
& ( ( c_Transcendental_Otan @ B )
= A )
& ! [C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ C @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
& ( ( c_Transcendental_Otan @ C )
= A ) )
=> ( C = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__total) ).
thf(4739,plain,
! [A: $i] :
? [B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
& ( ( c_Transcendental_Otan @ B )
= A )
& ! [C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ C @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
& ( ( c_Transcendental_Otan @ C )
= A ) )
=> ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(1043,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(4575,plain,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(24,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber__ring) ).
thf(1310,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(535,axiom,
class_Int_Onumber @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
thf(3004,plain,
class_Int_Onumber @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(639,axiom,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(3332,plain,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(1069,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(4647,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)],[1069]) ).
thf(643,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(3367,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)],[643]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(3649,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(572,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(3135,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)],[572]) ).
thf(880,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(4097,plain,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(886,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(4110,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)],[886]) ).
thf(1026,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(4528,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(584,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(3175,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)],[584]) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(2316,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(670,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(3446,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)],[670]) ).
thf(1068,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(4638,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)],[1068]) ).
thf(1223,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(5146,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( 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(1872,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( 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)],[183]) ).
thf(31,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(1327,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)],[31]) ).
thf(746,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(3693,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(1070,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(4650,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(2476,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(1228,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
thf(5163,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(416,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(2627,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)],[416]) ).
thf(270,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(2168,plain,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(866,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(4058,plain,
class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(502,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(2901,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)],[502]) ).
thf(635,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(3313,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)],[635]) ).
thf(1114,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(4792,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)],[1114]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(2723,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(524,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(2972,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)],[524]) ).
thf(1217,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(5123,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)],[1217]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(1441,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(775,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(3777,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)],[775]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( 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(2886,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
thf(2405,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(1105,axiom,
class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
thf(4775,plain,
class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(796,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(3836,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(289,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(2216,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)],[289]) ).
thf(609,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(3236,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)],[609]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( 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(3766,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( ( 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 ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(847,axiom,
! [A: $i] :
( ( c_RComplete_Onatceiling @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__number__of__eq) ).
thf(3994,plain,
! [A: $i] :
( ( c_RComplete_Onatceiling @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(373,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
thf(2491,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__divide) ).
thf(3915,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(394,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(2548,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)],[394]) ).
thf(122,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(1645,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)],[122]) ).
thf(1195,axiom,
class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
thf(5056,plain,
class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(107,axiom,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(1601,plain,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(675,axiom,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(3466,plain,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(915,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(4198,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)],[915]) ).
thf(824,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ A ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_arctan__ubound) ).
thf(3898,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ A ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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)],[824]) ).
thf(1056,axiom,
class_Int_Onumber__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
thf(4607,plain,
class_Int_Onumber__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(42,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__comm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
thf(1366,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__comm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(347,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(2400,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)],[347]) ).
thf(1172,axiom,
? [A: $i] :
! [B: $i] :
( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ C ) @ v_r )
& ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ C ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mth2) ).
thf(4963,plain,
? [A: $i] :
! [B: $i] :
( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ C ) @ v_r )
& ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ C ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(241,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(2067,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)],[241]) ).
thf(90,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
thf(1529,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(959,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(4322,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)],[959]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(4156,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(817,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
thf(3878,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(85,axiom,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1518,plain,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( 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(1265,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(77,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
thf(1482,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(3597,plain,
! [A: $i,B: $i,C: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(3,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 @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(1254,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 @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1020,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).
thf(4511,plain,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(1186,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
thf(5024,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(978,axiom,
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pi__half__neq__zero) ).
thf(4386,plain,
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( 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)],[978]) ).
thf(519,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(2957,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(789,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(3820,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)],[789]) ).
thf(17,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(1287,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)],[17]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ 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_diff__divide__distrib) ).
thf(4896,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ 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)],[1150]) ).
thf(475,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(2814,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)],[475]) ).
thf(622,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(3275,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)],[622]) ).
thf(683,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
thf(3495,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(1100,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(4761,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)],[1100]) ).
thf(1238,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(5188,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)],[1238]) ).
thf(1199,axiom,
class_Groups_Ozero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
thf(5064,plain,
class_Groups_Ozero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(6,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(1264,plain,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(575,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(3148,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)],[575]) ).
thf(1107,axiom,
class_Rings_Oordered__ring__abs @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
thf(4778,plain,
class_Rings_Oordered__ring__abs @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(894,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 @ ( 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 @ ( 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(4130,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[894]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(3744,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(438,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(2703,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ c_Int_OPls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(3248,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(927,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A )
= ( 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_diff__int__def) ).
thf(4238,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(1031,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(4539,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)],[1031]) ).
thf(1169,axiom,
class_Rings_Oring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
thf(4956,plain,
class_Rings_Oring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(128,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(1660,plain,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(20,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
thf(1298,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(568,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( 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(3116,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(898,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ c_Transcendental_Opi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pi__ge__two) ).
thf(4151,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ c_Transcendental_Opi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(103,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
= ( 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(1577,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
= ( 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
= ( 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)],[103]) ).
thf(624,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(3280,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)],[624]) ).
thf(769,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(3749,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)],[769]) ).
thf(801,axiom,
class_Groups_Ozero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
thf(3845,plain,
class_Groups_Ozero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(559,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(3089,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)],[559]) ).
thf(783,axiom,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
thf(3803,plain,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(1211,axiom,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ v_z____ ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ v_z____ ) ) @ v_d____ ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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_d_I2_J) ).
thf(5108,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ v_z____ ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ v_z____ ) ) @ v_d____ ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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)],[1211]) ).
thf(257,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(2126,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)],[257]) ).
thf(1102,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(4766,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)],[1102]) ).
thf(70,axiom,
! [A: $i] :
( ( c_RComplete_Onatceiling @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
thf(1462,plain,
! [A: $i] :
( ( c_RComplete_Onatceiling @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(994,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(4428,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(806,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(3855,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(453,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(2745,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)],[453]) ).
thf(403,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(2571,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(436,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(2691,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)],[436]) ).
thf(1142,axiom,
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ v_wa____ @ v_z____ ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ v_wa____ @ v_z____ ) ) @ v_d____ ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_wa____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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__0960_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_061_061_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).
thf(4862,plain,
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ v_wa____ @ v_z____ ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ v_wa____ @ v_z____ ) ) @ v_d____ ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_wa____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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)],[1142]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ c_Transcendental_Opi ) ) )
= ( c_Transcendental_Otan @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__periodic__nat) ).
thf(1704,plain,
! [A: $i,B: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ c_Transcendental_Opi ) ) )
= ( c_Transcendental_Otan @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ ( c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(1479,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ ( c_Nat_OSuc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(601,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(3216,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(1131,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) @ v_r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wr) ).
thf(4830,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) @ v_r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(101,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
thf(1568,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1006,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(4460,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)],[1006]) ).
thf(980,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cos__gt__zero__pi) ).
thf(4390,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(953,axiom,
? [A: $i] :
! [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ A @ B ) ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( hAPP @ A @ B ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096) ).
thf(4302,plain,
? [A: $i] :
! [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ A @ B ) ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( hAPP @ A @ B ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(1074,axiom,
class_Rings_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
thf(4669,plain,
class_Rings_Omult__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(1051,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(4595,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)],[1051]) ).
thf(798,axiom,
class_Groups_Osgn__if @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).
thf(3840,plain,
class_Groups_Osgn__if @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( B
= ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1379,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( B
= ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(645,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
thf(3374,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(271,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 @ ( 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(2169,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(349,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
thf(2403,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(729,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
thf(3638,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(907,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(4179,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)],[907]) ).
thf(1239,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ 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_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__special_I2_J) ).
thf(5193,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ 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_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1014,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
thf(4492,plain,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1159,axiom,
( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
thf(4928,plain,
( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(35,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
thf(1347,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__idom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oabs__class_Oabs @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).
thf(3919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__idom @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oabs__class_Oabs @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oabs__class_Oabs @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(2929,plain,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1076,axiom,
class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
thf(4675,plain,
class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(1168,axiom,
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ v_r )
& ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096) ).
thf(4952,plain,
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ v_r )
& ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(2730,plain,
! [A: $i,B: $i,C: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(384,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(2520,plain,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(895,axiom,
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pi__not__less__zero) ).
thf(4141,plain,
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(228,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(2024,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)],[228]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).
thf(1641,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(795,axiom,
class_Groups_Oabs__if @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).
thf(3835,plain,
class_Groups_Oabs__if @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1201,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(5076,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)],[1201]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(1963,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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)],[210]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).
thf(4400,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(184,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(1875,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)],[184]) ).
thf(1103,axiom,
class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
thf(4771,plain,
class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(607,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).
thf(3231,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( 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)],[607]) ).
thf(851,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(4008,plain,
class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(616,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(3258,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)],[616]) ).
thf(637,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(3322,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)],[637]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
thf(1465,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(666,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 @ ( 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(3431,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 @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(654,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(3393,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(532,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(2996,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)],[532]) ).
thf(739,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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(3670,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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(255,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Omult__zero @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
thf(2122,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Omult__zero @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1123,axiom,
class_Rings_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
thf(4815,plain,
class_Rings_Oidom @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(845,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(3973,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)],[845]) ).
thf(1227,axiom,
! [A: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( 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(5156,plain,
! [A: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( 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 ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(308,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(2291,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(243,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
thf(2073,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ 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_Oabs__class_Oabs @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sum__triangle__ineq) ).
thf(3851,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(1083,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) @ ( 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(4696,plain,
! [A: $i,B: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) @ ( 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)],[1083]) ).
thf(1180,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(4988,plain,
! [A: $i] :
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(3966,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
thf(2027,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(594,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ c_Transcendental_Opi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pi__ge__zero) ).
thf(3199,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ c_Transcendental_Opi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) @ ( 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 )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ A ) )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( 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(3934,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) @ ( 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 )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ A ) )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(1004,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(4454,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)],[1004]) ).
thf(1052,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit1 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).
thf(4600,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit1 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(500,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(2893,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)],[500]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( 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(2469,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( 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)],[366]) ).
thf(693,axiom,
! [A: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).
thf(3527,plain,
! [A: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(750,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ ( 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(3702,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(846,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 @ ( 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 @ ( 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(3983,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[846]) ).
thf(706,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Oring__char__0 @ B )
& ( class_Rings_Oidom @ B ) )
=> ( ( ( c_Polynomial_Opoly @ B @ A )
= ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).
thf(3569,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Oring__char__0 @ B )
& ( class_Rings_Oidom @ B ) )
=> ( ( ( ( c_Polynomial_Opoly @ B @ A )
= ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Polynomial_Opoly @ B @ A )
= ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(392,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(2540,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1220,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_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(5135,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_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(834,axiom,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
thf(3923,plain,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(209,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(1960,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1244,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(5210,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)],[1244]) ).
thf(371,axiom,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(2483,plain,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(527,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
thf(2979,plain,
class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(461,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(2772,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(1230,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(5169,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)],[1230]) ).
thf(1128,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(4825,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)],[1128]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
thf(1405,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(473,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(2804,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)],[473]) ).
thf(1221,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).
thf(5137,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(869,axiom,
class_Groups_Oone @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
thf(4065,plain,
class_Groups_Oone @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(1192,axiom,
! [A: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
thf(5045,plain,
! [A: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(381,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
thf(2508,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ ( 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)],[381]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( ( B
= ( c_Nat_OSuc @ ( 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_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(1843,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( ( B
= ( c_Nat_OSuc @ ( 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_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( c_Nat_OSuc @ ( 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_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(237,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(2058,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)],[237]) ).
thf(864,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
thf(4055,plain,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(556,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(3068,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)],[556]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(1896,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(1208,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(5096,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)],[1208]) ).
thf(664,axiom,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(3421,plain,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(172,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 ) )
=> ( ( 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(1796,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 ) )
=> ( ( 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 ) )
=> ( ( 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)],[172]) ).
thf(546,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(3036,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(2530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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)],[388]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
thf(1526,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(954,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
& ( ( c_Transcendental_Otan @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__total__pos) ).
thf(4307,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
& ( ( c_Transcendental_Otan @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(860,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__leI) ).
thf(4040,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A )
<=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
thf(2002,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A )
=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) )
& ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1030,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
thf(4536,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(841,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( 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_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(3955,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( 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_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_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 @ ( 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)],[841]) ).
