TSTP Solution File: SWW173+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW173+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 12:21:43 EDT 2023
% Result : Theorem 95.16s 24.33s
% Output : Refutation 95.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1267
% Syntax : Number of formulae : 2444 ( 812 unt; 92 typ; 0 def)
% Number of atoms : 6306 (1871 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 36452 ( 381 ~; 142 |; 672 &;32117 @)
% ( 294 <=>;2846 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 92 usr; 12 con; 0-3 aty)
% Number of variables : 4949 ( 0 ^;4931 !; 18 ?;4949 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Rings_Oinverse__class_Odivide_type,type,
c_Rings_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $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(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(class_Rings_Omult__zero_type,type,
class_Rings_Omult__zero: $i > $o ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(c_NthRoot_Osqrt_type,type,
c_NthRoot_Osqrt: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(c_Power_Opower_Opower_type,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(c_Int_OMin_type,type,
c_Int_OMin: $i ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i > $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(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(class_Rings_Oordered__cancel__semiring_type,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_type,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Groups_Oone_type,type,
class_Groups_Oone: $i > $o ).
thf(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
thf(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(class_Fields_Olinordered__field_type,type,
class_Fields_Olinordered__field: $i > $o ).
thf(class_Fields_Ofield_type,type,
class_Fields_Ofield: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_type,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(class_Groups_Oordered__ab__group__add_type,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(class_RealVector_Oreal__field_type,type,
class_RealVector_Oreal__field: $i > $o ).
thf(class_Rings_Ono__zero__divisors_type,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Int_Onumber_type,type,
class_Int_Onumber: $i > $o ).
thf(class_Rings_Osemiring_type,type,
class_Rings_Osemiring: $i > $o ).
thf(class_Rings_Oordered__semiring_type,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(class_Rings_Oordered__ring_type,type,
class_Rings_Oordered__ring: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_type,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_type,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(class_Rings_Odivision__ring_type,type,
class_Rings_Odivision__ring: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_type,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Rings_Ocomm__semiring_type,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(class_Rings_Odivision__ring__inverse__zero_type,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(class_Rings_Olinordered__semiring__1_type,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_Groups_Oab__semigroup__add_type,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Fields_Ofield__inverse__zero_type,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(class_Rings_Oring__1__no__zero__divisors_type,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(c_Complex_Ocomplex_OComplex_type,type,
c_Complex_Ocomplex_OComplex: $i > $i > $i ).
thf(class_Groups_Oab__group__add_type,type,
class_Groups_Oab__group__add: $i > $o ).
thf(class_Rings_Olinordered__ring__strict_type,type,
class_Rings_Olinordered__ring__strict: $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_Olinordered__ring_type,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_Rings_Ocomm__ring__1_type,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_type,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Rings_Oordered__comm__semiring_type,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(class_Rings_Oring__1_type,type,
class_Rings_Oring__1: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_type,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_Complex_Oii_type,type,
c_Complex_Oii: $i ).
thf(class_Groups_Oab__semigroup__mult_type,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_type,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Rings_Olinordered__semiring_type,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(class_Groups_Omonoid__add_type,type,
class_Groups_Omonoid__add: $i > $o ).
thf(class_Rings_Osemiring__0_type,type,
class_Rings_Osemiring__0: $i > $o ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Rings_Olinordered__comm__semiring__strict_type,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(v_z_type,type,
v_z: $i ).
thf(v_x_____type,type,
v_x____: $i ).
thf(v_y_____type,type,
v_y____: $i ).
thf(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
thf(class_Rings_Osemiring__1_type,type,
class_Rings_Osemiring__1: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).
thf(c_Transcendental_Oarctan_type,type,
c_Transcendental_Oarctan: $i > $i ).
thf(c_Complex_Ocomplex_Ocomplex__size_type,type,
c_Complex_Ocomplex_Ocomplex__size: $i > $i ).
thf(304,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__lt__0__iff) ).
thf(2163,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(48,axiom,
class_Rings_Oordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
thf(1322,plain,
class_Rings_Oordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(289,axiom,
class_Groups_Oab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
thf(2131,plain,
class_Groups_Oab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(130,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(1559,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)],[130]) ).
thf(598,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(3167,plain,
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(517,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(2876,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(3,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(1179,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)],[3]) ).
thf(1054,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(4728,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)],[1054]) ).
thf(600,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OMin )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I28_J) ).
thf(3172,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OMin )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OMin ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OMin )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OMin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(330,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(2250,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)],[330]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
thf(2822,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(899,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(4188,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).
thf(1586,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(905,axiom,
class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
thf(4201,plain,
class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(396,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(2452,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)],[396]) ).
thf(1004,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(4560,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(831,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(3962,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)],[831]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( 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(3944,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(80,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(1411,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)],[80]) ).
thf(344,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I26_J) ).
thf(2295,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(845,axiom,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
thf(4005,plain,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(1007,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(4571,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(566,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(3053,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)],[566]) ).
thf(872,axiom,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__power2) ).
thf(4101,plain,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
thf(2072,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(922,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(4262,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)],[922]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(1767,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(896,axiom,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(4183,plain,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(531,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(2921,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)],[531]) ).
thf(684,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(3477,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)],[684]) ).
thf(399,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(2463,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)],[399]) ).
thf(661,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(3397,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)],[661]) ).
thf(202,axiom,
( ( c_NthRoot_Osqrt @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__one) ).
thf(1840,plain,
( ( c_NthRoot_Osqrt @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(719,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(3581,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)],[719]) ).
thf(791,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(3830,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)],[791]) ).
thf(493,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(2787,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)],[493]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__comm__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(2595,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__comm__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(410,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(2499,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)],[410]) ).
thf(390,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(2427,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)],[390]) ).
thf(405,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(2480,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)],[405]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(1950,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1135,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(4992,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)],[1135]) ).
thf(744,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(3681,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)],[744]) ).
thf(318,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(2210,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)],[318]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(2622,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(437,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ c_Int_OMin ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Min) ).
thf(2590,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ c_Int_OMin ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(578,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(3098,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)],[578]) ).
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(2671,plain,
class_Int_Oring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__minus1__right) ).
thf(2099,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(2380,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
thf(1305,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(2363,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(8,axiom,
! [A: $i] :
( ( class_Power_Opower @ A )
=> ( ( c_Power_Opower__class_Opower @ A )
= ( c_Power_Opower_Opower @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Otimes__class_Otimes @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
thf(1200,plain,
! [A: $i] :
( ( class_Power_Opower @ A )
=> ( ( c_Power_Opower__class_Opower @ A )
= ( c_Power_Opower_Opower @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Otimes__class_Otimes @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono) ).
thf(2077,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1115,axiom,
! [A: $i] :
( ( c_Int_OMin
= ( c_Int_OBit1 @ A ) )
<=> ( c_Int_OMin = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
thf(4931,plain,
! [A: $i] :
( ( ( c_Int_OMin
= ( c_Int_OBit1 @ A ) )
=> ( c_Int_OMin = A ) )
& ( ( c_Int_OMin = A )
=> ( c_Int_OMin
= ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(1049,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(4714,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(956,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__mult__ge__zero) ).
thf(4376,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2117,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(1406,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(2104,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).
thf(2644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(997,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(4515,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(527,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(2908,plain,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
thf(2062,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__comm__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(3549,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__comm__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(94,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OMin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I31_J) ).
thf(1443,plain,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OMin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
thf(2776,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) )
<=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(3417,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(419,axiom,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(2527,plain,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff__number__of) ).
thf(4391,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(595,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(3153,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)],[595]) ).
thf(682,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(3460,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)],[682]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
thf(1422,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1079,axiom,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
thf(4807,plain,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(172,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(1728,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)],[172]) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(3108,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1020,axiom,
class_Rings_Osemiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
thf(4603,plain,
class_Rings_Osemiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(3012,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(282,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(2114,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)],[282]) ).
thf(506,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(2837,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)],[506]) ).
thf(240,axiom,
class_Fields_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
thf(1971,plain,
class_Fields_Ofield @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ 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_mult__eq__if) ).
thf(1793,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ 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)],[191]) ).
thf(106,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(1486,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)],[106]) ).
thf(874,axiom,
! [A: $i,B: $i] :
( ( ( class_Groups_Omonoid__mult @ B )
& ( class_Int_Onumber @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).
thf(4105,plain,
! [A: $i,B: $i] :
( ( ( class_Groups_Omonoid__mult @ B )
& ( class_Int_Onumber @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(189,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(1788,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)],[189]) ).
thf(969,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__ge__zero) ).
thf(4418,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(444,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(2607,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)],[444]) ).
thf(551,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(3004,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)],[551]) ).
thf(563,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
thf(3044,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(19,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(1233,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)],[19]) ).
thf(772,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(3781,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(148,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(1640,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)],[148]) ).
thf(641,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(3313,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)],[641]) ).
thf(297,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(2146,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)],[297]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2575,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(800,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge__zero) ).
thf(3848,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(313,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(2195,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)],[313]) ).
thf(778,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(3794,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)],[778]) ).
thf(142,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(1608,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)],[142]) ).
thf(1028,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(4633,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)],[1028]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(3439,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(870,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(4090,plain,
class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(154,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(1655,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)],[154]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
thf(3135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(825,axiom,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
thf(3942,plain,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(736,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(3649,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)],[736]) ).
thf(213,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(1867,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)],[213]) ).
thf(999,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(4528,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)],[999]) ).
thf(1034,axiom,
class_Int_Onumber__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
thf(4650,plain,
class_Int_Onumber__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(451,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(2627,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)],[451]) ).
thf(305,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(2168,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)],[305]) ).
thf(28,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(1260,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)],[28]) ).
thf(228,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(1919,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)],[228]) ).
thf(788,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(3826,plain,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(111,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(1507,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)],[111]) ).
thf(16,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
thf(1222,plain,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).
thf(1746,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(200,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(1835,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)],[200]) ).
thf(258,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(2046,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)],[258]) ).
thf(841,axiom,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
thf(3994,plain,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(547,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(2985,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)],[547]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).
thf(1366,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(193,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
thf(1803,plain,
class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1121,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(4948,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)],[1121]) ).
thf(1066,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__mult__squared__eq) ).
thf(4775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(2957,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(794,axiom,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
thf(3836,plain,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
thf(4343,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(732,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(3629,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(812,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_two__realpow__ge__one) ).
thf(3915,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(187,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(1782,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)],[187]) ).
thf(408,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(2491,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)],[408]) ).
thf(22,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(1243,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)],[22]) ).
thf(622,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(3249,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
= ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
thf(4371,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
= ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
= ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
thf(4266,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1023,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(4618,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)],[1023]) ).
thf(770,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(3777,plain,
class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
thf(3308,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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(1935,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C )
= A ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C )
= A )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(1076,axiom,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
thf(4803,plain,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(152,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(1650,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)],[152]) ).
thf(754,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(3730,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)],[754]) ).
thf(520,axiom,
class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
thf(2886,plain,
class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
thf(4916,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(591,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(3140,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)],[591]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(4137,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(102,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OMin )
= ( c_Groups_Ouminus__class_Ouminus @ A @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Min) ).
thf(1475,plain,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OMin )
= ( c_Groups_Ouminus__class_Ouminus @ A @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(502,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OMin )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I30_J) ).
thf(2825,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OMin )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OMin ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OMin )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OMin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
thf(1529,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(30,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(1265,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)],[30]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(1703,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(18,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(1228,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)],[18]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
thf(1254,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(995,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(4511,plain,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(917,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2__gt__zero) ).
thf(4249,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(785,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
thf(3820,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(676,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(3442,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)],[676]) ).
thf(607,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__less__iff) ).
thf(3195,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ C )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__2__times__iff) ).
thf(4563,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ C )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ C )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
=> ( C
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(49,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(1323,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)],[49]) ).
thf(1067,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(4778,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)],[1067]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(2682,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(760,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(3749,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)],[760]) ).
thf(246,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(1992,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)],[246]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(5108,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
thf(3713,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(915,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__m1__odd) ).
thf(4243,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(670,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(3425,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
thf(1430,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(178,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(1760,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)],[178]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(40,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(1298,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(3116,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(461,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(2667,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(3617,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(52,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(1330,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)],[52]) ).
thf(211,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(1860,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(3542,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(948,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(4349,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(229,axiom,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(1922,plain,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
thf(2713,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B )
= A ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B )
= A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(613,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(3216,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)],[613]) ).
thf(939,axiom,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
thf(4317,plain,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(533,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(2929,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)],[533]) ).
thf(828,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(3951,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)],[828]) ).
thf(793,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(3835,plain,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(923,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__gt__zero) ).
thf(4265,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(978,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)],[978]) ).
thf(65,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(1362,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)],[65]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).
thf(3866,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(221,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__0__iff) ).
thf(1892,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
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 @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
thf(3374,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(951,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(4353,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)],[951]) ).
thf(1072,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
thf(4788,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(901,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 @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ 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_th_I1_J) ).
thf(4194,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 @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ 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)],[901]) ).
thf(259,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(2049,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ c_Int_OPls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(894,axiom,
! [A: $i] :
( ( c_Transcendental_Oarctan @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__half) ).
thf(4179,plain,
! [A: $i] :
( ( c_Transcendental_Oarctan @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(485,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2767,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1002,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit1 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OMin @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I4_J) ).
thf(4551,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit1 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OMin @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(233,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(1931,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)],[233]) ).
thf(416,axiom,
c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I2_J) ).
thf(2520,plain,
c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(1122,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(4952,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(602,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(3180,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)],[602]) ).
thf(961,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(4390,plain,
class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1165,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(5091,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)],[1165]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__odd__eq) ).
thf(4471,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(1074,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
<=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
thf(4793,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
thf(5020,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(710,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
thf(3557,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(215,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__one) ).
thf(1875,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(509,axiom,
! [A: $i] :
( ( c_NthRoot_Osqrt @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__minus) ).
thf(2852,plain,
! [A: $i] :
( ( c_NthRoot_Osqrt @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(1064,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(4771,plain,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(1127,axiom,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(4967,plain,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(3268,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(3258,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(322,axiom,
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I3_J) ).
thf(2222,plain,
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(107,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(1489,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)],[107]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(1302,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(635,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(3295,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)],[635]) ).
thf(518,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(2880,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)],[518]) ).
thf(1083,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
thf(4815,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(714,axiom,
class_Power_Opower @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(3569,plain,
class_Power_Opower @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(577,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(3093,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)],[577]) ).
thf(360,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(2335,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)],[360]) ).
thf(1069,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(4783,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)],[1069]) ).
thf(252,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(2017,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)],[252]) ).
thf(701,axiom,
class_Rings_Oring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(3524,plain,
class_Rings_Oring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(3431,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(1105,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1) ).
thf(4903,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
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(1811,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(70,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__minus1) ).
thf(1373,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(753,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(3724,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)],[753]) ).
thf(210,axiom,
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I7_J) ).
thf(1858,plain,
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(285,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(2122,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)],[285]) ).
thf(702,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(3525,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)],[702]) ).
thf(212,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(1864,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)],[212]) ).
thf(879,axiom,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
thf(4134,plain,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(651,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(3357,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)],[651]) ).
thf(204,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__zero__def) ).
thf(1843,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
thf(4718,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).
thf(1928,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(406,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(2483,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)],[406]) ).
thf(219,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(1886,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)],[219]) ).
thf(60,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(1351,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(250,axiom,
! [A: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
thf(2002,plain,
! [A: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(89,axiom,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1433,plain,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(481,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(2750,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)],[481]) ).
thf(866,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(4082,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(657,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
<=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(3378,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) )
& ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1152,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(5045,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)],[1152]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).
thf(2508,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(542,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(2964,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)],[542]) ).
thf(504,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(2833,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)],[504]) ).
thf(604,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(3189,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)],[604]) ).
thf(1091,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(4842,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)],[1091]) ).
thf(13,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(1215,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)],[13]) ).
thf(560,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(3036,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)],[560]) ).
thf(421,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I25_J) ).
thf(2530,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(389,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(2424,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)],[389]) ).
thf(373,axiom,
class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
thf(2371,plain,
class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(545,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(2979,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)],[545]) ).
thf(742,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(3676,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)],[742]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(2137,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(496,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(2799,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)],[496]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(4038,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(456,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(2639,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)],[456]) ).
thf(720,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(3588,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)],[720]) ).
thf(21,axiom,
class_Groups_Oone @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
thf(1242,plain,
class_Groups_Oone @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(931,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(4285,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)],[931]) ).
thf(611,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(3211,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)],[611]) ).
thf(380,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(2392,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)],[380]) ).
thf(1026,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(4628,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)],[1026]) ).
thf(910,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(4211,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(436,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(2586,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)],[436]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
thf(2982,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).
thf(2954,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(3591,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(403,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
thf(2473,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).
thf(3635,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(1107,axiom,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OMin )
= ( c_Int_OBit1 @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Min) ).
thf(4910,plain,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OMin )
= ( c_Int_OBit1 @ c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(936,axiom,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
thf(4312,plain,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(526,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(2905,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)],[526]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
thf(2000,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(3679,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(10,axiom,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I20_J) ).
thf(1206,plain,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1021,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(4604,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)],[1021]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(3503,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(903,axiom,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
thf(4199,plain,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(638,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(3301,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)],[638]) ).
thf(1059,axiom,
class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
thf(4753,plain,
class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(713,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)],[713]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
thf(1691,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(430,axiom,
class_Rings_Oordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(2574,plain,
class_Rings_Oordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(92,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(1438,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)],[92]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ D @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
thf(3984,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ D @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(599,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(3169,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)],[599]) ).
thf(986,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(4480,plain,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(842,axiom,
! [A: $i] :
( ( c_Int_OBit1 @ A )
!= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
thf(3995,plain,
! [A: $i] :
( ( c_Int_OBit1 @ A )
!= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(643,axiom,
~ ! [A: $i,B: $i] :
( v_z
!= ( c_Complex_Ocomplex_OComplex @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Az_A_061_AComplex_Ax_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(3318,plain,
~ ! [A: $i,B: $i] :
( v_z
!= ( c_Complex_Ocomplex_OComplex @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).
thf(1470,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(275,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(2093,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)],[275]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).
thf(1311,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1009,axiom,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
thf(4576,plain,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(171,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(1723,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)],[171]) ).
thf(789,axiom,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
thf(3827,plain,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(2541,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(1355,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1100,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__m1__even) ).
thf(4878,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(110,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I9_J) ).
thf(1502,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(158,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(1666,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)],[158]) ).
thf(726,axiom,
! [A: $i,B: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus1__divide) ).
thf(3610,plain,
! [A: $i,B: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OMin ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(871,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(4091,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)],[871]) ).
thf(620,axiom,
class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
thf(3239,plain,
class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(993,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__minus) ).
thf(4499,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(4449,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(783,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(3814,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)],[783]) ).
thf(771,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(3778,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)],[771]) ).
thf(625,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(3261,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(17,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__1__iff) ).
thf(1223,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(750,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(3711,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)],[750]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(2733,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(851,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(4016,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)],[851]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ D @ C )
= ( c_Complex_Ocomplex_OComplex @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex_Oinject) ).
thf(2805,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ D @ C )
= ( c_Complex_Ocomplex_OComplex @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Complex_Ocomplex_OComplex @ D @ C )
= ( c_Complex_Ocomplex_OComplex @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(133,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(1570,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)],[133]) ).
thf(291,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(2133,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)],[291]) ).
thf(653,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__zero) ).
thf(3371,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(4204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(930,axiom,
class_Orderings_Olinorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
thf(4284,plain,
class_Orderings_Olinorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(784,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(3816,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(290,axiom,
class_Rings_Olinordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(2132,plain,
class_Rings_Olinordered__idom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(2890,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(888,axiom,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
thf(4160,plain,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(2528,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(3514,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(852,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__eq__power2) ).
thf(4021,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
thf(3286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(629,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(3271,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)],[629]) ).
thf(882,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(4140,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)],[882]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(4849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(664,axiom,
class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
thf(3403,plain,
class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(3578,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(958,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(4385,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)],[958]) ).
thf(314,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(2200,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)],[314]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
thf(2179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(7,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(1195,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)],[7]) ).
thf(34,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(1281,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)],[34]) ).
thf(281,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(2112,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)],[281]) ).
thf(862,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(4063,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)],[862]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Int_Onumber__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).
thf(3191,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Int_Onumber__ring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(516,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(2873,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)],[516]) ).
thf(858,axiom,
( ( v_y____
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt @ v_z ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= v_z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).