thf(604,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(3226,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(206,axiom,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(1943,plain,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(712,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(3588,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(702,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(3559,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)],[702]) ).
thf(945,axiom,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
thf(4285,plain,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(344,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(2392,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)],[344]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
thf(2154,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
thf(1521,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1049,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
thf(4588,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(444,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(2718,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)],[444]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E @ C @ ( 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(2205,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E @ C @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(139,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(1696,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)],[139]) ).
thf(588,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(3184,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)],[588]) ).
thf(606,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(3229,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)],[606]) ).
thf(1054,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(4604,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)],[1054]) ).
thf(685,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(3503,plain,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(713,axiom,
class_Rings_Osemiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
thf(3591,plain,
class_Rings_Osemiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(705,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(3567,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(3720,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ 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_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(1028,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(4531,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)],[1028]) ).
thf(335,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(2364,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)],[335]) ).
thf(236,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 @ ( 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 @ ( 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(2047,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[236]) ).
thf(973,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(4370,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)],[973]) ).
thf(1044,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(4576,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)],[1044]) ).
thf(1085,axiom,
! [A: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Transcendental_Otan @ A ) )
= ( c_Transcendental_Otan @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_tan__inverse) ).
thf(4700,plain,
! [A: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Transcendental_Otan @ A ) )
= ( c_Transcendental_Otan @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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)],[1085]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(2954,plain,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(1651,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1231,axiom,
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_r )
=> ? [A: $i] :
! [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).
thf(5174,plain,
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_r )
=> ? [A: $i] :
! [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(576,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
thf(3151,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(563,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(3097,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)],[563]) ).
thf(1065,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
thf(4629,plain,
class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
thf(2473,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(583,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(3169,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)],[583]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).
thf(2646,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(882,axiom,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
thf(4100,plain,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(955,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(4312,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(867,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
thf(4059,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(164,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
thf(1768,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
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_less__imp__le__nat) ).
thf(1868,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(238,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(2061,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)],[238]) ).
thf(698,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).
thf(3550,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(902,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
thf(4172,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(462,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Olinordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
thf(2773,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Olinordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(118,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
thf(1636,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1216,axiom,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(5122,plain,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(663,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( 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(3418,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(1157,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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
thf(4925,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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(150,axiom,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1730,plain,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(547,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Int_Onumber @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber) ).
thf(3037,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Int_Onumber @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(743,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(3679,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)],[743]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
thf(1274,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(718,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 ) @ ( 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(3603,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 ) @ ( 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)],[718]) ).
thf(38,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(1355,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)],[38]) ).
thf(997,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(4434,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)],[997]) ).
thf(102,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(1570,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)],[102]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(1502,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(131,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 @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(1666,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 @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(79,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(1487,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)],[79]) ).
thf(722,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(3610,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)],[722]) ).
thf(513,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
thf(2937,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(1110,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).
thf(4785,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(113,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(1619,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)],[113]) ).
thf(1126,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
=> ( ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
=> ( 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__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096) ).
thf(4821,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
=> ( ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(353,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(2414,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)],[353]) ).
thf(738,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(3664,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)],[738]) ).
thf(411,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(2601,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(790,axiom,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
thf(3827,plain,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( 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(3711,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( 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)],[755]) ).
thf(450,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( 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(2733,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( 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)],[450]) ).
thf(86,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(1519,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)],[86]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
thf(4397,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(770,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( 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_less__Suc0) ).
thf(3752,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( 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 @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(610,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(3239,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(577,axiom,
class_Rings_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(3154,plain,
class_Rings_Oidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1015,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(4493,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)],[1015]) ).
thf(1205,axiom,
class_Rings_Oidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
thf(5085,plain,
class_Rings_Oidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(599,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(3207,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)],[599]) ).
thf(744,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(3682,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)],[744]) ).
thf(641,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
= ( 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(3339,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
= ( 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
= ( 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)],[641]) ).
thf(224,axiom,
class_Groups_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(2015,plain,
class_Groups_Omonoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(626,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3286,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(187,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(1883,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)],[187]) ).
thf(840,axiom,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__def) ).
thf(3948,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(108,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( 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(1602,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( 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)],[108]) ).
thf(555,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 @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(3065,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 @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(816,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
thf(3877,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(961,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(4327,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)],[961]) ).
thf(275,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(2179,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)],[275]) ).
thf(1190,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(5038,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)],[1190]) ).
thf(126,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(1656,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)],[126]) ).
thf(286,axiom,
class_Rings_Olinordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(2211,plain,
class_Rings_Olinordered__idom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(772,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(3763,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)],[772]) ).
thf(425,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( 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(2653,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( 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)],[425]) ).
thf(620,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(3271,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(3166,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
thf(1938,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(942,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 @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).
thf(4280,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 @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(41,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(1365,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(912,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ B ) @ ( c_Transcendental_Oarctan @ A ) )
= ( c_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__add) ).
thf(4192,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ B ) @ ( c_Transcendental_Oarctan @ A ) )
= ( c_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(431,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(2670,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)],[431]) ).
thf(786,axiom,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
thf(3810,plain,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(1057,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).
thf(4608,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( 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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( 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(1920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( 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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(1047,axiom,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
thf(4585,plain,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(358,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(2433,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)],[358]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(1968,plain,
! [A: $i,B: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( 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(2565,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( 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)],[401]) ).
thf(98,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(1555,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)],[98]) ).
thf(324,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Osgn__if @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).
thf(2332,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Osgn__if @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(900,axiom,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
thf(4155,plain,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(494,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(2872,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)],[494]) ).
thf(977,axiom,
class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
thf(4385,plain,
class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1185,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_RealVector_Oreal__normed__algebra__1 @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__number__of) ).
thf(5021,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_RealVector_Oreal__normed__algebra__1 @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(1106,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).
thf(4776,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(716,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(3600,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(175,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(1836,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)],[175]) ).
thf(1213,axiom,
! [A: $i] :
( ( c_Transcendental_Oarctan @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__minus) ).
thf(5113,plain,
! [A: $i] :
( ( c_Transcendental_Oarctan @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(276,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(2181,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)],[276]) ).
thf(988,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(4417,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)],[988]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(3028,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(330,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(2345,plain,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(761,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 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(3727,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 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(15,axiom,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1281,plain,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1094,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(4732,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)],[1094]) ).
thf(292,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 @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).
thf(2228,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 @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(545,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(3033,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(155,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(1740,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(460,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
thf(2769,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(858,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(4027,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)],[858]) ).
thf(957,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Transcendental_Oarctan @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ A ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_arctan__bounded) ).
thf(4316,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Transcendental_Oarctan @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ A ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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)],[957]) ).
thf(39,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(1360,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)],[39]) ).
thf(661,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(3413,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(1534,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1013,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(4486,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)],[1013]) ).
thf(648,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
thf(3381,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( class_Groups_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(440,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(2709,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(3218,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ 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_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
thf(1672,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(842,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(3963,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)],[842]) ).
thf(1135,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
thf(4840,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(1203,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(5081,plain,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
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(4012,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(885,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
thf(4109,plain,
class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(533,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(3001,plain,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(553,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(3060,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)],[553]) ).
thf(676,axiom,
class_Rings_Osemiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(3467,plain,
class_Rings_Osemiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(312,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(2300,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ A )
= ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit0) ).
thf(1983,plain,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ A )
= ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(1170,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ 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 @ tc_Nat_Onat ) )
| ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__2__cases) ).
thf(4957,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ 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 @ tc_Nat_Onat ) )
| ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(793,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(3831,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)],[793]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(2115,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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)],[252]) ).
thf(9,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(1270,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1209,axiom,
! [A: $i] :
( ( c_SEQ_Osubseq @ A )
<=> ! [B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__def) ).
thf(5098,plain,
! [A: $i] :
( ( ( c_SEQ_Osubseq @ A )
=> ! [B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) ) ) )
& ( ! [B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) ) )
=> ( c_SEQ_Osubseq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(5,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(1259,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)],[5]) ).
thf(570,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
thf(3122,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(515,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(2946,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)],[515]) ).
thf(530,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(2990,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)],[530]) ).
thf(340,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(2377,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)],[340]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
thf(2801,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1025,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( 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(4525,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( 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)],[1025]) ).
thf(1082,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ 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 @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).
thf(4693,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ 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 @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1137,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(4845,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)],[1137]) ).
thf(185,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(1878,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(651,axiom,
class_Groups_Osgn__if @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
thf(3386,plain,
class_Groups_Osgn__if @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1160,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
thf(4930,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(1719,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
thf(4227,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(391,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(2537,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)],[391]) ).
thf(879,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(4095,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)],[879]) ).
thf(569,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( 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(3119,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(161,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( 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(1755,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(838,axiom,
! [A: $i] :
( ( c_Int_OBit1 @ A )
!= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
thf(3941,plain,
! [A: $i] :
( ( c_Int_OBit1 @ A )
!= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(668,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ 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_diff__0__eq__0) ).
thf(3440,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ 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)],[668]) ).
thf(597,axiom,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(3205,plain,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(1077,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(4676,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)],[1077]) ).
thf(1229,axiom,
! [A: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( 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_Transcendental_Opi ) ) )
= ( c_Transcendental_Otan @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__periodic) ).
thf(5166,plain,
! [A: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( 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_Transcendental_Opi ) ) )
= ( c_Transcendental_Otan @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(205,axiom,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
thf(1942,plain,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(802,axiom,
~ ! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ~ ! [B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(3846,plain,
~ ! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ~ ! [B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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)],[802]) ).
thf(1104,axiom,
! [A: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Transcendental_Otan @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__minus) ).
thf(4772,plain,
! [A: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Transcendental_Otan @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
thf(2830,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(756,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
thf(3714,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(2419,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(281,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(2196,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)],[281]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(2613,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C )
= A ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C )
= A )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( 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(3294,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
thf(1419,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(81,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(1493,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)],[81]) ).
thf(471,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(2798,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)],[471]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).
thf(3775,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(634,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(3311,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)],[634]) ).
thf(1046,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(4582,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)],[1046]) ).
thf(586,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(3179,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(18,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(1292,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)],[18]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( 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__mult) ).
thf(3622,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( 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)],[725]) ).
thf(154,axiom,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1739,plain,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(993,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( 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(4425,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( 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)],[993]) ).
thf(492,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 @ ( 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(2868,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(979,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(4389,plain,
class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(991,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(4421,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)],[991]) ).
thf(57,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(1424,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)],[57]) ).
thf(317,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(2312,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)],[317]) ).
thf(1099,axiom,
! [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ C ) @ v_r )
& ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ C ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ v_s____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s) ).
thf(4750,plain,
! [A: $i] :
( ( ? [B: $i] :
( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ C ) @ v_r )
& ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ C ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ v_s____ ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ v_s____ )
=> ? [B: $i] :
( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ C ) @ v_r )
& ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ C ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1034,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(4545,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)],[1034]) ).
thf(244,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
thf(2080,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( 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_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1162,axiom,
class_Rings_Osemiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
thf(4938,plain,
class_Rings_Osemiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(986,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Oring__char__0 @ C )
& ( class_Rings_Oidom @ C ) )
=> ( ( ( c_Polynomial_Opoly @ C @ B )
= ( c_Polynomial_Opoly @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
thf(4406,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Oring__char__0 @ C )
& ( class_Rings_Oidom @ C ) )
=> ( ( ( ( c_Polynomial_Opoly @ C @ B )
= ( c_Polynomial_Opoly @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Polynomial_Opoly @ C @ B )
= ( c_Polynomial_Opoly @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(911,axiom,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
thf(4191,plain,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(1021,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(4513,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)],[1021]) ).
thf(592,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( 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(3194,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(332,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(2349,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)],[332]) ).
thf(233,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
thf(2038,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( 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(1446,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( 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)],[66]) ).
thf(732,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(3643,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)],[732]) ).
thf(1000,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 @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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_e2) ).
thf(4444,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 @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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)],[1000]) ).
thf(429,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
thf(2666,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(700,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(3555,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)],[700]) ).
thf(1005,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Transcendental_Oarctan @ ( c_Transcendental_Otan @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__tan) ).
thf(4457,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Transcendental_Oarctan @ ( c_Transcendental_Otan @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( 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(1612,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1061,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( v_g____ @ A ) ) @ v_r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_g_I1_J) ).