thf(4053,plain,
( ( v_y____
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt @ v_z ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= v_z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1013,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(4585,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)],[1013]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
thf(2332,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(886,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).
thf(4155,plain,
c_Int_OMin != c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(2820,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1061,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 @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ 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_th_I2_J) ).
thf(4757,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 @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ 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)],[1061]) ).
thf(590,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(3137,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)],[590]) ).
thf(649,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(3349,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)],[649]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= A )
<=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
thf(3894,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= A )
=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).
thf(1624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
thf(3546,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(593,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(3144,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)],[593]) ).
thf(964,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(4402,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(2181,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
thf(2327,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(319,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(2213,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)],[319]) ).
thf(1057,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(4740,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(818,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(3926,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Oring @ D ) )
=> ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).
thf(3050,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Oring @ D ) )
=> ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(362,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(2345,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)],[362]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__realpow__diff) ).
thf(2547,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(350,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(2313,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)],[350]) ).
thf(765,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(3763,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)],[765]) ).
thf(873,axiom,
class_Groups_Oone @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
thf(4104,plain,
class_Groups_Oone @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(820,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(3931,plain,
class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(559,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(3033,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)],[559]) ).
thf(225,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(1910,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)],[225]) ).
thf(1042,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(4680,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
thf(3799,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(677,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(3445,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)],[677]) ).
thf(853,axiom,
class_Int_Oring__char__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
thf(4027,plain,
class_Int_Oring__char__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1157,axiom,
! [A: $i] :
( ( ( c_Int_OBit1 @ A )
= c_Int_OMin )
<=> ( A = c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).
thf(5066,plain,
! [A: $i] :
( ( ( ( c_Int_OBit1 @ A )
= c_Int_OMin )
=> ( A = c_Int_OMin ) )
& ( ( A = c_Int_OMin )
=> ( ( c_Int_OBit1 @ A )
= c_Int_OMin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(507,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(2840,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1804,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(524,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(2895,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)],[524]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
= A )
<=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).
thf(4108,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
= A )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).
thf(4636,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(998,axiom,
( v_y____
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_y0) ).
thf(4525,plain,
( v_y____
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(748,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(3704,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)],[748]) ).
thf(697,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(3518,plain,
class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
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(2858,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(1102,axiom,
! [A: $i,B: $i] :
( ( c_NthRoot_Osqrt @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__power) ).
thf(4883,plain,
! [A: $i,B: $i] :
( ( c_NthRoot_Osqrt @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(1161,axiom,
( ( c_Int_OBit1 @ c_Int_OMin )
= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__Min) ).
thf(5081,plain,
( ( c_Int_OBit1 @ c_Int_OMin )
= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(177,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__0__iff) ).
thf(1755,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1080,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( 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_power__Suc__0) ).
thf(4808,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( 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)],[1080]) ).
thf(64,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(1360,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)],[64]) ).
thf(580,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(3105,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)],[580]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).
thf(1592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(345,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(2300,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)],[345]) ).
thf(728,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(3615,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)],[728]) ).
thf(124,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(1541,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)],[124]) ).
thf(244,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(1983,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)],[244]) ).
thf(1124,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(4957,plain,
! [A: $i,B: $i] :
( ( c_Int_OBit0 @ B )
!= ( c_Int_OBit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(685,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
thf(3482,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(1153,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(5053,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)],[1153]) ).
thf(208,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(1851,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)],[208]) ).
thf(1168,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(5098,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)],[1168]) ).
thf(121,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(1534,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(238,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(1953,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)],[238]) ).
thf(996,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OPls )
!= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).
thf(4512,plain,
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OPls )
!= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OMin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).
thf(2841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(51,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(1328,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)],[51]) ).
thf(856,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OMin @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I6_J) ).
thf(4048,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OMin @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(209,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(1856,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)],[209]) ).
thf(733,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(3632,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(585,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq) ).
thf(3119,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(759,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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(3746,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(3205,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(912,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2) ).
thf(4219,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(576,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(3087,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)],[576]) ).
thf(76,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(1397,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)],[76]) ).
thf(592,axiom,
class_Rings_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
thf(3143,plain,
class_Rings_Oidom @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(1159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(5075,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(928,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(4276,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)],[928]) ).
thf(1065,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(4772,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
<=> ( ( 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_Complex__eq__0) ).
thf(1461,plain,
! [A: $i,B: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
=> ( ( 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_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(514,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(2868,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)],[514]) ).
thf(387,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(2419,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)],[387]) ).
thf(1116,axiom,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(4938,plain,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(203,axiom,
class_Groups_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(1842,plain,
class_Groups_Omonoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(446,axiom,
class_Int_Onumber @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
thf(2613,plain,
class_Int_Onumber @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(671,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(3428,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)],[671]) ).
thf(606,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(3194,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(2551,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(220,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(1889,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)],[220]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
thf(1744,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(132,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(1567,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)],[132]) ).
thf(1040,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(4676,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(3775,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
thf(3311,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).
thf(4582,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(355,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(2323,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)],[355]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
thf(2830,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(1182,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
| ( B
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OMin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).
thf(1424,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
| ( B
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OMin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(349,axiom,
class_Rings_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
thf(2312,plain,
class_Rings_Oring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
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(2455,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(1058,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__power__le__0__imp__0) ).
thf(4750,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(966,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power3__eq__cube) ).
thf(4406,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(900,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2__right) ).
thf(4191,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(255,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(2038,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)],[255]) ).
thf(95,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(1446,plain,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OPls )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1097,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(4867,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)],[1097]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
thf(4444,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(460,axiom,
class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
thf(2666,plain,
class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(490,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(2781,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)],[490]) ).
thf(1000,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(4530,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)],[1000]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).
thf(1419,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1077,axiom,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(4804,plain,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(340,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(2285,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)],[340]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(4846,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(39,axiom,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(1297,plain,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(97,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__1__iff) ).
thf(1451,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(758,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_NthRoot_Osqrt @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__not__eq__zero) ).
thf(3743,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_NthRoot_Osqrt @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(127,axiom,
class_Rings_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1552,plain,
class_Rings_Omult__zero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(400,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(2465,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)],[400]) ).
thf(615,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(3222,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)],[615]) ).
thf(823,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(3937,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)],[823]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
<=> ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
| ( ( B
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OMin ) )
& ( A
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OMin ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__eq__1__iff) ).
thf(3333,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
| ( ( B
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OMin ) )
& ( A
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OMin ) ) ) ) )
& ( ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
| ( ( B
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OMin ) )
& ( A
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OMin ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(1143,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).
thf(5026,plain,
c_Int_OPls != c_Int_OMin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(814,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(3920,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)],[814]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(3083,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(954,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(4361,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)],[954]) ).
thf(534,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(2932,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)],[534]) ).
thf(286,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(2125,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)],[286]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).
thf(3654,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(103,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(1478,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)],[103]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
thf(1249,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(415,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(2519,plain,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(775,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(3787,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)],[775]) ).
thf(505,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
thf(2836,plain,
class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(98,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(1456,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)],[98]) ).
thf(864,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)],[864]) ).
thf(379,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(2387,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)],[379]) ).
thf(768,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(3770,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)],[768]) ).
thf(242,axiom,
( c_Int_OPls
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
thf(1974,plain,
( c_Int_OPls
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(367,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(2355,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)],[367]) ).
thf(988,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(4482,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)],[988]) ).
thf(764,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(3760,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)],[764]) ).
thf(666,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(3409,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)],[666]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(2862,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(880,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(4135,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)],[880]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(2052,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(468,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(2697,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)],[468]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(1246,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(569,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(3064,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)],[569]) ).
thf(170,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(1720,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)],[170]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(4259,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(294,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(2140,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)],[294]) ).
thf(868,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
thf(4086,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(2756,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(680,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
thf(3454,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(761,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(3755,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)],[761]) ).
thf(46,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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(1318,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1030,axiom,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
thf(4644,plain,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(1025,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2) ).
thf(4625,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(317,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(2208,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)],[317]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
thf(3856,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( A
= ( 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_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(1712,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(1106,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(4906,plain,
! [A: $i,B: $i] :
( ( c_Int_OBit1 @ B )
!= ( c_Int_OBit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(144,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(1616,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)],[144]) ).
thf(797,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(3841,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)],[797]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( c_NthRoot_Osqrt @ B )
= ( c_NthRoot_Osqrt @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__iff) ).
thf(1185,plain,
! [A: $i,B: $i] :
( ( ( ( c_NthRoot_Osqrt @ B )
= ( c_NthRoot_Osqrt @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_NthRoot_Osqrt @ B )
= ( c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(741,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(3675,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1136,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(4995,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)],[1136]) ).
thf(528,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(2909,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)],[528]) ).
thf(683,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(3476,plain,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(53,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(1333,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)],[53]) ).
thf(787,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__real__divide__sqrt__less) ).
thf(3824,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(90,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(1434,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)],[90]) ).
thf(897,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(4184,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(932,axiom,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(4288,plain,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(712,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( ( D = C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(3563,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( ( D = C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(632,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(3279,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)],[632]) ).
thf(603,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(3183,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)],[603]) ).
thf(843,axiom,
! [A: $i] :
( c_Complex_Oii
!= ( c_Int_Onumber__class_Onumber__of @ tc_Complex_Ocomplex @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__number__of) ).
thf(3999,plain,
! [A: $i] :
( c_Complex_Oii
!= ( c_Int_Onumber__class_Onumber__of @ tc_Complex_Ocomplex @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(36,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(1286,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)],[36]) ).
thf(372,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(2368,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)],[372]) ).
thf(157,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(1663,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)],[157]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(2089,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(115,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(1515,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)],[115]) ).
thf(321,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(2221,plain,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(325,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(2235,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)],[325]) ).
thf(536,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( 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(2936,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[536]) ).
thf(982,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(4470,plain,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(163,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(1698,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(2253,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(562,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(3042,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)],[562]) ).
thf(1017,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__sum) ).
thf(4594,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(125,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(1548,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)],[125]) ).
thf(442,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(2602,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)],[442]) ).
thf(925,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ c_Int_OPls ) @ A )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls) ).
thf(4269,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ c_Int_OPls ) @ A )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(5043,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(1112,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(4921,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)],[1112]) ).
thf(33,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(1278,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)],[33]) ).
thf(1111,axiom,
( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
thf(4919,plain,
( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(385,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(2413,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)],[385]) ).
thf(586,axiom,
( c_Int_OMin
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int_OMin__def) ).
thf(3130,plain,
( c_Int_OMin
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__even__eq) ).
thf(4872,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).
thf(1680,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(688,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(3491,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)],[688]) ).
thf(105,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(1483,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)],[105]) ).
thf(968,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
thf(4412,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).
thf(4256,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(972,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
<=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power2) ).
thf(4438,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(757,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(3738,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)],[757]) ).
thf(700,axiom,
class_Groups_Ozero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
thf(3523,plain,
class_Groups_Ozero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1139,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(5016,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(1010,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(4577,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)],[1010]) ).
thf(1167,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(5095,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)],[1167]) ).
thf(582,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(3111,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)],[582]) ).
thf(630,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(3274,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)],[630]) ).
thf(418,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(2524,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)],[418]) ).
thf(660,axiom,
class_Rings_Osemiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__1) ).
thf(3396,plain,
class_Rings_Osemiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(376,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(2376,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)],[376]) ).
thf(977,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(4453,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)],[977]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
thf(3158,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) )
& ( ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(333,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(2260,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)],[333]) ).
thf(1137,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) )
<=> ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq__number__of) ).
thf(4998,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(1038,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(4662,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)],[1038]) ).
thf(543,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(2970,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)],[543]) ).
thf(817,axiom,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
thf(3925,plain,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(992,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(4494,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)],[992]) ).
thf(698,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(3519,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)],[698]) ).
thf(1156,axiom,
class_Groups_Oab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
thf(5065,plain,
class_Groups_Oab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(176,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(1752,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)],[176]) ).
thf(1075,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__square__minus__le) ).
thf(4801,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(979,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(4465,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1 @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(1403,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1 @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(4328,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(724,axiom,
class_Rings_Osemiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
thf(3604,plain,
class_Rings_Osemiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(1120,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(4946,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)],[1120]) ).
thf(722,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(3599,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)],[722]) ).
thf(1070,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(4786,plain,
class_Groups_Oone @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(1119,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(4943,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)],[1119]) ).
thf(945,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).
thf(4341,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(571,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(3070,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)],[571]) ).
thf(767,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(3768,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)],[767]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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(1916,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ D @ C ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__add) ).
thf(3811,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ D @ C ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(621,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(3240,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)],[621]) ).
thf(756,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(3736,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)],[756]) ).
thf(762,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(3758,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1113,axiom,
class_Rings_Osemiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
thf(4926,plain,
class_Rings_Osemiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1041,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(4677,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)],[1041]) ).
thf(122,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(1535,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ c_Int_OPls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(548,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(2991,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)],[548]) ).
thf(1015,axiom,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(4590,plain,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(1131,axiom,
class_Power_Opower @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(4975,plain,
class_Power_Opower @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(117,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(1520,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)],[117]) ).
thf(665,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(3404,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)],[665]) ).
thf(499,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(2817,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)],[499]) ).
thf(918,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(4251,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(989,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(4485,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)],[989]) ).
thf(1133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A )
=> ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
thf(4978,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A )
=> ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(735,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(3646,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)],[735]) ).
thf(737,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(3651,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)],[737]) ).
thf(610,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(3208,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)],[610]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( 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(1997,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(3783,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(180,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(1765,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)],[180]) ).
thf(927,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(4273,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)],[927]) ).
thf(147,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(1638,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)],[147]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Oring @ D ) )
=> ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).
thf(2358,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Oring @ D ) )
=> ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(1148,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(5039,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(159,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(1669,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)],[159]) ).
thf(1146,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(5033,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)],[1146]) ).
thf(832,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(3964,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)],[832]) ).
thf(167,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OMin )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I11_J) ).
thf(1707,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OMin )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OMin ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OMin )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OMin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(2293,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(1371,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1088,axiom,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
thf(4837,plain,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(1031,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(4645,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(146,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_NthRoot_Osqrt @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__zero__cancel) ).
thf(1635,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_NthRoot_Osqrt @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(535,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(2935,plain,
class_Orderings_Olinorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).
thf(3436,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(393,axiom,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(2442,plain,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
thf(2759,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(398,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(2457,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)],[398]) ).
thf(222,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(1897,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)],[222]) ).
thf(428,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(2557,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)],[428]) ).
thf(417,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(2521,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)],[417]) ).
thf(650,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(3352,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)],[650]) ).
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(2679,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(298,axiom,
class_Power_Opower @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
thf(2151,plain,
class_Power_Opower @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(1170,axiom,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
thf(5103,plain,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(1024,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(4620,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)],[1024]) ).
thf(487,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(2774,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)],[487]) ).
thf(59,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(1349,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)],[59]) ).
thf(140,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(1603,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)],[140]) ).
thf(1078,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge1) ).
thf(4805,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(537,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
thf(2945,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(893,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(4176,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)],[893]) ).
thf(377,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(2378,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)],[377]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
thf(3384,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(71,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(1376,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)],[71]) ).
thf(270,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(2079,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)],[270]) ).
thf(369,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__real__sqrt__sumsq) ).
thf(2361,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(2538,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(79,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(1408,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)],[79]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
thf(2084,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(450,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(2624,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ c_Int_OPls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
thf(3551,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(935,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).
thf(4305,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
thf(1589,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(1933,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(865,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
thf(4073,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
thf(1801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(985,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).
thf(4477,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(239,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(1969,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)],[239]) ).
thf(265,axiom,
class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
thf(2065,plain,
class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(960,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(4388,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)],[960]) ).
thf(614,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(3219,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)],[614]) ).
thf(1175,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(5114,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)],[1175]) ).
thf(216,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(1877,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)],[216]) ).
thf(453,axiom,
class_Rings_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(2632,plain,
class_Rings_Osemiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( D != C )
& ( B != A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(3073,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( D != C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) )
=> ( ( D != C )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
<=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
thf(4818,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) )
& ( ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(395,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(2446,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)],[395]) ).
thf(909,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
thf(4208,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(934,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
thf(4296,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ D @ C ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff) ).
thf(1556,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ D @ C ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(432,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(2578,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
thf(1339,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
thf(2610,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(557,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(3027,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)],[557]) ).
thf(588,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(3133,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)],[588]) ).
thf(848,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(4009,plain,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(351,axiom,
class_Groups_Ozero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(2314,plain,
class_Groups_Ozero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__less__mono) ).
thf(2129,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1086,axiom,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
thf(4833,plain,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(2267,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(854,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(4028,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)],[854]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(3572,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(821,axiom,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
thf(3932,plain,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(976,axiom,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(4452,plain,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
thf(1838,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(50,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(1325,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)],[50]) ).
thf(492,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(2785,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)],[492]) ).
thf(438,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(2593,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)],[438]) ).
thf(679,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(3451,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)],[679]) ).
thf(636,axiom,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(3298,plain,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(1036,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(4652,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)],[1036]) ).
thf(686,axiom,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
thf(3483,plain,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(833,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(3971,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)],[833]) ).
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(1344,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(1052,axiom,
class_Int_Onumber @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
thf(4726,plain,
class_Int_Onumber @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
thf(2664,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(339,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(2278,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)],[339]) ).
thf(1138,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(5007,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(1,conjecture,
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ v_x ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_x @ ( 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_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ v_x ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_x @ ( 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_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1177,plain,
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ v_x ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_x @ ( 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_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(74,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(1381,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)],[74]) ).
thf(594,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(3150,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)],[594]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1__strict @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(2329,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1__strict @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).
thf(2710,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(529,axiom,
! [A: $i,B: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Complex__eq__1) ).
thf(2911,plain,
! [A: $i,B: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Complex_Ocomplex_OComplex @ B @ A )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1003,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
thf(4554,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(197,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(1820,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)],[197]) ).
thf(268,axiom,
( ( c_NthRoot_Osqrt @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__zero) ).
thf(2075,plain,
( ( c_NthRoot_Osqrt @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(371,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(2365,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)],[371]) ).
thf(364,axiom,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
thf(2350,plain,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(476,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(2725,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)],[476]) ).
thf(272,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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(2086,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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)],[272]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
thf(3917,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(745,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(3687,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)],[745]) ).
thf(867,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(4085,plain,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(454,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(2633,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)],[454]) ).
thf(422,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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(2535,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(1364,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(694,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(3512,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)],[694]) ).
thf(316,axiom,
class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
thf(2207,plain,
class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
thf(3876,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(763,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I23_J) ).
thf(3759,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(796,axiom,
! [A: $i,B: $i] :
( ( c_NthRoot_Osqrt @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ B ) ) @ ( c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__mult) ).
thf(3838,plain,
! [A: $i,B: $i] :
( ( c_NthRoot_Osqrt @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ B ) ) @ ( c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1166,axiom,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
thf(5094,plain,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(426,axiom,
class_Groups_Omonoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(2550,plain,
class_Groups_Omonoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(994,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(4502,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(149,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(1643,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)],[149]) ).
thf(1085,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(4827,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(2288,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(829,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit1 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OMin @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I5_J) ).
thf(3953,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit1 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OMin @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
thf(2797,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(1775,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(328,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(2244,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)],[328]) ).
thf(482,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(2752,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)],[482]) ).
thf(749,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(3706,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)],[749]) ).
thf(645,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(3325,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)],[645]) ).
thf(108,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(1496,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)],[108]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(4196,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(347,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(2303,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)],[347]) ).
thf(301,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(2156,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)],[301]) ).
thf(1164,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(5089,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)],[1164]) ).
thf(987,axiom,
class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
thf(4481,plain,
class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(887,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(4158,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)],[887]) ).
thf(413,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__one__def) ).
thf(2506,plain,
( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(131,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(1562,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)],[131]) ).
thf(81,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(1413,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)],[81]) ).
thf(943,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(4331,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)],[943]) ).
thf(498,axiom,
class_Rings_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
thf(2816,plain,
class_Rings_Omult__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(447,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(2614,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)],[447]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(4013,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(2107,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(32,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(1277,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1509,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(315,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(2202,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)],[315]) ).
thf(815,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(3921,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)],[815]) ).
thf(101,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(1472,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)],[101]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(4688,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(440,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(2597,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)],[440]) ).
thf(952,axiom,
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ c_Complex_Oii ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Complex_Ocomplex @ c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__i) ).