thf(4621,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( v_g____ @ A ) ) @ v_r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(423,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(2649,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)],[423]) ).
thf(976,axiom,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(4384,plain,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1225,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(5149,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)],[1225]) ).
thf(1219,axiom,
class_Groups_Oab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
thf(5134,plain,
class_Groups_Oab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(1251,axiom,
class_Int_Onumber @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
thf(5234,plain,
class_Int_Onumber @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
thf(4244,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(376,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(2497,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(965,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(4347,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)],[965]) ).
thf(727,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(3628,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)],[727]) ).
thf(969,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( 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_Transcendental_Opi ) ) @ c_Transcendental_Opi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m2pi__less__pi) ).
thf(4361,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( 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_Transcendental_Opi ) ) @ c_Transcendental_Opi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1117,axiom,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
thf(4804,plain,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
thf(3242,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(522,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(2968,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)],[522]) ).
thf(1198,axiom,
class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
thf(5063,plain,
class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(30,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_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
thf(1324,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_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(2285,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(511,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(2932,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)],[511]) ).
thf(735,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(3654,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ 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__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(481,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(2836,plain,
class_Groups_Ozero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
thf(1456,plain,
! [A: $i,B: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1019,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__MVT) ).
thf(4508,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(49,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
= ( 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(1382,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
= ( 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
= ( 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)],[49]) ).
thf(871,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(4068,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)],[871]) ).
thf(342,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(2387,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)],[342]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Nat_OSuc @ B )
!= A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(1552,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Nat_OSuc @ B )
!= A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(296,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(2243,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)],[296]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
thf(2505,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(653,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).
thf(3390,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( 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)],[653]) ).
thf(1130,axiom,
class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
thf(4829,plain,
class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
thf(1429,plain,
! [A: $i,B: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1247,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ ( c_Nat_OSuc @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(5217,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ ( c_Nat_OSuc @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(613,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
thf(3247,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(489,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_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(2862,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_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)],[489]) ).
thf(459,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).
thf(2766,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(106,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
thf(1599,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1152,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(4902,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)],[1152]) ).
thf(146,axiom,
! [A: $i] :
( ( 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(1715,plain,
! [A: $i] :
( ( 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)],[146]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B )
= ( 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(3333,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
thf(4152,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(933,axiom,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
thf(4259,plain,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(565,axiom,
! [A: $i] :
( ( 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(3109,plain,
! [A: $i] :
( ( 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)],[565]) ).
thf(536,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(3005,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)],[536]) ).
thf(260,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(2140,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)],[260]) ).
thf(457,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(2756,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ 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 @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(1226,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(5153,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)],[1226]) ).
thf(173,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 ) )
=> ( ( 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(1814,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 ) )
=> ( ( 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 ) )
=> ( ( 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)],[173]) ).
thf(913,axiom,
( ( c_Transcendental_Otan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( 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_tan__45) ).
thf(4195,plain,
( ( c_Transcendental_Otan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( 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)],[913]) ).
thf(167,axiom,
! [A: $i] :
( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
thf(1779,plain,
! [A: $i] :
( ( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(920,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(4212,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)],[920]) ).
thf(1010,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(4476,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)],[1010]) ).
thf(454,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 @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(2748,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 @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(348,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(2402,plain,
class_Groups_Omonoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(291,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 ) @ ( 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(2221,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 ) @ ( 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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(799,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(3841,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)],[799]) ).
thf(61,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(1434,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)],[61]) ).
thf(826,axiom,
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( 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_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit1 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) @ ( c_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_machin) ).
thf(3903,plain,
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( 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_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit1 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) @ ( c_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(908,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(4184,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)],[908]) ).
thf(220,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 @ ( 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 @ ( 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(1991,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[220]) ).
thf(794,axiom,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(3834,plain,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(284,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(2208,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)],[284]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Oring @ D ) )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).
thf(4782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Oring @ D ) )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(1173,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(4966,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)],[1173]) ).
thf(138,axiom,
class_Rings_Olinordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1695,plain,
class_Rings_Olinordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(714,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(3592,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ 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 @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
thf(1712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(633,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
<=> ( 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_real__of__nat__gt__zero__cancel__iff) ).
thf(3306,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( 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 )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(361,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(2440,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)],[361]) ).
thf(1003,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__interval__iff) ).
thf(4448,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(351,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).
thf(2408,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( 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)],[351]) ).
thf(469,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(2793,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(1243,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(5209,plain,
class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(130,axiom,
! [A: $i] :
( ( 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(1663,plain,
! [A: $i] :
( ( 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)],[130]) ).
thf(590,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(3190,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)],[590]) ).
thf(421,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(2645,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(278,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
thf(2189,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1242,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 @ ( 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 @ ( 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(5198,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[1242]) ).
thf(112,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(1616,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)],[112]) ).
thf(665,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( B
= ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(3422,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( B
= ( c_Nat_OSuc @ A ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( B
= ( c_Nat_OSuc @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(504,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Ocos @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cos__le__one) ).
thf(2909,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Ocos @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1036,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) @ v_r )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s1m) ).
thf(4550,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) @ v_r )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(785,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(3807,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)],[785]) ).
thf(1156,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(4921,plain,
! [A: $i,B: $i] :
( ( c_Int_OBit1 @ B )
!= ( c_Int_OBit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(123,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(1648,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield__inverse__zero @ E )
=> ( ( 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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
thf(3707,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield__inverse__zero @ E )
=> ( ( 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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(1144,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 @ c_Transcendental_Opi @ ( 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_pi__half__gt__zero) ).
thf(4872,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 @ c_Transcendental_Opi @ ( 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)],[1144]) ).
thf(822,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
thf(3890,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(11,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(1273,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Oring @ D ) )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).
thf(5048,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Oring @ D ) )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(3289,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(747,axiom,
( ( 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(3696,plain,
( ( 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)],[747]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( 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(2524,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( 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)],[386]) ).
thf(579,axiom,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(3158,plain,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(295,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( 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(2235,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(262,axiom,
( c_Int_OPls
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
thf(2144,plain,
( c_Int_OPls
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( B
= ( 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(1698,plain,
! [A: $i,B: $i] :
( ( B
= ( 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)],[140]) ).
thf(967,axiom,
class_Groups_Ogroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
thf(4354,plain,
class_Groups_Ogroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(398,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
thf(2556,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(888,axiom,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
thf(4116,plain,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ B )
= ( 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(3358,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ B )
= ( 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 ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ B )
= ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(812,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(3871,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)],[812]) ).
thf(231,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(2033,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)],[231]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
thf(2149,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(443,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(2717,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(720,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 ) @ ( 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(3607,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 ) @ ( 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)],[720]) ).
thf(987,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(4412,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)],[987]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(1747,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(765,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(3738,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)],[765]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(4340,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(104,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(1595,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(821,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(3888,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)],[821]) ).
thf(46,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(1374,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)],[46]) ).
thf(971,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(4365,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)],[971]) ).
thf(1164,axiom,
class_Rings_Osemiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__1) ).
thf(4943,plain,
class_Rings_Osemiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(644,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(3372,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)],[644]) ).
thf(636,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
thf(3319,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(3504,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).
thf(2789,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(679,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)],[679]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
thf(3086,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(1087,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(4709,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)],[1087]) ).
thf(211,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(1965,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1166,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ 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 ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).
thf(4946,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ 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 ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(4,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(1256,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)],[4]) ).
thf(479,axiom,
! [A: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ c_Transcendental_Opi ) )
= ( c_Transcendental_Otan @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__periodic__pi) ).
thf(2827,plain,
! [A: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ c_Transcendental_Opi ) )
= ( c_Transcendental_Otan @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(600,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(3213,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)],[600]) ).
thf(849,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(4000,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)],[849]) ).
thf(652,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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( 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(3387,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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(589,axiom,
! [A: $i] :
( ( 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(3187,plain,
! [A: $i] :
( ( 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)],[589]) ).
thf(766,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(3741,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( 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)],[766]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(1833,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(3234,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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)],[608]) ).
thf(488,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(2859,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)],[488]) ).
thf(944,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(4283,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)],[944]) ).
thf(111,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
thf(1615,plain,
class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(615,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(3255,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)],[615]) ).
thf(787,axiom,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(3811,plain,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(468,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
thf(2791,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(1200,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 @ ( 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 @ ( 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(5065,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[1200]) ).
thf(721,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(3609,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(427,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
thf(2657,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(485,axiom,
class_Rings_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(2849,plain,
class_Rings_Oring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(764,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(3736,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(201,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(1929,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(839,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(3945,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)],[839]) ).
thf(625,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(3283,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
thf(2016,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(402,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(2568,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1007,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(4465,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)],[1007]) ).
thf(825,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(3900,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)],[825]) ).
thf(51,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(1403,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)],[51]) ).
thf(672,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(3458,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(171,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(1795,plain,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
thf(1701,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1050,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
thf(4590,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ 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_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(1059,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
thf(4612,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( D = C )
=> ( B = A ) )
& ( ( B = A )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1237,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(5185,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__iff) ).
thf(4978,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(25,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(1312,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)],[25]) ).
thf(897,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 @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).
thf(4149,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 @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(534,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(3002,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)],[534]) ).
thf(1206,axiom,
! [A: $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 @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
thf(5086,plain,
! [A: $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 @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(456,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(2753,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)],[456]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
thf(3783,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(1765,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(939,axiom,
class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
thf(4273,plain,
class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ 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_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
thf(1638,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ 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_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( 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(1675,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( ( 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 ) ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(695,axiom,
class_Rings_Oring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(3532,plain,
class_Rings_Oring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(3223,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(931,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
thf(4251,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(541,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 @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(3023,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 @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( 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_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(1669,plain,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
thf(2193,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(168,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(1786,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sgn) ).
thf(1707,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(309,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
thf(2293,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ ( c_RComplete_Onatceiling @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__mono) ).
thf(2891,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ ( c_RComplete_Onatceiling @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(315,axiom,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
thf(2308,plain,
! [A: $i] :
( ( class_Groups_Ozero @ A )
=> ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(45,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(1371,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)],[45]) ).
thf(1134,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_Ominus__class_Ominus @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).
thf(4837,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_Ominus__class_Ominus @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(3077,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).
thf(1332,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1101,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).
thf(4764,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(749,axiom,
( ( c_RComplete_Onatceiling @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).
thf(3700,plain,
( ( c_RComplete_Onatceiling @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Int_Onumber__ring @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).
thf(2706,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Int_Onumber__ring @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(758,axiom,
class_Groups_Oabs__if @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
thf(3719,plain,
class_Groups_Oabs__if @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(333,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 @ ( 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(2358,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(320,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(2319,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)],[320]) ).
thf(996,axiom,
class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
thf(4433,plain,
class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( 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(2361,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( 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)],[334]) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Complex_Ocomplex @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff__def) ).
thf(4498,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Complex_Ocomplex @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(578,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(3155,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(288,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(2214,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)],[288]) ).
thf(503,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(2906,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)],[503]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(1933,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ 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_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(677,axiom,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
thf(3468,plain,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(573,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(3138,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)],[573]) ).
thf(650,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
thf(3384,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( 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(1376,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( 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)],[47]) ).
thf(240,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(2065,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)],[240]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(2346,plain,
! [A: $i,B: $i,C: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1090,axiom,
! [A: $i] :
( ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s1) ).
thf(4716,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(385,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
thf(2521,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(1112,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( 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_pi__half__le__two) ).
thf(4790,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( 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)],[1112]) ).
thf(445,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
thf(2721,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(2119,plain,
! [A: $i,B: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(728,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(3631,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)],[728]) ).
thf(53,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(1408,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)],[53]) ).
thf(190,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
thf(1894,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Rings_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(374,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_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(2493,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_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(418,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 ) )
=> ( ( 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(2637,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 ) )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(356,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(2422,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)],[356]) ).
thf(88,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(1524,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1129,axiom,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
thf(4828,plain,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(690,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
thf(3515,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(1084,axiom,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
thf(4699,plain,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(36,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(1349,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)],[36]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
thf(2097,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(1118,axiom,
class_RealVector_Oreal__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).
thf(4805,plain,
class_RealVector_Oreal__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(1249,axiom,
class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
thf(5222,plain,
class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).
thf(4586,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(2839,plain,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(165,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(1771,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)],[165]) ).