thf(4355,plain,
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ c_Complex_Oii ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Complex_Ocomplex @ c_Int_OMin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
thf(2054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(908,axiom,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
thf(4207,plain,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1203,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1208,plain,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1103,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Complex_Ocomplex_OComplex @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ tc_Complex_Ocomplex @ A ) )
<=> ( ( C
= ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) )
& ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Complex__eq__number__of) ).
thf(4886,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Complex_Ocomplex_OComplex @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ tc_Complex_Ocomplex @ A ) )
=> ( ( C
= ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) )
& ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( C
= ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) )
& ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Complex_Ocomplex_OComplex @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ tc_Complex_Ocomplex @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(549,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(2994,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)],[549]) ).
thf(353,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(2318,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)],[353]) ).
thf(491,axiom,
class_Groups_Oone @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(2784,plain,
class_Groups_Oone @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(337,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(2271,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)],[337]) ).
thf(402,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
thf(2471,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1019,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(4598,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)],[1019]) ).
thf(740,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(3672,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(224,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(1905,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)],[224]) ).
thf(837,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
thf(3981,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(412,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(2503,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)],[412]) ).
thf(452,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(2629,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)],[452]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(2927,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(835,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
thf(3975,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1082,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus1__odd) ).
thf(4812,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(126,axiom,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(1551,plain,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
thf(4168,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(434,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(2582,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocomplex_OComplex @ D @ C ) ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mult) ).
thf(1845,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Ocomplex_OComplex @ D @ C ) ) @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(659,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__1__iff) ).
thf(3391,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(382,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(2397,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)],[382]) ).
thf(811,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
thf(3913,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(573,axiom,
class_Rings_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(3082,plain,
class_Rings_Oidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(612,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(3214,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)],[612]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1605,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ C ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__triangle__ineq) ).
thf(3833,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ C ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(120,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(1531,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)],[120]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__minus) ).
thf(2160,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Complex_Ocomplex @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Complex_Ocomplex_OComplex @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(183,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(1770,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)],[183]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
thf(3376,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(544,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(2977,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)],[544]) ).
thf(143,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(1611,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)],[143]) ).
thf(1174,axiom,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__power2) ).
thf(5111,plain,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(926,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(4272,plain,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1117,axiom,
class_Rings_Oring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
thf(4939,plain,
class_Rings_Oring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) )
<=> ( ( D = B )
| ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(1941,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) )
=> ( ( D = B )
| ( C = A ) ) )
& ( ( ( D = B )
| ( C = A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(25,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(1252,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)],[25]) ).
thf(904,axiom,
class_Rings_Omult__zero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(4200,plain,
class_Rings_Omult__zero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(68,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(1368,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)],[68]) ).
thf(618,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(3228,plain,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(981,axiom,
class_Fields_Ofield @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
thf(4469,plain,
class_Fields_Ofield @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(1780,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(1060,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).
thf(4754,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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(2407,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) )
& ( ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(1125,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__diff) ).
thf(4961,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(1129,axiom,
class_Rings_Osemiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(4971,plain,
class_Rings_Osemiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(2720,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(914,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(4240,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)],[914]) ).
thf(530,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(2920,plain,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
thf(4003,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(709,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(3554,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)],[709]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(1785,plain,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1063,axiom,
! [A: $i,B: $i] :
( ( class_Power_Opower @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
thf(4768,plain,
! [A: $i,B: $i] :
( ( class_Power_Opower @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(134,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(1579,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)],[134]) ).
thf(752,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(3715,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)],[752]) ).
thf(554,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(3019,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)],[554]) ).
thf(480,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(2747,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)],[480]) ).
thf(109,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(1499,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)],[109]) ).
thf(967,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).
thf(4409,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(429,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(2569,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)],[429]) ).
thf(971,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(4437,plain,
class_Groups_Omonoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(678,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(3448,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)],[678]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus1__even) ).
thf(4314,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1005,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(4561,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)],[1005]) ).
thf(947,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield__inverse__zero @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ C ) ) @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
thf(4346,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield__inverse__zero @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ C ) ) @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__mult) ).
thf(1790,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(323,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(2224,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)],[323]) ).
thf(88,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(1432,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__sum__zero__iff) ).
thf(3885,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(583,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(3114,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)],[583]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
<=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
thf(2688,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) )
& ( ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(913,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
<=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).
thf(4222,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(214,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(1869,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)],[214]) ).
thf(29,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
thf(1262,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [A: $i] :
( ( ( c_NthRoot_Osqrt @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__0__iff) ).
thf(1235,plain,
! [A: $i] :
( ( ( ( c_NthRoot_Osqrt @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_NthRoot_Osqrt @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(786,axiom,
class_Rings_Osemiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
thf(3823,plain,
class_Rings_Osemiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(361,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(2337,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)],[361]) ).
thf(338,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(2276,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)],[338]) ).
thf(1145,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__diff) ).
thf(5030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(780,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(3801,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)],[780]) ).
thf(199,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__lt__1__iff) ).
thf(1830,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(179,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(1763,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)],[179]) ).
thf(950,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
thf(4351,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(705,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(3544,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)],[705]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(3828,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power2) ).
thf(4132,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(155,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(1658,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)],[155]) ).
thf(123,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(1538,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)],[123]) ).
thf(470,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(2701,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)],[470]) ).
thf(407,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(2486,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)],[407]) ).
thf(799,axiom,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
thf(3847,plain,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1134,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(4982,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(731,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(3623,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)],[731]) ).
thf(667,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_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(3412,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)],[667]) ).
thf(1068,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(4781,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(1056,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
thf(4737,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(257,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(2044,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)],[257]) ).
thf(14,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(1218,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)],[14]) ).
thf(802,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_four__x__squared) ).
thf(3853,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).
thf(1336,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1099,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(4875,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)],[1099]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(2468,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(1155,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(5062,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)],[1155]) ).
thf(538,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
thf(2948,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(668,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(3415,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(164,axiom,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1702,plain,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ring__1__class_Opower__minus__even) ).
thf(4246,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(296,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(2145,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(433,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(2579,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)],[433]) ).
thf(555,axiom,
class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
thf(3024,plain,
class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(652,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__iff) ).
thf(3366,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(552,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I8_J) ).
thf(3007,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
thf(2584,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(634,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(3288,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)],[634]) ).
thf(262,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(2056,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
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(1358,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(329,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(2247,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)],[329]) ).
thf(860,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_NthRoot_Osqrt @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__unique) ).
thf(4057,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_NthRoot_Osqrt @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(207,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(1849,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)],[207]) ).
thf(27,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(1257,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)],[27]) ).
thf(1022,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).
thf(4611,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1132,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
thf(4976,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(15,axiom,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(1221,plain,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
thf(4488,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(35,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(1284,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)],[35]) ).
thf(241,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(1972,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)],[241]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
thf(2320,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(175,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
thf(1749,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(883,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Int_OBit1 @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit1) ).
thf(4143,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Int_OBit1 @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(616,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(3224,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)],[616]) ).
thf(86,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(1427,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)],[86]) ).
thf(906,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(4202,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(136,axiom,
class_Rings_Olinordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1585,plain,
class_Rings_Olinordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).
thf(2860,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(475,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(2722,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)],[475]) ).
thf(477,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(2728,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)],[477]) ).
thf(826,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(3943,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)],[826]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(1717,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(254,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(2030,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)],[254]) ).
thf(1089,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square) ).
thf(4838,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(1162,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(5083,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)],[1162]) ).
thf(523,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ c_Complex_Oii ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ c_Complex_Oii ) @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Complex_Ocomplex @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__mult__minus) ).
thf(2892,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ c_Complex_Oii ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ c_Complex_Oii ) @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Complex_Ocomplex @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(596,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(3156,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(1169,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(5100,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(392,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(2435,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)],[392]) ).
thf(662,axiom,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(3400,plain,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(1094,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
thf(4851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(570,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(3067,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)],[570]) ).
thf(519,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(2885,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(128,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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(1553,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(515,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(2870,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)],[515]) ).
thf(312,axiom,
class_Rings_Osemiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(2194,plain,
class_Rings_Osemiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
thf(2347,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
thf(1517,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(4646,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(75,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(1390,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)],[75]) ).
thf(1008,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(4574,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(673,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(3433,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)],[673]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A )
<=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
thf(4289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A )
=> ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) )
& ( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(1035,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(4651,plain,
class_Groups_Ozero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(730,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(3620,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)],[730]) ).
thf(681,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
thf(3457,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(45,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(1316,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)],[45]) ).
thf(151,axiom,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1649,plain,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(366,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(2352,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)],[366]) ).
thf(663,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(3401,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)],[663]) ).
thf(1053,axiom,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
thf(4727,plain,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(941,axiom,
! [A: $i,B: $i] :
( ( ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
= A )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel2) ).
thf(4325,plain,
! [A: $i,B: $i] :
( ( ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
= A )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(1014,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(4587,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)],[1014]) ).
thf(970,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
<=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= B ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).
thf(4419,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= B ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= B ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(47,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(1321,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(226,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(1913,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)],[226]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(2310,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__ge__zero) ).
thf(3874,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(356,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(2325,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(819,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(3928,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(898,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
thf(4185,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(550,axiom,
! [A: $i] :
( ( ( c_NthRoot_Osqrt @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__1__iff) ).
thf(2997,plain,
! [A: $i] :
( ( ( ( c_NthRoot_Osqrt @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( c_NthRoot_Osqrt @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(96,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(1448,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)],[96]) ).
thf(846,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__gt__one) ).
thf(4006,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(37,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(1289,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)],[37]) ).
thf(567,axiom,
class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
thf(3056,plain,
class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(494,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(2792,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)],[494]) ).