thf(754,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(3710,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(593,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
thf(3197,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(872,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(4073,plain,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(136,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oabs__if @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).
thf(1690,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oabs__if @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(711,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(3586,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)],[711]) ).
thf(1067,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(4635,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)],[1067]) ).
thf(995,axiom,
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
!= ( 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_pi__half__neq__two) ).
thf(4430,plain,
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
!= ( 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)],[995]) ).
thf(1032,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( 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_pi__half__less__two) ).
thf(4541,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( 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)],[1032]) ).
thf(318,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(2314,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)],[318]) ).
thf(1204,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(5082,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)],[1204]) ).
thf(1154,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(4911,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)],[1154]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
thf(1630,plain,
! [A: $i,B: $i] :
( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(196,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(1909,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)],[196]) ).
thf(941,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(4277,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)],[941]) ).
thf(591,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(3192,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(176,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(1838,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)],[176]) ).
thf(671,axiom,
! [A: $i,B: $i] :
( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
thf(3451,plain,
! [A: $i,B: $i] :
( ( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
= ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(632,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(3298,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)],[632]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ 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__diff) ).
thf(4296,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ 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)],[951]) ).
thf(1234,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(5180,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)],[1234]) ).
thf(810,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(3861,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)],[810]) ).
thf(484,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(2842,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)],[484]) ).
thf(505,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(2911,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)],[505]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) )
= ( 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(2824,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) )
= ( 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)],[478]) ).
thf(917,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(4203,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)],[917]) ).
thf(1189,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
thf(5035,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) )
= ( 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(1471,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) )
= ( 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)],[73]) ).
thf(768,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(3747,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)],[768]) ).
thf(990,axiom,
class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
thf(4420,plain,
class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1001,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
thf(4445,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(1148,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(4882,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)],[1148]) ).
thf(552,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 @ ( c_Nat_OSuc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(3055,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 @ ( c_Nat_OSuc @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).
thf(4009,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(151,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(1731,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)],[151]) ).
thf(782,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(3800,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)],[782]) ).
thf(936,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(4264,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)],[936]) ).
thf(844,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 ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
thf(3971,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 ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(709,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
thf(3583,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(34,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(1344,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)],[34]) ).
thf(396,axiom,
class_Rings_Oordered__ring__abs @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
thf(2553,plain,
class_Rings_Oordered__ring__abs @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1182,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Transcendental_Oarctan @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ A ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
& ( ( c_Transcendental_Otan @ ( c_Transcendental_Oarctan @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan) ).
thf(5007,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Transcendental_Oarctan @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oarctan @ A ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
& ( ( c_Transcendental_Otan @ ( c_Transcendental_Oarctan @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(1196,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(5057,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)],[1196]) ).
thf(336,axiom,
class_Groups_Ozero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(2365,plain,
class_Groups_Ozero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(447,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(2725,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(65,axiom,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1445,plain,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(121,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(1643,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)],[121]) ).
thf(745,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(3687,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)],[745]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( 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(2288,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(540,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(3016,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)],[540]) ).
thf(407,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(2592,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)],[407]) ).
thf(1155,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(4918,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)],[1155]) ).
thf(1086,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
<=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
thf(4703,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
=> ( 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_Groups_Oabs__class_Oabs @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(343,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(2390,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(313,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
thf(2303,plain,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ C )
& ( class_RealVector_Oreal__normed__field @ C ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__divide) ).
thf(3908,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ C )
& ( class_RealVector_Oreal__normed__field @ C ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(1973,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
thf(4473,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(1161,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(4933,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)],[1161]) ).
thf(1133,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(4832,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)],[1133]) ).
thf(74,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(1474,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)],[74]) ).
thf(926,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
<=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
thf(4232,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(287,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(2212,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)],[287]) ).
thf(272,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(2171,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)],[272]) ).
thf(1246,axiom,
class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
thf(5216,plain,
class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(771,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(3759,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(1241,axiom,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
thf(5197,plain,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(458,axiom,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(2765,plain,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(395,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(2550,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)],[395]) ).
thf(876,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(4085,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)],[876]) ).
thf(580,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_Otimes__class_Otimes @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(3159,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_Otimes__class_Otimes @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(239,axiom,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(2064,plain,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( 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(4362,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( 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)],[970]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
thf(3674,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(75,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(1477,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)],[75]) ).
thf(752,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(3706,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(3512,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(943,axiom,
class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
thf(4282,plain,
class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(1064,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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( 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(4626,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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(3881,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(919,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Groups_Oabs__class_Oabs @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Groups_Oabs__class_Oabs @ ( tc_Polynomial_Opoly @ B ) @ A )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__poly__def) ).
thf(4207,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Groups_Oabs__class_Oabs @ ( tc_Polynomial_Opoly @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
=> ( ( c_Groups_Oabs__class_Oabs @ ( tc_Polynomial_Opoly @ B ) @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(854,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(4013,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)],[854]) ).
thf(250,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
thf(2107,plain,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(424,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(2652,plain,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1027,axiom,
( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( 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_semiring__norm_I115_J) ).
thf(4529,plain,
( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( 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)],[1027]) ).
thf(1147,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(4879,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)],[1147]) ).
thf(968,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
<=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def) ).
thf(4355,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
& ( ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(629,axiom,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
thf(3292,plain,
! [A: $i] :
( ( class_Groups_Ocancel__comm__monoid__add @ A )
=> ( class_Groups_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(1121,axiom,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
thf(4812,plain,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(114,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(1626,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)],[114]) ).
thf(692,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
thf(3522,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( 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 @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(538,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(3009,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( 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(2914,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( 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 ) ) )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1080,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(4690,plain,
class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).
thf(4394,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(999,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).
thf(4441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__0 @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(934,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
thf(4260,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(1122,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_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Otan @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__gt__zero) ).
thf(4813,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_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Otan @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(1187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
thf(5025,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(655,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 ) @ ( 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(3395,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 ) @ ( 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)],[655]) ).
thf(598,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(3206,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(3161,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ 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_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(195,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(1905,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(740,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
thf(3672,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1095,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__vector @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).
thf(4735,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__vector @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(379,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
thf(2503,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(135,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(1684,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)],[135]) ).
thf(13,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(1277,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)],[13]) ).
thf(863,axiom,
! [A: $i] :
( ( c_Transcendental_Ocos @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Transcendental_Ocos @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cos__minus) ).
thf(4052,plain,
! [A: $i] :
( ( c_Transcendental_Ocos @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Transcendental_Ocos @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(256,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(2124,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(294,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(2234,plain,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(949,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(4292,plain,
class_Groups_Oordered__ab__group__add__abs @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) @ ( 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(1509,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) @ ( 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)],[84]) ).
thf(905,axiom,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(4177,plain,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(509,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(2927,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(1040,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(4566,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)],[1040]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__field @ F )
=> ( ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ ( c_Groups_Otimes__class_Otimes @ F @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).
thf(4859,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_RealVector_Oreal__field @ F )
=> ( ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ ( c_Groups_Otimes__class_Otimes @ F @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(282,axiom,
! [A: $i] :
( ( 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(2202,plain,
! [A: $i] :
( ( 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)],[282]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
thf(4113,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(400,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(2564,plain,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(409,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(2597,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)],[409]) ).
thf(1045,axiom,
class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
thf(4581,plain,
class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(862,axiom,
! [A: $i] :
( ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096) ).
thf(4045,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(311,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
thf(2298,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
thf(3376,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(3640,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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)],[730]) ).
thf(1143,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(4864,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)],[1143]) ).
thf(279,axiom,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(2192,plain,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(223,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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( 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(2012,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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(3260,plain,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(974,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(4377,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)],[974]) ).
thf(497,axiom,
class_Groups_Oone @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(2888,plain,
class_Groups_Oone @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(1184,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(5018,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(346,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(2397,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)],[346]) ).
thf(687,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(3507,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(800,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(3842,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)],[800]) ).
thf(566,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(3112,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( c_SEQ_Osubseq @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_seq__suble) ).
thf(2977,plain,
! [A: $i,B: $i] :
( ( c_SEQ_Osubseq @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(109,axiom,
class_Rings_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1611,plain,
class_Rings_Omult__zero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(938,axiom,
class_Orderings_Olinorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
thf(4272,plain,
class_Orderings_Olinorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1163,axiom,
! [A: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
thf(4939,plain,
! [A: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(1400,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1029,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ c_Transcendental_Opi ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
=> ( ( 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 @ ( c_Transcendental_Otan @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__less__zero) ).
thf(4534,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ c_Transcendental_Opi ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
=> ( ( 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 @ ( c_Transcendental_Otan @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(736,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_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(3659,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_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(204,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp) ).
thf(1941,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(916,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(4200,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)],[916]) ).
thf(43,axiom,
class_Rings_Oordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
thf(1368,plain,
class_Rings_Oordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1023,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(4517,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)],[1023]) ).
thf(605,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(3228,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(947,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
thf(4287,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__0 @ B )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(2821,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( 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_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(1753,plain,
! [A: $i,B: $i] :
( ( 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_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ 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_Odiff) ).
thf(3786,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ 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)],[778]) ).
thf(91,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(1531,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)],[91]) ).
thf(960,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(4324,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)],[960]) ).
thf(1066,axiom,
! [A: $i] :
? [B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
& ( ( c_Transcendental_Otan @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__tan__total1) ).
thf(4630,plain,
! [A: $i] :
? [B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
& ( ( c_Transcendental_Otan @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(486,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2850,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(78,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(1484,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)],[78]) ).
thf(267,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
thf(2160,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( 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)],[267]) ).
thf(1024,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).
thf(4522,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1252,axiom,
class_Rings_Osemiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
thf(5235,plain,
class_Rings_Osemiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(731,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(3642,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(169,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 ) @ ( 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(1790,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 ) @ ( 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)],[169]) ).
thf(1183,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( 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(5015,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( 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)],[1183]) ).
thf(850,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(4003,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)],[850]) ).
thf(327,axiom,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
thf(2337,plain,
! [A: $i] :
( ( class_Groups_Oab__group__add @ A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( 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 @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ c_Transcendental_Opi )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cos__monotone__0__pi_H) ).
thf(1901,plain,
! [A: $i,B: $i] :
( ( 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 @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ c_Transcendental_Opi )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(928,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A ) @ c_Transcendental_Opi ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Transcendental_Oarctan @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__inverse) ).
thf(4241,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A ) @ c_Transcendental_Opi ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Transcendental_Oarctan @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(889,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(4117,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)],[889]) ).
thf(426,axiom,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(2656,plain,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( 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(1499,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( 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)],[82]) ).
thf(60,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
thf(1432,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(269,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(2165,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ c_Int_OPls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
<=> ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
thf(1300,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( 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 @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(567,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 @ ( 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(3114,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(434,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(2688,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(621,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_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(3273,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_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(680,axiom,
! [A: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
thf(3475,plain,
! [A: $i] :
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(542,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(3026,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(301,axiom,
! [A: $i] :
( ( 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(2276,plain,
! [A: $i] :
( ( 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)],[301]) ).
thf(258,axiom,
! [A: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ c_Transcendental_Opi ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__npi) ).
thf(2128,plain,
! [A: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ c_Transcendental_Opi ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ D @ B @ ( 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(1317,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(162,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
thf(1763,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(791,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__vector @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__add__less) ).
thf(3828,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__vector @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(127,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(1658,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 ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(321,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(2322,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)],[321]) ).
thf(1179,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
<=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def2) ).
thf(4982,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
=> ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
& ( ? [C: $i] :
! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(704,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(3564,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)],[704]) ).
thf(638,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(3329,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)],[638]) ).
thf(1096,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(4737,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)],[1096]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).
thf(2044,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(16,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
thf(1285,plain,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(561,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(3095,plain,
class_Groups_Oone @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(805,axiom,
! [A: $i,B: $i] :
( ( 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_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
thf(3853,plain,
! [A: $i,B: $i] :
( ( 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_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(1224,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 @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(5147,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 @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(516,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(2948,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)],[516]) ).
thf(1116,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(4802,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)],[1116]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(2379,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(525,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
thf(2975,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(302,axiom,
class_Groups_Ogroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
thf(2279,plain,
class_Groups_Ogroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(896,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
thf(4143,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(382,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(2511,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)],[382]) ).
thf(878,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Transcendental_Oarctan @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__lbound) ).