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(1807,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(861,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(4061,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)],[861]) ).
thf(561,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(3039,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(739,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(3665,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)],[739]) ).
thf(1055,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(4730,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)],[1055]) ).
thf(1047,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(4710,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(342,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(2290,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)],[342]) ).
thf(292,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(2135,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)],[292]) ).
thf(980,axiom,
class_Power_Opower @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
thf(4468,plain,
class_Power_Opower @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(1043,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(4681,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)],[1043]) ).
thf(876,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
thf(4126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(944,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(4338,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)],[944]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(3252,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(2416,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(299,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(2152,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)],[299]) ).
thf(150,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(1646,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)],[150]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
thf(2443,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(727,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(3613,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)],[727]) ).
thf(1109,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(4913,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).
thf(1341,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(276,axiom,
class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
thf(2098,plain,
class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(687,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(3484,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)],[687]) ).
thf(160,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(1674,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)],[160]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
thf(2855,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(1481,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1044,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left__number__of) ).
thf(4683,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1050,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(4715,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)],[1050]) ).
thf(1073,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).
thf(4791,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(840,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(3991,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)],[840]) ).
thf(849,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(4010,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)],[849]) ).
thf(1087,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(4834,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
thf(3516,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).
thf(5087,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(647,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_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__mono) ).
thf(3331,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_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(1101,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(4881,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(1171,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(5104,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(381,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(2394,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)],[381]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
thf(3085,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(836,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(3978,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(1033,axiom,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
thf(4649,plain,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(1062,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(4759,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(965,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge2) ).
thf(4404,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(1513,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(974,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(4446,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)],[974]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(2315,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(409,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(2494,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)],[409]) ).
thf(388,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(2421,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)],[388]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(2009,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(895,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(4182,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(404,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__0__iff) ).
thf(2475,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(1095,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).
thf(4855,plain,
! [A: $i,B: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(1126,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(4964,plain,
! [A: $i] :
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( hAPP @ ( hAPP @ ( 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(2041,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( hAPP @ ( hAPP @ ( 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)],[256]) ).
thf(892,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(4175,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)],[892]) ).
thf(690,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)],[690]) ).
thf(885,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(4153,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)],[885]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
thf(3879,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(911,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(4214,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)],[911]) ).
thf(798,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(3844,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)],[798]) ).
thf(185,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(1777,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)],[185]) ).
thf(1016,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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(4591,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( 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)],[1016]) ).
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(3267,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(38,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(1294,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)],[38]) ).
thf(1149,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(5040,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(93,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(1440,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)],[93]) ).
thf(1142,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Int_OBit0 @ B ) ) @ A )
= ( c_Int_OBit0 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit0) ).
thf(5023,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Int_OBit0 @ B ) ) @ A )
= ( c_Int_OBit0 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(959,axiom,
class_Groups_Ogroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
thf(4387,plain,
class_Groups_Ogroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(266,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(2066,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)],[266]) ).
thf(166,axiom,
class_Int_Onumber @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).
thf(1706,plain,
class_Int_Onumber @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(6,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(1193,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)],[6]) ).
thf(777,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(3793,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(309,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_OMin ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__minus1) ).
thf(2183,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_OMin ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(12,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(1212,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)],[12]) ).
thf(525,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(2902,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)],[525]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(2120,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1176,axiom,
class_Int_Onumber @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
thf(5119,plain,
class_Int_Onumber @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(247,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(1994,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)],[247]) ).
thf(1114,axiom,
! [A: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
thf(4927,plain,
! [A: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(489,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(2779,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)],[489]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq) ).
thf(2019,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(295,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(2142,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)],[295]) ).
thf(320,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(2218,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)],[320]) ).
thf(375,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(2374,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)],[375]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(2102,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(113,axiom,
c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I6_J) ).
thf(1512,plain,
c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OMin @ c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(346,axiom,
class_Rings_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
thf(2302,plain,
class_Rings_Osemiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
thf(4399,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(473,axiom,
class_Rings_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(2719,plain,
class_Rings_Oring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(626,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(3264,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)],[626]) ).
thf(579,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(3100,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)],[579]) ).
thf(699,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(3521,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(587,axiom,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(3132,plain,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1018,axiom,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
thf(4597,plain,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1150,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(5041,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)],[1150]) ).
thf(774,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(3785,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(693,axiom,
class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
thf(3511,plain,
class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(300,axiom,
class_Groups_Ogroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
thf(2155,plain,
class_Groups_Ogroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(957,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(4378,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)],[957]) ).
thf(332,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(2255,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)],[332]) ).
thf(619,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(3232,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
thf(4254,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(755,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(3733,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)],[755]) ).
thf(1081,axiom,
class_RealVector_Oreal__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).
thf(4811,plain,
class_RealVector_Oreal__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(723,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(3601,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)],[723]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
thf(2233,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(3882,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel) ).
thf(3987,plain,
! [A: $i,B: $i] :
( ( ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(654,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(3373,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)],[654]) ).
thf(795,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(3837,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(73,axiom,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1380,plain,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(443,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(2604,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)],[443]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(2951,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(1160,axiom,
! [A: $i,B: $i] :
( ( c_Complex_Ocomplex_Ocomplex__size @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex_Osize_I1_J) ).
thf(5078,plain,
! [A: $i,B: $i] :
( ( c_Complex_Ocomplex_Ocomplex__size @ ( c_Complex_Ocomplex_OComplex @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).
thf(2736,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1071,axiom,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(4787,plain,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1090,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(4841,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(776,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(3790,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)],[776]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
thf(1527,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(991,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(4491,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(953,axiom,
! [A: $i] :
( c_Int_OMin
!= ( c_Int_OBit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).
thf(4357,plain,
! [A: $i] :
( c_Int_OMin
!= ( c_Int_OBit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(1011,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
thf(4579,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).
thf(3690,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(455,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(2636,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)],[455]) ).
thf(830,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(3956,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)],[830]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(3328,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(1314,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(949,axiom,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(4350,plain,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(711,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(3560,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)],[711]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
thf(4474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(1140,axiom,
class_Rings_Oidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
thf(5019,plain,
class_Rings_Oidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
thf(3850,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(1147,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(5036,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)],[1147]) ).
thf(462,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(2668,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)],[462]) ).
thf(692,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(3506,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)],[692]) ).
thf(58,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(1346,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)],[58]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
thf(4318,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
= A )
=> ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(91,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(1436,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)],[91]) ).
thf(884,axiom,
! [A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2__iff) ).
thf(4146,plain,
! [A: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(1989,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__0) ).
thf(4051,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1104,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(4895,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)],[1104]) ).
thf(631,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(3277,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)],[631]) ).
thf(310,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OMin )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I13_J) ).
thf(2186,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OMin )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OMin ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OMin )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OMin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(929,axiom,
! [A: $i,B: $i] :
( ( c_NthRoot_Osqrt @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__divide) ).
thf(4281,plain,
! [A: $i,B: $i] :
( ( c_NthRoot_Osqrt @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ B ) @ ( c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(4631,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(601,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(3177,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(781,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(3804,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)],[781]) ).
thf(1128,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(4968,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(847,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__sqrt__hcomplex__capprox) ).
thf(4007,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(1172,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(5105,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(274,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(2091,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)],[274]) ).
thf(383,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(2404,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)],[383]) ).
thf(644,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(3323,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)],[644]) ).
thf(558,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(3030,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)],[558]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
thf(3765,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(448,axiom,
( c_Complex_Oii
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).
thf(2619,plain,
( c_Complex_Oii
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1108,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(4912,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(877,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__squared__expand) ).
thf(4129,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(568,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(3057,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)],[568]) ).
thf(72,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(1378,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)],[72]) ).
thf(863,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).
thf(4066,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(1923,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(3939,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(217,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(1880,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)],[217]) ).
thf(1123,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
thf(4955,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(223,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(1902,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)],[223]) ).
thf(374,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(2372,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)],[374]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).
thf(4674,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(411,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I24_J) ).
thf(2502,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OMin @ c_Int_OMin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(327,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(2241,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)],[327]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
thf(2127,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(302,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(2159,plain,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(61,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(1352,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)],[61]) ).
thf(834,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(3974,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(556,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(3025,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)],[556]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1827,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(391,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(2430,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)],[391]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(1268,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(747,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
thf(3701,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(441,axiom,
( v_z
= ( c_Complex_Ocomplex_OComplex @ v_x____ @ v_y____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xy) ).
thf(2600,plain,
( v_z
= ( c_Complex_Ocomplex_OComplex @ v_x____ @ v_y____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(715,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(3570,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)],[715]) ).
thf(725,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(3605,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)],[725]) ).
thf(1130,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(4972,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)],[1130]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).
thf(1582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(334,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(2265,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)],[334]) ).
thf(1154,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(5061,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(243,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(1976,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)],[243]) ).
thf(1037,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(4659,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)],[1037]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(1925,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(1048,axiom,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
thf(4713,plain,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
thf(4691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(469,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__zero) ).
thf(2699,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(3494,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(336,axiom,
class_Int_Onumber__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
thf(2270,plain,
class_Int_Onumber__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(869,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(4088,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)],[869]) ).
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(2672,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(1144,axiom,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(5029,plain,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(1158,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).
thf(5073,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(816,axiom,
class_Groups_Ozero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
thf(3924,plain,
class_Groups_Ozero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(637,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
thf(3299,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(521,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(2887,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)],[521]) ).
thf(889,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(4161,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)],[889]) ).
thf(82,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(1416,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)],[82]) ).
thf(182,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(1769,plain,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(859,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(4056,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(822,axiom,
! [A: $i] :
( ( c_Int_OBit0 @ A )
!= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).
thf(3933,plain,
! [A: $i] :
( ( c_Int_OBit0 @ A )
!= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(891,axiom,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
thf(4174,plain,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(458,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(2655,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)],[458]) ).
thf(486,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(2771,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)],[486]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).
thf(4533,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(703,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(3526,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)],[703]) ).
thf(153,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__mult__self__sum__ge__zero) ).
thf(1653,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(617,axiom,
class_Rings_Oring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
thf(3227,plain,
class_Rings_Oring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(206,axiom,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
thf(1848,plain,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(263,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(2059,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)],[263]) ).
thf(326,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(2238,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)],[326]) ).
thf(937,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(4313,plain,
class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(642,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(3316,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)],[642]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
thf(2170,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(365,axiom,
class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
thf(2351,plain,
class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(608,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(3200,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)],[608]) ).
thf(311,axiom,
( c_Complex_Oii
!= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__one) ).
thf(2191,plain,
( c_Complex_Oii
!= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(1096,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__1__iff) ).
thf(4858,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) )
& ( ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(564,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(3047,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)],[564]) ).
thf(1118,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(4940,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)],[1118]) ).
thf(717,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(3575,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)],[717]) ).
thf(36459,plain,
$false,
inference(cvc4,[status(thm)],[2163,1322,2131,1559,3167,2876,1179,4728,3172,2250,2822,4188,1586,4201,2452,4560,3962,3944,1411,2295,4005,4571,3053,4101,2072,4262,1767,4183,2921,3477,2463,3397,1840,3581,3830,2787,2595,2499,2427,2480,1950,4992,3681,2210,2622,2590,3098,2671,2099,2380,1305,2363,1200,2077,4931,4714,4376,2117,1406,2104,2644,4515,2908,2062,3549,1443,2776,3417,2527,4391,3153,3460,1422,4807,1728,3108,4603,3012,2114,2837,1971,1793,1486,4105,1788,4418,2607,3004,3044,1233,3781,1640,3313,2146,2575,3848,2195,3794,1608,4633,3439,4090,1655,3135,3942,3649,1867,4528,4650,2627,2168,1260,1919,3826,1507,1222,1746,1835,2046,3994,2985,1366,1803,4948,4775,2957,3836,4343,3629,3915,1782,2491,1243,3249,4371,4266,4618,3777,3308,1935,4803,1650,3730,2886,4916,3140,4137,1475,2825,1529,1265,1703,1228,1254,4511,4249,3820,3442,3195,4563,1323,4778,2682,3749,1992,5108,3713,4243,3425,1430,1760,1660,1298,3116,2667,3617,1330,1860,3542,4349,1922,2713,3216,4317,2929,3951,3835,4265,4460,1362,3866,1892,3374,4353,4788,4194,2049,4179,2767,4551,1931,2520,4952,3180,4390,5091,4471,4793,5020,3557,1875,2852,4771,4967,3268,3258,2222,1489,1302,3295,2880,4815,3569,3093,2335,4783,2017,3524,3431,4903,1811,1373,3724,1858,2122,3525,1864,4134,3357,1843,4718,1928,2483,1886,1351,2002,1433,2750,4082,3378,5045,2508,2964,2833,3189,4842,1215,3036,2530,2424,2371,2979,3676,2137,2799,4038,2639,3588,1242,4285,3211,2392,4628,4211,2586,2982,2954,3591,2473,3635,4910,4312,2905,2000,3679,1206,4604,3503,4199,3301,4753,3567,1691,2574,1438,3984,3169,4480,3995,3318,1470,2093,1311,4576,1723,3827,2541,1355,4878,1502,1666,3610,4091,3239,4499,4449,3814,3778,3261,1223,3711,2733,4016,2805,1570,2133,3371,4204,4284,3816,2132,2890,4160,2528,3514,4021,3286,1883,3271,4140,4849,3403,3578,4385,2200,2179,1195,1281,2112,4063,3191,2873,4053,4585,2332,4155,2820,4757,3137,3349,3894,1624,3546,3144,4402,2181,2327,2213,4740,3926,3050,2345,2547,2313,3763,4104,3931,3033,1910,4680,3799,3445,4027,5066,2840,1804,2895,4108,4636,4525,3704,3518,2858,4883,5081,1755,4808,1360,3105,1592,2300,3615,1541,1983,4957,3482,5053,1851,5098,1534,1953,4512,2841,1328,4048,1856,3632,3119,3746,3205,4219,3087,1397,3143,5075,4276,4772,1461,2868,2419,4938,1842,2613,3428,3194,2551,1889,1744,1567,4676,3775,3311,4582,2323,2830,1182,1424,2312,2455,4750,4406,4191,2038,1446,4867,4444,2666,2781,4530,1419,4804,2285,4846,1297,1451,3743,1552,2465,3222,3937,3333,5026,3920,3083,4361,2932,2125,3654,1478,1249,2519,3787,2836,1456,4068,2387,3770,1974,2355,4482,3760,3409,2862,4135,2052,2697,1246,3064,1720,4259,2140,4086,2756,3454,3755,1318,4644,4625,2208,3856,1712,4906,1616,3841,1185,3675,4995,2909,3476,1333,3824,1434,4184,4288,3563,3279,3183,3999,1286,2368,1663,2089,1515,2221,2235,2936,4470,1698,2253,3042,4594,1548,2602,4269,5043,4921,1278,4919,2413,3130,4872,1680,3491,1483,4412,4256,4438,3738,3523,5016,4577,5095,3111,3274,2524,3396,2376,4453,3158,2260,4998,4662,2970,3925,4494,3519,5065,1752,4801,4465,1403,4328,3604,4946,3599,4786,4943,4341,3070,3768,1916,3811,3240,3736,3758,4926,4677,1535,2991,4590,4975,1520,3404,2817,4251,4485,4978,3646,3651,3208,1997,3783,1765,4273,1638,2358,5039,1669,5033,3964,1707,2293,1371,4837,4645,1635,2935,3436,2442,2759,2457,1897,2557,2521,3352,2679,2151,5103,4620,2774,1349,1603,4805,2945,4176,2378,3384,1376,2079,2361,2538,1408,2084,2624,3551,4305,1589,1933,4073,1801,4477,1969,2065,4388,3219,5114,1877,2632,3073,4818,2446,4208,4296,1556,2578,1339,2610,3027,3133,4009,2314,2129,4833,2267,4028,3572,3932,4452,1838,1325,2785,2593,3451,3298,4652,3483,3971,1344,4726,2664,2278,5007,1177,1381,3150,2329,2710,2911,4554,1820,2075,2365,2350,2725,2086,3917,3687,4085,2633,2535,1364,3512,2207,3876,3759,3838,5094,2550,4502,1643,4827,2288,3953,2797,1775,2244,2752,3706,3325,1496,4196,2303,2156,5089,4481,4158,2506,1562,1413,4331,2816,2614,4013,2107,1277,1509,2202,3921,1472,4688,2597,4355,2054,4207,1203,1208,4886,2994,2318,2784,2271,2471,4598,3672,1905,3981,2503,2629,2927,3975,4812,1551,4168,2582,1845,3391,2397,3913,3082,3214,1605,3833,1531,2160,1770,3376,2977,1611,5111,4272,4939,1941,1252,4200,1368,3228,4469,1780,4754,2407,4961,4971,2720,4240,2920,4003,3554,1785,4768,1579,3715,3019,2747,1499,4409,2569,4437,3448,4314,4561,4346,1790,2224,1432,3885,3114,2688,4222,1869,1262,1235,3823,2337,2276,5030,3801,1830,1763,4351,3544,3828,4132,1658,1538,2701,2486,3847,4982,3623,3412,4781,4737,2044,1218,3853,1336,4875,2468,5062,2948,3415,1702,4246,2145,2579,3024,3366,3007,2584,3288,2056,1358,2247,4057,1849,1257,4611,4976,1221,4488,1284,1972,2320,1749,4143,3224,1427,4202,1585,2860,2722,2728,3943,1717,2030,4838,5083,2892,3156,5100,2435,3400,4851,3067,2885,1553,2870,2194,2347,1517,4646,1390,4574,3433,4289,4651,3620,3457,1316,1649,2352,3401,4727,4325,4587,4419,1321,1913,2310,3874,2325,3928,4185,2997,1448,4006,1289,3056,2792,1807,4061,3039,3665,4730,4710,2290,2135,4468,4681,4126,4338,3252,2416,2152,1646,2443,3613,4913,1341,2098,3484,1674,2855,1481,4683,4715,4791,3991,4010,4834,3516,5087,3331,4881,5104,2394,3085,3978,4649,4759,4404,1513,4446,2315,2494,2421,2009,4182,2475,4855,4964,2041,4175,3497,4153,3879,4214,3844,1777,4591,3267,1294,5040,1440,5023,4387,2066,1706,1193,3793,2183,1212,2902,2120,5119,1994,4927,2779,2019,2142,2218,2374,2102,1512,2302,4399,2719,3264,3100,3521,3132,4597,5041,3785,3511,2155,4378,2255,3232,4254,3733,4811,3601,2233,3882,3987,3373,3837,1380,2604,2951,5078,2736,4787,4841,3790,1527,4491,4357,4579,3690,2636,3956,3328,1314,4350,3560,4474,5019,3850,5036,2668,3506,1346,4318,1436,4146,1989,4051,4895,3277,2186,4281,4631,3177,3804,4968,4007,5105,2091,2404,3323,3030,3765,2619,4912,4129,3057,1378,4066,1923,3939,1880,4955,1902,2372,4674,2502,2241,2127,2159,1352,3974,3025,1827,2430,1268,3701,2600,3570,3605,4972,1582,2265,5061,1976,4659,1925,4713,4691,2699,3494,2270,4088,2672,5029,5073,3924,3299,2887,4161,1416,1769,4056,3933,4174,2655,2771,4533,3526,1653,3227,1848,2059,2238,4313,3316,2170,2351,3200,2191,4858,3047,4940,3575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW173+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n001.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 22:51:51 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.98/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.08/1.22 % [INFO] Parsing done (315ms).
% 2.08/1.24 % [INFO] Running in sequential loop mode.
% 2.71/1.47 % [INFO] eprover registered as external prover.
% 2.71/1.47 % [INFO] cvc4 registered as external prover.
% 2.71/1.47 % [INFO] Scanning for conjecture ...
% 3.30/1.63 % [INFO] Found a conjecture and 1174 axioms. Running axiom selection ...
% 4.27/1.86 % [INFO] Axiom selection finished. Selected 1174 axioms (removed 0 axioms).
% 5.81/2.30 % [INFO] Problem is first-order (TPTP FOF).
% 5.81/2.34 % [INFO] Type checking passed.
% 5.81/2.35 % [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 ...
% 95.16/24.32 % External prover 'cvc4' found a proof!
% 95.16/24.32 % [INFO] Killing All external provers ...