thf(4093,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Transcendental_Oarctan @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(691,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
thf(3520,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(657,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(3398,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)],[657]) ).
thf(921,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [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 @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_Transcendental_Otan @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__tan__total) ).
thf(4217,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [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 @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_Transcendental_Otan @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(352,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(2411,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)],[352]) ).
thf(377,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
thf(2500,plain,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(865,axiom,
class_Int_Onumber @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).
thf(4057,plain,
class_Int_Onumber @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(734,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(3652,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)],[734]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( 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(2558,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(662,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(3415,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)],[662]) ).
thf(1250,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 @ ( 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 @ ( 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(5223,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[1250]) ).
thf(216,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 @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(1981,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 @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1063,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(4624,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)],[1063]) ).
thf(1058,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ c_Transcendental_Opi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pi__gt__zero) ).
thf(4611,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ c_Transcendental_Opi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(1177,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
thf(4976,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(998,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(4436,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)],[998]) ).
thf(393,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(2543,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)],[393]) ).
thf(930,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(4246,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)],[930]) ).
thf(441,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(2711,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).
thf(4106,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1181,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
<=> ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(4991,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
=> ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(448,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Int_Oring__char__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
thf(2728,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Int_Oring__char__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(937,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(4267,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)],[937]) ).
thf(230,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(2030,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)],[230]) ).
thf(474,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(2807,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)],[474]) ).
thf(10,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(1272,plain,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1115,axiom,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__abs__def) ).
thf(4795,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( 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(2266,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( 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)],[298]) ).
thf(1022,axiom,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
thf(4516,plain,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1125,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(4819,plain,
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(981,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( v_g____ @ A ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_g_I2_J) ).
thf(4392,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( v_g____ @ A ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(627,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(3288,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)],[627]) ).
thf(495,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 @ ( 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 @ ( 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(2875,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[495]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
thf(2435,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(3433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1071,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(4651,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)],[1071]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( 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(2088,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(476,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(2818,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(212,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 @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(1966,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 @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(437,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(2696,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)],[437]) ).
thf(493,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(2870,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)],[493]) ).
thf(696,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(3533,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)],[696]) ).
thf(420,axiom,
( ( c_Transcendental_Ocos @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cos__zero) ).
thf(2643,plain,
( ( c_Transcendental_Ocos @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(681,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 @ ( 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 @ ( 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(3478,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[681]) ).
thf(658,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_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(3400,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_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)],[658]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Otimes__class_Otimes @ E @ ( 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(2924,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(415,axiom,
class_Rings_Oordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(2626,plain,
class_Rings_Oordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(197,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(1918,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)],[197]) ).
thf(992,axiom,
class_Rings_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
thf(4424,plain,
class_Rings_Oring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(369,axiom,
c_SEQ_Osubseq @ v_f____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fz_I1_J) ).
thf(2479,plain,
c_SEQ_Osubseq @ v_f____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1139,axiom,
! [A: $i] :
( ( c_SEQ_Osubseq @ A )
<=> ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__Suc__iff) ).
thf(4851,plain,
! [A: $i] :
( ( ( c_SEQ_Osubseq @ A )
=> ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) ) )
& ( ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) )
=> ( c_SEQ_Osubseq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(1055,axiom,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
thf(4606,plain,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(69,axiom,
( c_Transcendental_Opi
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pi__neq__zero) ).
thf(1459,plain,
( c_Transcendental_Opi
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(560,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(3092,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)],[560]) ).
thf(1165,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).
thf(4944,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(1145,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(4873,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)],[1145]) ).
thf(989,axiom,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
thf(4419,plain,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(316,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(2310,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(814,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(3874,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)],[814]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
<=> ( 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_le__diff__conv) ).
thf(2325,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__norm__divide) ).
thf(4185,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(726,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(3625,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)],[726]) ).
thf(875,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(4078,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)],[875]) ).
thf(760,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(3725,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)],[760]) ).
thf(314,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(2305,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)],[314]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(2342,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(180,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(1866,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(463,axiom,
class_Int_Oring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
thf(2775,plain,
class_Int_Oring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( 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(1734,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1236,axiom,
class_Rings_Ocomm__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
thf(5184,plain,
class_Rings_Ocomm__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(1078,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_Groups_Oabs__class_Oabs @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ 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_abs__number__of) ).
thf(4678,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_Groups_Oabs__class_Oabs @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ 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)],[1078]) ).
thf(548,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(3039,plain,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(1042,axiom,
class_Rings_Osemiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
thf(4574,plain,
class_Rings_Osemiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(781,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_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__Suc) ).
thf(3797,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_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(362,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(2443,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)],[362]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( 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(2273,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( 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)],[300]) ).
thf(779,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(3789,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)],[779]) ).
thf(397,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(2554,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)],[397]) ).
thf(389,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(2532,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(157,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Groups_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
thf(1745,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__0 @ A )
=> ( class_Groups_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(523,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(2971,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(357,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(2431,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)],[357]) ).
thf(808,axiom,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
thf(3859,plain,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(762,axiom,
! [A: $i] :
( ( c_Transcendental_Ocos @ ( c_Transcendental_Oarctan @ A ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cos__arctan__not__zero) ).
thf(3729,plain,
! [A: $i] :
( ( c_Transcendental_Ocos @ ( c_Transcendental_Oarctan @ A ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(829,axiom,
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 @ c_Transcendental_Opi @ ( 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_pi__half__ge__zero) ).
thf(3911,plain,
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 @ c_Transcendental_Opi @ ( 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)],[829]) ).
thf(723,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(3613,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)],[723]) ).
thf(1,conjecture,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_wa____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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',conj_0) ).
thf(2,negated_conjecture,
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_wa____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1253,plain,
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_wa____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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)],[2]) ).
thf(811,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(3864,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)],[811]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( ( 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(1721,plain,
! [A: $i,B: $i] :
( ( ( ( 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 ) ) )
=> ( ( 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)],[149]) ).
thf(273,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(2174,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)],[273]) ).
thf(305,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(2283,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(1119,axiom,
? [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
& ! [B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).
thf(4806,plain,
? [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
& ! [B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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)],[1119]) ).
thf(194,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Oring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
thf(1903,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Oring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1073,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).
thf(4666,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1079,axiom,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).
thf(4683,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(649,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(3383,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)],[649]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ 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 ) ) ) ) @ B )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) @ ( 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__average__minus__first) ).
thf(4126,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ 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 ) ) ) ) @ B )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) @ ( 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)],[892]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
thf(4042,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1033,axiom,
! [A: $i] :
? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th) ).
thf(4542,plain,
! [A: $i] :
? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(1113,axiom,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
thf(4791,plain,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(115,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(1629,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
thf(2416,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(776,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).
thf(3780,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(99,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(1558,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)],[99]) ).
thf(512,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( 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(2934,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( 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)],[512]) ).
thf(265,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(2152,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)],[265]) ).
thf(935,axiom,
! [A: $i] :
? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096) ).
thf(4261,plain,
! [A: $i] :
? [B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(345,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).
thf(2394,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( 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)],[345]) ).
thf(914,axiom,
class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
thf(4197,plain,
class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(323,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 @ ( 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(2330,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 @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(23,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(1308,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)],[23]) ).
thf(404,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 @ ( 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 @ ( 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(2576,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[404]) ).
thf(742,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
thf(3677,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Rings_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).
thf(4404,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(129,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
thf(1661,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring__1 @ A )
=> ( class_Rings_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1215,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(5119,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(873,axiom,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
thf(4074,plain,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(232,axiom,
( ( c_Transcendental_Otan @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__zero) ).
thf(2036,plain,
( ( c_Transcendental_Otan @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1158,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(4927,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(222,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(2009,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)],[222]) ).
thf(179,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 ) )
<=> ( ( c_Groups_Otimes__class_Otimes @ E @ B @ C )
= ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
thf(1861,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 ) )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ B @ C )
= ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) )
& ( ( ( c_Groups_Otimes__class_Otimes @ E @ B @ C )
= ( 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)],[179]) ).
thf(587,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(3181,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
thf(2786,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(470,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
thf(2796,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(950,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(4293,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)],[950]) ).
thf(958,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
thf(4321,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( 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(2041,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(904,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [B: $i] :
! [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( v_g____ @ ( hAPP @ v_f____ @ C ) ) @ v_z____ ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fz_I2_J) ).
thf(4175,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [B: $i] :
! [C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( v_g____ @ ( hAPP @ v_f____ @ C ) ) @ v_z____ ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(684,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 @ A )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(3497,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 @ A )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(710,axiom,
class_Rings_Ocomm__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
thf(3585,plain,
class_Rings_Ocomm__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(166,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_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(1777,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_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(619,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(3267,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)],[619]) ).
thf(952,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
thf(4299,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(19,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1294,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(365,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(2462,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)],[365]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C )
= ( 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(2739,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(881,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(4098,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)],[881]) ).
thf(1240,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ v_wa____ @ v_z____ ) ) @ v_d____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w) ).
thf(5196,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ v_wa____ @ v_z____ ) ) @ v_d____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).
thf(4025,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(226,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(2019,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)],[226]) ).
thf(1060,axiom,
( ( c_Transcendental_Oarctan @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan1__eq__pi4) ).
thf(4619,plain,
( ( c_Transcendental_Oarctan @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
thf(2374,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(1124,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 @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(4816,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 @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( 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_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(383,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(2517,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)],[383]) ).
thf(1008,axiom,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(4472,plain,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(390,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
thf(2534,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 @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( 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)],[390]) ).
thf(848,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).
thf(3997,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(717,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(3601,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)],[717]) ).
thf(95,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_Ominus__class_Ominus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ 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__diff1) ).
thf(1546,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_Ominus__class_Ominus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ 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)],[95]) ).
thf(618,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(3264,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)],[618]) ).
thf(564,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) ) )
<=> ( ( D = B )
| ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(3100,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 @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) ) )
=> ( ( D = B )
| ( C = A ) ) )
& ( ( ( D = B )
| ( C = A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1136,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).
thf(4843,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
thf(4663,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__vector @ C )
=> ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
= ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(1149,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 @ ( 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 @ ( 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(4885,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 @ ( 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 @ ( 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 @ ( 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 @ ( 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)],[1149]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
thf(4367,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(2142,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(647,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 ) @ ( 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(3379,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 ) @ ( 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)],[647]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__vector @ D )
=> ( ( 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_RealVector_Onorm__class_Onorm @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
thf(2218,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__vector @ D )
=> ( ( 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_RealVector_Onorm__class_Onorm @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(891,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pi__less__4) ).
thf(4125,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(1194,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(5051,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)],[1194]) ).
thf(751,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(3705,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(14,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
thf(1280,plain,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(809,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(3860,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1075,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(4670,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)],[1075]) ).
thf(1120,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).
thf(4809,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(529,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(2983,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(932,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(4254,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)],[932]) ).
thf(763,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(3733,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)],[763]) ).
thf(405,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( 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(2587,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(797,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(3837,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)],[797]) ).
thf(674,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_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(3464,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_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(517,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(2951,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)],[517]) ).
thf(1202,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(5078,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)],[1202]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(2736,plain,
! [A: $i,B: $i,C: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(1111,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
thf(4787,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring @ C )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(218,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 @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(1986,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 @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(596,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(3203,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)],[596]) ).
thf(554,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(3062,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)],[554]) ).
thf(678,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ ( 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(3469,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(1191,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(5041,plain,
! [A: $i,B: $i] :
( ( c_Int_OBit0 @ B )
!= ( c_Int_OBit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(574,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(3145,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)],[574]) ).
thf(539,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(3015,plain,
class_Orderings_Olinorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(455,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 @ ( c_Transcendental_Oarctan @ B ) @ ( c_Transcendental_Oarctan @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__monotone_H) ).
thf(2751,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 @ ( c_Transcendental_Oarctan @ B ) @ ( c_Transcendental_Oarctan @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(906,axiom,
class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
thf(4178,plain,
class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(219,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__one) ).
thf(1989,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(40,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(1363,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)],[40]) ).
thf(966,axiom,
( ? [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096) ).
thf(4350,plain,
( ( ? [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) )
=> ? [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) @ v_r )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(325,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_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(2334,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_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)],[325]) ).
thf(701,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(3558,plain,
class_Groups_Oordered__ab__group__add__abs @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(815,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(3875,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)],[815]) ).
thf(803,axiom,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
thf(3850,plain,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(337,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).
thf(2366,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(506,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(2913,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(544,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(3030,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)],[544]) ).
thf(1245,axiom,
class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
thf(5215,plain,
class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( 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(2619,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
= ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(1232,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
thf(5176,plain,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( 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(2021,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(1212,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ 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 )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ 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__average__minus__second) ).
thf(5110,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ 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 )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ 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)],[1212]) ).
thf(465,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(2783,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)],[465]) ).
thf(156,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(1742,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)],[156]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
thf(1436,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(178,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
thf(1859,plain,
! [A: $i] :
( ( class_Rings_Ocomm__ring @ A )
=> ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(277,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(2186,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)],[277]) ).
thf(946,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(4286,plain,
class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(623,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
thf(3277,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 @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ ( 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)],[623]) ).
thf(585,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_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(3177,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_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)],[585]) ).
thf(784,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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 @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Otan @ B ) @ ( c_Transcendental_Otan @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__monotone_H) ).
thf(3804,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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 @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Otan @ B ) @ ( c_Transcendental_Otan @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Otan @ B ) @ ( c_Transcendental_Otan @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1174,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(4968,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)],[1174]) ).
thf(1210,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
thf(5105,plain,
! [A: $i,B: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( 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(1335,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( 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 )
= ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(856,axiom,
class_Int_Oring__char__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
thf(4024,plain,
class_Int_Oring__char__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( 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(2070,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
= ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
thf(3716,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(520,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(2961,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)],[520]) ).
thf(144,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
thf(1710,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) @ c_Transcendental_Opi ) ) )
= ( c_Transcendental_Otan @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__periodic__n) ).
thf(2714,plain,
! [A: $i,B: $i] :
( ( c_Transcendental_Otan @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) @ c_Transcendental_Opi ) ) )
= ( c_Transcendental_Otan @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(189,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(1891,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)],[189]) ).
thf(328,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(2340,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)],[328]) ).
thf(430,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(2668,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)],[430]) ).
thf(37,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(1352,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)],[37]) ).
thf(1222,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(5140,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)],[1222]) ).
thf(890,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( 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 )
=> ( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).
thf(4118,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( 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 )
=> ( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(1132,axiom,
class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
thf(4831,plain,
class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(925,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).
thf(4229,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
= ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(820,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(3886,plain,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OPls )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(378,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(2502,plain,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
thf(4848,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(571,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 ) )
<=> ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
thf(3128,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 ) )
=> ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
= A ) )
& ( ( ( 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)],[571]) ).
thf(893,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(4129,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(521,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 ) @ ( 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(2966,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 ) @ ( 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)],[521]) ).
thf(8,axiom,
( ( c_Transcendental_Otan @ c_Transcendental_Opi )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__pi) ).
thf(1268,plain,
( ( c_Transcendental_Otan @ c_Transcendental_Opi )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(410,axiom,
class_Groups_Omonoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(2600,plain,
class_Groups_Omonoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( 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 @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ B ) @ ( 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(2898,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( 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 @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(975,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(4382,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)],[975]) ).
thf(719,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(3605,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)],[719]) ).
thf(93,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(1537,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)],[93]) ).
thf(1175,axiom,
class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
thf(4972,plain,
class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(1146,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(4876,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)],[1146]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
thf(1976,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ 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_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1018,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
thf(4506,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(870,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
thf(4066,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D2) ).
thf(4484,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( 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(3489,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( 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 ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(1923,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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)],[199]) ).
thf(612,axiom,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
thf(3245,plain,
! [A: $i] :
( ( class_Groups_Ocomm__monoid__add @ A )
=> ( class_Groups_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(1197,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(5060,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)],[1197]) ).
thf(918,axiom,
class_Fields_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
thf(4206,plain,
class_Fields_Ofield @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(200,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 @ ( c_Groups_Otimes__class_Otimes @ F @ E @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F @ E @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(1925,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 @ ( c_Groups_Otimes__class_Otimes @ F @ E @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F @ E @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1089,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(4713,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)],[1089]) ).
thf(1248,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ? [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 ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ E @ B ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ E @ B ) ) @ D ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ E ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__cont) ).
thf(5219,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ? [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 ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ E @ B ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ E @ B ) ) @ D ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ E ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(962,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(4330,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)],[962]) ).
thf(490,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
thf(2864,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Olinordered__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(186,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(1880,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)],[186]) ).
thf(372,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(2484,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)],[372]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
<=> ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(1885,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
=> ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) )
& ( ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1081,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ 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_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).
thf(4691,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ 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_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(788,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( ( c_Polynomial_Oorder @ C @ A @ B )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
thf(3812,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( ( c_Polynomial_Oorder @ C @ A @ B )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
| ( ( c_Polynomial_Oorder @ C @ A @ B )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(964,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_Transcendental_Otan @ B ) @ ( c_Transcendental_Otan @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__monotone) ).
thf(4345,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( 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_Transcendental_Otan @ B ) @ ( c_Transcendental_Otan @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(1017,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(4501,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)],[1017]) ).
thf(877,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
& ( ( c_Transcendental_Otan @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tan__total__pi4) ).
thf(4088,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
& ( ( c_Transcendental_Otan @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(832,axiom,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
thf(3918,plain,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
thf(2270,plain,
! [A: $i,B: $i,C: $i] :
( ( 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 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(922,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(4221,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)],[922]) ).
thf(338,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(2372,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)],[338]) ).
thf(419,axiom,
! [A: $i] :
( ( 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(2640,plain,
! [A: $i] :
( ( 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)],[419]) ).
thf(1108,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).
thf(4779,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
= ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(940,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).
thf(4274,plain,
! [A: $i] :
( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(835,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ c_Int_OPls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).
thf(3924,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ c_Int_OPls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1091,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(4723,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)],[1091]) ).
thf(491,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
thf(2866,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Rings_Oordered__ring__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(1035,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).
thf(4547,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__ring @ D )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(903,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_e) ).
thf(4174,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(631,axiom,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
thf(3296,plain,
! [A: $i] :
( ( class_Rings_Ocomm__semiring__1 @ A )
=> ( class_Groups_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(3461,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(28,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 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(1320,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 @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(125,axiom,
! [A: $i] :
( ( 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(1653,plain,
! [A: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ c_Int_OPls @ A )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(1944,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1038,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(4555,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)],[1038]) ).
thf(562,axiom,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(3096,plain,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(153,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add__imp__le @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1737,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__semigroup__add__imp__le @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1167,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
thf(4949,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( 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(3405,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(435,axiom,
class_Int_Onumber @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
thf(2690,plain,
class_Int_Onumber @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1235,axiom,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
thf(5183,plain,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(100,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_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ B )
= ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
thf(1565,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_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ B )
= ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(360,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(2438,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)],[360]) ).
thf(80,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(1490,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(956,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ A )
= ( 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(4313,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ A )
= ( 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)],[956]) ).
thf(669,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( 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(3443,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 @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(2993,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(595,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(3200,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)],[595]) ).
thf(67,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
<=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(1449,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) )
& ( ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) )
=> ( 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)],[67]) ).
thf(245,axiom,
class_Rings_Omult__zero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(2087,plain,
class_Rings_Omult__zero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(699,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(3553,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)],[699]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( 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(1468,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
= ( 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)],[72]) ).
thf(550,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 @ ( 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(3047,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 @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
= ( 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(2980,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
= ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(707,axiom,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(3575,plain,
! [A: $i] :
( ( class_Rings_Oidom @ A )
=> ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(1037,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(4552,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)],[1037]) ).
thf(274,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
thf(2177,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( class_Groups_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(54,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(1417,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)],[54]) ).
thf(182,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
thf(1870,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(5239,plain,
$false,
inference(cvc4,[status(thm)],[2163,1322,2094,1633,4899,2480,3927,2280,2630,3873,4188,4560,4447,1718,3883,5116,5088,1369,2889,2295,4571,4101,2336,3008,2131,4909,2109,4824,3661,4062,4729,4022,4290,3698,3397,1899,1315,3830,2595,5028,4728,1950,5131,1549,3534,1750,4037,2210,4226,4075,3905,2495,3509,2590,3912,4960,2837,1305,4747,4479,2117,2940,1596,2231,2622,3858,1443,2776,2659,2527,3040,1422,2248,1544,2676,4711,4603,2099,2282,1793,3402,2854,1692,4623,4973,3794,2686,2448,3616,4856,2459,3562,5178,3577,2146,3895,1426,3530,3049,4739,4575,1310,3004,3332,4647,3367,3649,3135,4097,4110,4528,3175,2316,3446,4638,5146,1872,1327,3693,4650,2476,5163,2627,2168,4058,2901,3313,4792,2723,2972,5123,1441,3777,2886,2405,4775,3836,2216,3236,3766,3994,2491,3915,2548,1645,5056,1601,3466,4198,3898,4607,1366,2400,4963,2067,1529,4322,4156,3878,1518,1265,1482,3597,1254,4511,5024,4386,2957,3820,1287,4896,2814,3275,3495,4761,5188,5064,1264,3148,4778,4130,3744,2703,3248,4238,4539,4956,1660,1298,3116,4151,1577,3280,3749,3845,3089,3803,5108,2126,4766,1462,4428,3855,2745,2571,2691,4862,1704,1479,3216,4830,1568,4460,4390,4302,4669,4595,3840,1379,3374,2169,2403,3638,4179,5193,4492,4928,1347,3919,2929,4675,4952,2730,2520,4141,2024,1641,3835,5076,1963,4400,1875,4771,3231,4008,3258,3322,1465,3431,3393,2996,3670,2122,4815,3973,5156,2291,2073,3851,4696,4988,3966,2027,3199,3934,4454,4600,2893,2469,3527,3702,3983,3569,2540,5135,3923,1960,5210,2483,2979,2772,5169,4825,1405,2804,5137,4065,5045,2508,1843,2058,4055,3068,1896,5096,3421,1796,3036,2530,1526,4307,4040,2002,4536,3955,3226,1943,3588,3559,4285,2392,2154,1521,4588,2718,2205,1696,3184,3229,4604,3503,3591,3567,3720,4531,2364,2047,4370,4576,4700,2954,1651,5174,3151,3097,4629,2473,3169,2646,4100,4312,4059,1768,1868,2061,3550,4172,2773,1636,5122,3418,4925,1730,3037,3679,1274,3603,1355,4434,1570,1502,1666,1487,3610,2937,4785,1619,4821,2414,3664,2601,3827,3711,2733,1519,4397,3752,3239,3154,4493,5085,3207,3682,3339,2015,3286,1883,3948,1602,3065,3877,4327,2179,5038,1656,2211,3763,2653,3271,3166,1938,4280,1365,4192,2670,3810,4608,1920,4585,2433,1968,2565,1555,2332,4155,2872,4385,5021,4776,3600,1836,5113,2181,4417,3028,2345,3727,1281,4732,2228,3033,1740,2769,4027,4316,1360,3413,1534,4486,3381,2709,3218,1672,3963,4840,5081,4012,4109,3001,3060,3467,2300,1983,4957,3831,2115,1270,5098,1259,3122,2946,2990,2377,2801,4525,4693,4845,1878,3386,4930,1719,4227,2537,4095,3119,1755,3941,3440,3205,4676,5166,1942,3846,4772,2830,3714,2419,2196,2613,3294,1419,1493,2798,3775,3311,4582,3179,1292,3622,1739,4425,2868,4389,4421,1424,2312,4750,4545,2080,4938,4406,4191,4513,3194,2349,2038,1446,3643,4444,2666,3555,4457,1612,4621,2649,4384,5149,5134,5234,4244,2497,4347,3628,4361,4804,3242,2968,5063,1324,2285,2932,3654,2836,1456,4508,1382,4068,2387,1552,2243,2505,3390,4829,1429,5217,3247,2862,2766,1599,4902,1715,3333,4152,4259,3109,3005,2140,2756,5153,1814,4195,1779,4212,4476,2748,2402,2221,3841,1434,3903,4184,1991,3834,2208,4782,4966,1695,3592,1712,3306,2440,4448,2408,2793,5209,1663,3190,2645,2189,5198,1616,3422,2909,4550,3807,4921,1648,3707,4872,3890,1273,5048,3289,3696,2524,3158,2235,2144,1698,4354,2556,4116,3358,3871,2033,2149,2717,3607,4412,1747,3738,4340,1595,3888,1374,4365,4943,3372,3319,3504,2789,3472,3086,4709,1965,4946,1256,2827,3213,4000,3387,3187,3741,1833,3234,2859,4283,1615,3255,3811,2791,5065,3609,2657,2849,3736,1929,3945,3283,2016,2568,4465,3900,1403,3458,1795,1701,4590,4612,5185,4978,1312,4149,3002,5086,2753,3783,1765,4273,1638,1675,3532,3223,4251,3023,1669,2193,1786,1707,2293,2891,2308,1371,4837,3077,1332,4764,3700,2706,3719,2358,2319,4433,2361,4498,3155,2214,2906,1933,3468,3138,3384,1376,2065,2346,4716,2521,4790,2721,2119,3631,1408,1894,2493,2637,2422,1524,4828,3515,4699,1349,2097,4805,5222,4586,2839,1771,3710,3197,4073,1690,3586,4635,4430,4541,2314,5082,4911,1630,1909,4277,3192,1838,3451,3298,4296,5180,3861,2842,2911,2824,4203,5035,1471,3747,4420,4445,4882,3055,4009,1731,3800,4264,3971,3583,1344,2553,5007,5057,2365,2725,1445,1643,3687,2288,3016,2592,4918,4703,2390,2303,3908,1973,4473,4933,4832,1474,4232,2212,2171,5216,3759,5197,2765,2550,4085,3159,2064,4362,3674,1477,3706,3512,4282,4626,3881,4207,4013,2107,2652,4529,4879,4355,3292,4812,1626,3522,3009,2914,4690,4394,4441,4260,4813,5025,3395,3206,3161,1905,3672,4735,2503,1684,1277,4052,2124,2234,4292,1509,4177,2927,4566,4859,2202,4113,2564,2597,4581,4045,2298,3376,3640,4864,2192,2012,3260,4377,2888,5018,2397,3507,3842,3112,2977,1611,4272,4939,1400,4534,3659,1941,4200,1368,4517,3228,4287,2821,1753,3786,1531,4324,4630,2850,1484,2160,4522,5235,3642,1790,5015,4003,2337,1901,4241,4117,2656,1499,1432,2165,1300,3114,2688,3273,3475,3026,2276,2128,1317,1763,3828,1658,2322,4982,3564,3329,4737,2044,1285,3095,3853,5147,2948,4802,2379,2975,2279,4143,2511,4093,3520,3398,4217,2411,2500,4057,3652,2558,3415,5223,1981,4624,4611,4976,4436,2543,4246,2711,4106,4991,2728,4267,2030,2807,1272,4795,2266,4516,4819,4392,3288,2875,2435,3433,4651,2088,2818,1966,2696,2870,3533,2643,3478,3400,2924,2626,1918,4424,2479,4851,4606,1459,3092,4944,4873,4419,2310,3874,2325,4185,3625,4078,3725,2305,2342,1866,2775,1734,5184,4678,3039,4574,3797,2443,2273,3789,2554,2532,1745,2971,2431,3859,3729,3911,3613,1253,3864,1721,2174,2283,4806,1903,4666,4683,3383,4126,4042,4542,4791,1629,2416,3780,1558,2934,2152,4261,2394,4197,2330,1308,2576,3677,4404,1661,5119,4074,2036,4927,2009,1861,3181,2786,2796,4293,4321,2041,4175,3497,3585,1777,3267,4299,1294,2462,2739,4098,5196,4025,2019,4619,2374,4816,2517,4472,2534,3997,3601,1546,3264,3100,4843,4663,4885,4367,2142,3379,2218,4125,5051,3705,1280,3860,4670,4809,2983,4254,3733,2587,3837,3464,2951,5078,2736,4787,1986,3203,3062,3469,5041,3145,3015,2751,4178,1989,1363,4350,2334,3558,3875,3850,2366,2913,3030,5215,2619,5176,2021,5110,2783,1742,1436,1859,2186,4286,3277,3177,3804,4968,5105,1335,4024,2070,3716,2961,1710,2714,1891,2340,2668,1352,5140,4118,4831,4229,3886,2502,4848,3128,4129,2966,1268,2600,2898,4382,3605,1537,4972,4876,1976,4506,4066,4484,3489,1923,3245,5060,4206,1925,4713,5219,4330,2864,1880,2484,1885,4691,3812,4345,4501,4088,3918,2270,4221,2372,2640,4779,4274,3924,4723,2866,4547,4174,3296,3461,1320,1653,1944,4555,3096,1737,4949,3405,2690,5183,1565,2438,1490,4313,3443,2993,3200,1449,2087,3553,1468,3047,2980,3575,4552,2177,1417,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW222+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Thu May 18 22:35:28 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.85/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.93/1.09 % [INFO] Parsing done (254ms).
% 1.93/1.10 % [INFO] Running in sequential loop mode.
% 2.38/1.28 % [INFO] eprover registered as external prover.
% 2.38/1.28 % [INFO] cvc4 registered as external prover.
% 2.38/1.29 % [INFO] Scanning for conjecture ...
% 2.74/1.41 % [INFO] Found a conjecture and 1250 axioms. Running axiom selection ...
% 3.58/1.60 % [INFO] Axiom selection finished. Selected 1250 axioms (removed 0 axioms).
% 4.78/1.91 % [INFO] Problem is first-order (TPTP FOF).
% 4.78/1.94 % [INFO] Type checking passed.
% 4.78/1.95 % [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 ...
% 25.12/6.39 % External prover 'cvc4' found a proof!
% 25.12/6.40 % [INFO] Killing All external provers ...
% 25.12/6.40 % Time passed: 5890ms (effective reasoning time: 5297ms)
% 25.12/6.40 % 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)>
% 25.12/6.40 % Axioms used in derivation (1250): fact_less__eq__int__code_I14_J, fact_le__SucI, arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, fact_le__imp__diff__is__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_Numeral1__eq1__nat, fact_arctan__monotone, fact_minus__Bit0, fact_complex__diff__def, 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_Nat_Oadd__0__right, fact_right__inverse__eq, fact_real__squared__diff__one__factored, fact_tan__inverse, fact_numeral__2__eq__2, fact_abs__of__pos, fact_real__le__refl, fact_abs__le__D2, arity_Complex__Ocomplex__Rings_Oidom, fact_nat_Osimps_I3_J, fact_real__less__def, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_number__of__diff, fact_mult__right__le__imp__le, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, fact_neg__le__divide__eq, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, fact_mult__poly__0__right, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_mult__1__left, fact_diff__0__eq__0, fact_minus__mult__left, fact_neg__divide__le__eq, fact_fz_I2_J, fact_semiring__norm_I112_J, fact_diff__add__inverse, fact_diff__bin__simps_I10_J, fact_abs__if, fact_bin__less__0__simps_I4_J, fact_le__eq__less__or__eq, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, arity_Polynomial__Opoly__Int_Onumber, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_mult__nonneg__nonpos, fact_one__is__num__one, fact_add__poly__code_I2_J, fact_abs__ge__self, arity_RealDef__Oreal__Rings_Oordered__comm__semiring, arity_Complex__Ocomplex__Groups_Oab__group__add, fact_diff__0__right, fact_mult__less__cancel__left__disj, fact_nat__add__left__commute, fact_real__mult__left__cancel, fact_mult__nonpos__nonpos, fact_tan__pi, fact_neg__equal__0__iff__equal, fact_arctan1__eq__pi4, fact_real__of__nat__zero, fact_mult__left_Ominus, fact_number__of__minus, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_real__sgn__eq, fact_abs__minus__commute, fact_tan__npi, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_divide__nonpos__neg, fact_one__is__add, fact_diff__le__mono2, fact_mult__nat__number__of, arity_Int__Oint__Rings_Olinordered__semiring__strict, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_minus__mult__right, fact_real__of__nat__diff, fact_norm__mult__less, fact_odd__nonzero, fact_tan__total__pi4, fact_add__nat__number__of, fact_zminus__zminus, fact_norm__diff__triangle__ineq, fact_less__int__code_I14_J, fact_mult__eq__0__iff, fact_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_add__leD1, fact_diff__number__of__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_eq__divide__eq__number__of, fact_pi__half__neq__two, fact_abs__div__pos, arity_RealDef__Oreal__Rings_Olinordered__ring, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_add__less__mono, fact_real__0__less__add__iff, fact_abs__triangle__ineq2__sym, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_mult__right__less__imp__less, fact_abs__eq__mult, fact_split__mult__neg__le, fact_real__gt__half__sum, fact_rel__simps_I49_J, fact_rel__simps_I27_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, arity_Int__Oint__Rings_Osemiring__1, fact_divide__numeral__1, fact_numeral__1__eq__Suc__0, fact_Suc__mono, arity_Nat__Onat__Rings_Ocomm__semiring__0, fact_psize__eq__0__iff, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, fact_mult__le__less__imp__less, fact_zadd__commute, arity_Nat__Onat__Groups_Omonoid__mult, fact_diff__Suc__less, fact_real__add__le__0__iff, fact_mult__0, fact_mult__poly__0__left, arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, fact_add__right__imp__eq, fact_iszero__0, fact_diff__diff__cancel, fact_gr0__conv__Suc, fact_abs__diff__triangle__ineq, arity_Complex__Ocomplex__Int_Onumber__ring, fact_Suc__le__mono, fact_le__number__of__eq__not__less, fact_norm__add__less, arity_Nat__Onat__Rings_Ozero__neq__one, fact_poly__zero, fact_nat__number__of__Pls, fact_eq__neg__iff__add__eq__0, arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, fact_iszero__def, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, arity_Polynomial__Opoly__Rings_Oidom, fact_zero__less__diff, fact_abs__poly__def, fact_mult__mono, fact_cos__gt__zero__pi, fact_nat__add__right__cancel, fact_neg__le__iff__le, arity_RealDef__Oreal__Groups_Omonoid__add, fact_neg__0__less__iff__less, fact_less__special_I4_J, arity_RealDef__Oreal__Rings_Oidom, fact_int__pos__lt__two__imp__zero__or__one, fact_mult__le__mono2, fact_Suc__diff__diff, fact_rel__simps_I31_J, fact_le__neq__implies__less, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, fact_not__iszero__Numeral1, fact_lemma__NBseq__def2, fact_zero__le__one, arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add, fact_poly__add, arity_RealDef__Oreal__Rings_Ocomm__ring__1, fact_diff__bin__simps_I7_J, fact_Bit1__def, fact_int__0__less__1, fact_le__minus__iff, fact_left__diff__distrib__number__of, fact_mult_Oadd__right, fact_mult_Ominus__right, fact_le__add__iff2, fact_mult__eq__self__implies__10, fact_mult__left__le__imp__le, fact_divide__pos__neg, fact_minus__add__cancel, fact_add__pos__nonneg, fact_expand__Suc, arity_Polynomial__Opoly__Rings_Ocomm__ring, fact_tan__minus, fact_mult__numeral__1__right, fact_zle__linear, fact_nat__add__left__cancel__less, fact_add__Bit0__Bit1, fact_tan__arctan, fact_pos__le__divide__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_add__strict__increasing2, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_linorder__neqE__linordered__idom, fact_minus__number__of__mult, fact_mult__imp__le__div__pos, fact_abs__of__neg, arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, fact_seq__suble, arity_Polynomial__Opoly__Rings_Olinordered__semidom, fact_abs__triangle__ineq2, fact_neg__less__0__iff__less, fact_divide__right__mono, fact_rel__simps_I5_J, arity_RealDef__Oreal__Fields_Ofield__inverse__zero, fact_natceiling__mono, arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, fact_add__nonneg__eq__0__iff, fact_real__mult__commute, fact_real__of__nat__zero__iff, arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, arity_Polynomial__Opoly__Orderings_Olinorder, fact_zadd__left__mono, fact_sum__squares__le__zero__iff, fact_divide__1, fact_mult__strict__left__mono, fact_number__of__is__id, arity_Int__Oint__Rings_Olinordered__semiring__1__strict, fact_mult__right_Ozero, fact_mult__le__cancel__left__neg, fact_minus__real__def, fact_add__le__imp__le__left, fact_sum__squares__ge__zero, fact_add__increasing2, fact_zero__le__mult__iff, arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero, arity_Int__Oint__Groups_Ozero, arity_RealDef__Oreal__Groups_Oabs__if, fact_divide__le__eq, fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, fact_mult_Ozero__left, fact_even__less__0__iff, fact_poly__0, arity_Int__Oint__Rings_Olinordered__ring, fact_add__0__iff, fact_add__right__mono, arity_Int__Oint__Groups_Ocancel__comm__monoid__add, fact_nat__less__real__le, fact_real__of__nat__less__iff, fact_real__mult__assoc, arity_Int__Oint__Groups_Ocomm__monoid__add, fact_eq__divide__2__times__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_RealDef__Oreal__Groups_Omonoid__mult, fact_add__0__left, fact_add__mono, fact_tan__monotone, fact_gr0I, fact_sgn__minus, fact_add__eq__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_le__nat__number__of, fact_less__int__code_I13_J, fact_minus__add, fact_divide__eq__imp, arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, fact_norm__triangle__ineq3, fact_abs__add__one__gt__zero, fact_lemma__NBseq__def, fact_rabs__ratiotest__lemma, fact_diff__le__self, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, fact_mult__eq__1__iff, fact_minus__less__iff, fact_half__gt__zero__iff, fact_less__add__eq__less, fact_nat__mult__1__right, fact_divide__strict__left__mono__neg, 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fact_numeral__3__eq__3, fact_abs__zero, fact_less__add__Suc1, fact_ab__left__minus, fact_sgn0, fact_add__neg__neg, arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, fact_minus__diff__eq, fact_comm__semiring__class_Odistrib, fact_add__number__of__left, fact_square__eq__iff, fact_zero__less__abs__iff, fact_abs__add__abs, fact_nonzero__minus__divide__right, fact_add__is__0, fact_rel__simps_I10_J, fact_eq__number__of, fact_add__less__imp__less__left, fact_tan__total, arity_Int__Oint__Rings_Oordered__ring, fact_abs__le__iff, fact_eq__number__of__0, fact_times__divide__times__eq, fact_right__diff__distrib__number__of, fact_sgn__zero__iff, fact_Deriv_Oadd__diff__add, fact_mult__right__mono, fact_abs__minus__cancel, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, fact_add__0, arity_Polynomial__Opoly__Rings_Oordered__ring, fact_diff__minus__eq__add, fact_tan__total__pos, fact_mult__le__mono1, fact_diff__self__eq__0, fact_add__eq__0__iff, arity_RealDef__Oreal__Rings_Olinordered__semidom, fact_neg__equal__iff__equal, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, fact_diff__add__0, fact_add__pos__pos, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_diff__cancel2, fact_add__nonneg__nonneg, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, arity_RealDef__Oreal__Groups_Oab__group__add, fact_Suc__eq__plus1, fact_arctan__inverse, arity_Int__Oint__Rings_Olinordered__idom, arity_Int__Oint__Rings_Ocomm__semiring__1, fact_sgn__greater, fact_machin, fact_divide__le__eq__number__of1, fact_tan__monotone_H, arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, fact_mult__nonpos__nonneg, fact_Suc__diff__le, arity_Polynomial__Opoly__Rings_Osemiring, fact_Zero__neq__Suc, fact_less__eq__int__code_I16_J, arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, fact_less__special_I3_J, arity_Nat__Onat__Groups_Oab__semigroup__add, fact_zabs__def, fact_less__1__mult, arity_Int__Oint__Rings_Oordered__comm__semiring, fact_le0, fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096, fact_square__eq__1__iff, fact_Suc__pred, arity_Int__Oint__Groups_Oab__semigroup__add, fact_divide__less__eq, arity_Int__Oint__Groups_Oone, arity_Nat__Onat__Rings_Olinordered__semidom, fact_add__le__cancel__right, arity_Complex__Ocomplex__Groups_Omonoid__mult, arity_Int__Oint__Groups_Ocomm__monoid__mult, fact_add__left__mono, fact_real__add__eq__0__iff, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_mult__right_Ominus, fact_less__not__refl, fact_double__add__le__zero__iff__single__add__le__zero, fact_mult__less__cancel__left__neg, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_poly__diff, fact_le__diff__conv2, fact_mult__pos__pos, fact_minus__mult__minus, fact_right__distrib__number__of, fact_crossproduct__eq, fact_neg__less__divide__eq, fact_le__trans, arity_Int__Oint__Groups_Oabs__if, fact_add__Pls__right, fact_zmult__zless__mono2, fact_diff__Suc__diff__eq1, fact_comm__mult__left__mono, fact_divide__eq__eq__number__of1, fact_plus__numeral__code_I9_J, fact_gr__implies__not0, fact_mult__strict__right__mono__neg, fact_pi__neq__zero, fact_abs__triangle__ineq, fact_real__two__squares__add__zero__iff, fact_less__add__one, fact_int__one__le__iff__zero__less, fact_mult__less__imp__less__right, fact_zero__neq__one, fact_less__Suc__eq, fact_add__leE, fact_mult_Odiff__left, fact_diff__Suc__1, fact_add__less__le__mono, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_real__of__nat__Suc__gt__zero, fact_wr, arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero, arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, arity_Nat__Onat__Int_Onumber, fact_double__number__of__Bit0, arity_Nat__Onat__Rings_Olinordered__semiring__strict, fact_number__of1, fact_norm__mult__ineq, fact_nat__add__commute, arity_Int__Oint__Rings_Ono__zero__divisors, fact_add__poly__code_I1_J, fact_diff__eq__diff__less__eq, fact_less__int__code_I15_J, fact_divide__strict__left__mono, fact_arctan, arity_RealDef__Oreal__Rings_Ocomm__semiring__0, fact_Suc__less__eq, fact_mult__neg__neg, arity_Int__Oint__Rings_Oring__1, fact_right__minus__eq, arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, fact_neg__0__le__iff__le, fact_cos__zero, arity_RealDef__Oreal__Rings_Osemiring__1, arity_Polynomial__Opoly__Groups_Ogroup__add, fact_zmult__zminus, fact_sgn__one, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, arity_RealDef__Oreal__Rings_Oring__1, fact_divide_Odiff, fact_zero__less__Suc, fact_iszero__Numeral0, fact_rel__simps_I2_J, arity_Complex__Ocomplex__Rings_Ocomm__ring, fact_less__divide__eq, fact_mult_Ocomm__neutral, arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_add__nonpos__neg, fact_number__of__Bit1, arity_RealDef__Oreal__Rings_Oordered__semiring, fact_le__SucE, fact_divide__Numeral1, fact_add1__zle__eq, fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096, arity_Polynomial__Opoly__Rings_Olinordered__semiring, fact_eq__imp__le, fact_diff__add__inverse2, arity_Complex__Ocomplex__Int_Oring__char__0, arity_Int__Oint__Rings_Olinordered__semiring__1, fact_plus__nat_Oadd__0, fact_subseq__Suc__iff, arity_RealDef__Oreal__Int_Onumber, fact_neg__divide__less__eq, fact_diff__eq__diff__eq, fact_minus__le__self__iff, fact_pi__half__ge__zero, fact_real__add__left__mono, fact_less__int__code_I16_J, fact_add__strict__increasing, fact_tan__periodic__pi, fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096, fact_real__mult__order, fact_le__less__Suc__eq, fact_real__norm__def, fact_d_I2_J, fact_neq0__conv, fact_mult__left__mono__neg, fact_le__antisym, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, fact_abs__mult__pos, arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, fact_mult__Suc__right, fact_le__special_I4_J, fact_nonzero__abs__divide, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, arity_Polynomial__Opoly__Rings_Ocomm__ring__1, fact_add__2__eq__Suc, fact_s1, fact_Suc__n__not__n, fact_nat__numeral__1__eq__1, fact_add__frac__num, fact_minus__equation__iff, fact_half, fact_real__of__nat__gt__zero__cancel__iff, fact_divide__strict__right__mono, fact_mult__0__right, fact_real__add__less__0__iff, fact_zless__linear, fact_mult__less__cancel__left__pos, fact_real__mult__le__cancel__iff2, fact_bin__less__0__simps_I1_J, fact_trans__le__add1, fact_zadd__0__right, fact_e2, fact_add__divide__distrib, fact_divide__less__eq__number__of, fact_lemma__MVT, fact_diff__le__mono, fact_zero__less__mult__pos, arity_Polynomial__Opoly__Rings_Ocomm__semiring, arity_Complex__Ocomplex__Rings_Omult__zero, fact_zmult__1__right, arity_Polynomial__Opoly__Rings_Ono__zero__divisors, fact_double__eq__0__iff, fact_le__0__eq, fact_real__0__le__add__iff, fact_mult__less__cancel2, fact_zle__add1__eq__le, fact_mult__1__right, fact_less__Suc0, fact_rel__simps_I32_J, fact_divide__nonneg__neg, arity_Nat__Onat__Rings_Osemiring, arity_Polynomial__Opoly__Groups_Oabs__if, fact_less__iff__Suc__add, fact_real__average__minus__first, fact_zero__less__two, fact_diff__is__0__eq, fact_number__of__Pls, fact_real__of__nat__one, arity_Polynomial__Opoly__Groups_Ozero, fact_rp, fact_add__le__imp__le__right, fact__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096, fact_real__of__nat__le__iff, fact_abs__mult__self, fact_real__mult__less__mono2, fact_sum__squares__eq__zero__iff, fact_abs__norm__cancel, fact_le__add__diff__inverse, fact_zabs__less__one__iff, arity_Int__Oint__Rings_Ocomm__ring__1, fact_add__le__mono, fact_add__diff__inverse, fact_convex__bound__le, arity_Int__Oint__Groups_Olinordered__ab__group__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_mult__less__imp__less__left, fact_le__diff__iff, arity_Nat__Onat__Groups_Oone, fact_diff__Suc__Suc, fact_add__imp__eq, arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_le__square, fact_less__iff__diff__less__0, fact_zadd__zmult__distrib, fact_real__le__linear, fact_zadd__zminus__inverse2, fact_nonzero__eq__divide__eq, fact_ab__semigroup__add__class_Oadd__ac_I1_J, arity_RealDef__Oreal__Groups_Oab__semigroup__mult, arity_Int__Oint__Rings_Ozero__neq__one, arity_RealDef__Oreal__Fields_Ofield, fact_half__gt__zero, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_minus__poly__code_I1_J, fact_nat__less__le, arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, fact_no__zero__divisors, fact_less__SucE, fact_gt__half__sum, fact_le__cube, fact_zless__add1__eq, fact_add__less__mono1, fact_add__le__cancel__left, fact_eq__divide__eq, fact_divisors__zero, arity_Polynomial__Opoly__Rings_Olinordered__ring, fact_nonzero__norm__divide, fact_mult__sgn__abs, arity_RealDef__Oreal__Groups_Ogroup__add, arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, arity_Polynomial__Opoly__Groups_Oone, fact_poly__eq__iff, fact_double__add__less__zero__iff__single__add__less__zero, fact_minus__divide__left, fact_DERIV__mult__lemma, arity_RealDef__Oreal__Groups_Olinordered__ab__group__add, fact_arctan__bounded, fact_less__diff__iff, fact_odd__less__0, fact_tan__45, fact_pi__less__4, arity_Int__Oint__Groups_Omonoid__add, fact_add__Suc__shift, fact_real__of__nat__add, fact_mult__1, fact_rel__simps_I22_J, fact_less__special_I1_J, fact_le__special_I2_J, arity_Complex__Ocomplex__Int_Onumber, fact_divide__self, fact_diff__special_I2_J, fact_arctan__tan, fact_pi__half__less__two, fact_real__of__nat__inject, fact_norm__triangle__ineq2, fact_less__half__sum, arity_Int__Oint__Rings_Ocomm__semiring__0, fact_less__SucI, fact_Suc__not__Zero, arity_Complex__Ocomplex__Groups_Ozero, fact__0960_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_061_061_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096, arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, fact_add__2__eq__Suc_H, fact_not__square__less__zero, fact_Suc__lessI, fact_add__Suc__right, fact_less__bin__lemma, arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_mult_Odiff__right, arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 25.12/6.40 % No. of inferences in proof: 2504
% 25.12/6.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5890 ms resp. 5297 ms w/o parsing
% 26.33/6.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.33/6.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------