% 95.16/24.33 % Time passed: 23812ms (effective reasoning time: 23083ms)
% 95.16/24.33 % 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)>
% 95.16/24.33 % Axioms used in derivation (1174): fact_less__eq__int__code_I14_J, fact_le__SucI, fact_numeral__2__eq__2, fact_not__sum__power2__lt__zero, fact_le__imp__diff__is__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_Numeral1__eq1__nat, fact_zero__power2, 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_real__le__refl, fact_real__sqrt__sum__squares__mult__squared__eq, 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, fact_power__strict__decreasing, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact_lemma__sqrt__hcomplex__capprox, fact_rel__simps_I6_J, fact_mult__1__left, fact_diff__0__eq__0, fact_minus__mult__left, fact_neg__divide__le__eq, fact_neg__equal__0__iff__equal, fact_semiring__norm_I112_J, fact_diff__bin__simps_I10_J, fact_le__eq__less__or__eq, fact_power__0__left__number__of, fact_odd__nonzero, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_mult__nonneg__nonpos, fact_q__pos__lemma, fact_one__is__num__one, 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, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_power__power__power, fact_number__of__minus, fact_realpow__two__sum__zero__iff, fact_diff__add__inverse, fact_bin__less__0__simps_I4_J, fact_power__inject__base, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_divide__nonpos__neg, fact_bin__less__0__simps_I2_J, fact_one__is__add, fact_diff__le__mono2, fact_mult__nat__number__of, arity_Int__Oint__Rings_Olinordered__semiring__strict, fact_minus__mult__right, fact_Complex__eq__1, fact_less__int__code_I14_J, fact_add__nat__number__of, fact_zminus__zminus, fact_mult__eq__0__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, 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_zero__less__power, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_add__less__mono, fact_real__0__less__add__iff, fact_real__sqrt__one, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_mult__right__less__imp__less, fact_complex__zero__def, fact_split__mult__neg__le, fact_real__gt__half__sum, fact_rel__simps_I49_J, fact_rel__simps_I27_J, fact_n__less__m__mult__n, fact_eq__divide__eq__number__of, 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__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, arity_RealDef__Oreal__Rings_Osemiring__0, arity_RealDef__Oreal__Rings_Olinordered__ring, fact_mult__le__less__imp__less, fact_zadd__commute, arity_Nat__Onat__Groups_Omonoid__mult, fact_diff__Suc__less, fact_complex__add, fact_power__increasing, fact_real__add__le__0__iff, fact_mult__0, fact_le__number__of__eq__not__less, fact_eq__neg__iff__add__eq__0, fact_real__sqrt__sum__squares__ge2, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, fact_zero__less__diff, fact_diff__diff__cancel, fact_mult__mono, fact_gr0__conv__Suc, fact_real__sqrt__divide, fact_field__power__not__zero, arity_Complex__Ocomplex__Int_Onumber__ring, fact_Suc__le__mono, arity_Nat__Onat__Rings_Ozero__neq__one, fact_nat__number__of__Pls, fact_add__right__imp__eq, fact_realpow__two__diff, fact_rel__simps_I25_J, 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_power2__eq__imp__eq, fact_rel__simps_I31_J, fact_le__neq__implies__less, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, fact_power2__eq__square, fact_zero__le__one, fact_diff__bin__simps_I7_J, fact_Bit1__def, fact_int__0__less__1, fact_le__minus__iff, fact_pos__le__divide__eq, fact_left__diff__distrib__number__of, fact_real__sqrt__sum__squares__mult__ge__zero, 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, fact_real__sqrt__two__gt__one, fact_mult__numeral__1__right, fact_zle__linear, fact_zero__less__power__nat__eq__number__of, arity_RealDef__Oreal__Rings_Ocomm__ring__1, fact_nat__add__left__cancel__less, fact_add__Bit0__Bit1, fact_complex__i__mult__minus, 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, arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, fact_lemma__realpow__diff, fact_sum__power2__eq__zero__iff, fact_neg__less__0__iff__less, fact_divide__right__mono, fact_rel__simps_I5_J, arity_RealDef__Oreal__Fields_Ofield__inverse__zero, arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, fact_add__nonneg__eq__0__iff, fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, fact_real__sqrt__le__0__iff, fact_real__mult__commute, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J, 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__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, fact_divide__le__eq, fact_add__mono, fact_gr0I, arity_Int__Oint__Rings_Olinordered__ring, fact_add__0__iff, fact_power__minus, fact_real__sqrt__eq__0__iff, fact_one__less__power, fact_power__strict__increasing, fact_real__mult__assoc, fact_power__one__over, fact_one__le__power, fact_mult__eq__1__iff, fact_even__less__0__iff, fact_self__quotient__aux1, fact_complex__i__not__zero, fact_power__commutes, fact_two__realpow__ge__one, 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__eq__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_add__right__mono, fact_power__minus1__odd, fact_le__nat__number__of, fact_less__int__code_I13_J, fact_minus__add, fact_divide__eq__imp, arity_Nat__Onat__Rings_Osemiring__0, fact_diff__le__self, fact_minus__less__iff, fact_less__add__eq__less, fact_divide__strict__left__mono__neg, fact_minus__mult__commute, arity_Complex__Ocomplex__Rings_Osemiring__0, fact_eq__iff__diff__eq__0, fact_number__of__add, fact_Bit1__Min, fact_divide__le__eq__number__of, fact_less__eq__nat_Osimps_I1_J, fact_add__numeral__0__right, fact_number__of__Min, fact_add__numeral__0, arity_RealDef__Oreal__Rings_Olinordered__idom, fact_le__iff__add, fact_one__reorient, fact_le__number__of, fact_diff__commute, fact_rel__simps_I44_J, arity_Nat__Onat__Rings_Oordered__comm__semiring, fact_power__eq__0__iff, fact_half__gt__zero__iff, fact_diff__Suc__eq__diff__pred, fact_less__eq__number__of__int__code, fact_less__divide__eq__number__of1, fact_divide__add__eq__iff, fact_nat__mult__1__right, fact_mult__Min, fact_add__lessD1, fact_add__le__mono1, arity_Int__Oint__Rings_Oidom, fact_divide__less__eq__number__of1, arity_Complex__Ocomplex__Fields_Ofield, fact_mult__numeral__1, fact_lessI, fact_zero__le__square, fact_nat__1__add__1, fact_zero__reorient, fact_real__sqrt__mult__self__sum__ge__zero, fact_rel__simps_I15_J, arity_Int__Oint__Groups_Oordered__ab__group__add, fact_minus__le__iff, arity_Int__Oint__Rings_Oring__no__zero__divisors, fact_less__0__number__of, fact_add__0__right, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_nat__eq__add__iff2, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_split__mult__pos__le, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_le__special_I1_J, fact_nat_Oinject, fact_mult__left__le__one__le, fact_not__add__less2, fact_less__or__eq__imp__le, fact_Suc__diff__eq__diff__pred, fact_Suc__less__SucD, fact_power__strict__mono, arity_Int__Oint__Rings_Oordered__cancel__semiring, fact_real__add__minus__iff, arity_RealDef__Oreal__Groups_Ocancel__semigroup__add, fact_minus__divide__divide, fact_zadd__strict__right__mono, arity_Int__Oint__Int_Onumber__ring, arity_Complex__Ocomplex__RealVector_Oreal__field, fact_q__neg__lemma, fact_zadd__zless__mono, fact_power2__diff, fact_mult__pos__neg, fact_power__gt1__lemma, fact_pos__less__divide__eq, fact_add__number__of__diff2, fact_real__le__eq__diff, fact_mult__less__mono1, fact_Suc__leI, fact_add__neg__nonpos, fact_unique__quotient__lemma__neg, arity_RealDef__Oreal__Rings_Ozero__neq__one, fact_diff__less, fact_mult__pos__neg2, fact_power__Suc2, fact_convex__bound__lt, fact_pos__zmult__eq__1__iff__lemma, fact_zpower__zadd__distrib, fact_rel__simps_I12_J, fact_zadd__assoc, fact_pos__divide__le__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_real__0__le__divide__iff, fact_less__irrefl__nat, fact_ring__1__class_Opower__minus__even, fact_real__sqrt__le__1__iff, fact_Suc__lessD, arity_RealDef__Oreal__RealVector_Oreal__normed__algebra, fact_not__less__less__Suc__eq, fact_diff__def, arity_RealDef__Oreal__RealVector_Oreal__field, fact_nat__mult__1, fact_diff__is__0__eq_H, fact_real__sqrt__le__iff, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_mult__right__mono__neg, fact_rel__simps_I48_J, fact_arctan__zero__zero, fact_divide__strict__right__mono__neg, fact_le__add2, fact_minus__divide__right, fact_diff__self, fact_minus__nat_Odiff__0, fact_pos__zmult__eq__1__iff, arity_Int__Oint__Groups_Ocancel__semigroup__add, fact_mult_Oprod__diff__prod, fact_zle__diff1__eq, fact_divide__eq__eq__number__of, fact_Suc__n__not__le__n, arity_Int__Oint__Power_Opower, fact_diff__0, fact_add__left__imp__eq, arity_Int__Oint__Rings_Osemiring__0, fact_zero__eq__power2, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_zpower__zpower, fact_add__leD2, fact_mult__mono_H, fact_real__add__mult__distrib, fact_divide__left__mono, fact_realpow__minus__mult, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_complex__mult, fact_add__diff__assoc, arity_Nat__Onat__Power_Opower, fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_not__less0, fact_mult__Pls, fact_trans__less__add2, fact_minus__numeral__code_I5_J, fact_less__Suc__eq__le, fact_Suc3__eq__add__3, fact_nat__diff__split, fact_zadd__0, fact_add__frac__eq, fact_divide__left__mono__neg, fact_real__zero__not__eq__one, arity_RealDef__Oreal__Rings_Omult__zero, fact_real__sqrt__eq__1__iff, fact_real__sqrt__sum__squares__ge1, arity_Complex__Ocomplex__Groups_Oab__semigroup__add, arity_Complex__Ocomplex__Fields_Ofield__inverse__zero, arity_Int__Oint__Int_Onumber, fact_rel__simps_I21_J, arity_Nat__Onat__Rings_Ocomm__semiring__1, arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, fact_mult__imp__div__pos__less, fact_nat_Osimps_I2_J, arity_Int__Oint__Groups_Oab__semigroup__mult, fact_mult__left__less__imp__less, fact_diff__mult__distrib2, fact_odd__0__le__power__imp__0__le, fact_semiring__norm_I115_J, fact_neg__less__iff__less, fact_add__Bit0__Bit0, fact_rel__simps_I30_J, arity_Complex__Ocomplex__Rings_Osemiring, fact_real__sqrt__gt__0__iff, fact_rel__simps_I34_J, fact_real__mult__right__cancel, fact_less__zeroE, fact_minus__zero, arity_Complex__Ocomplex__Groups_Ogroup__add, fact_not__one__less__zero, fact_one__le__mult__iff, arity_RealDef__Oreal__Rings_Olinordered__semiring, fact_not__less__eq, fact_rel__simps_I51_J, fact_real__sqrt__ge__one, fact_less__nat__number__of, fact_mult__le__cancel1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, fact_real__sqrt__ge__1__iff, fact_mult__divide__mult__cancel__left, fact_zero__le__double__add__iff__zero__le__single__add, fact_power2__less__imp__less, fact_times__numeral__code_I5_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_nat__neq__iff, fact_nat__1__eq__mult__iff, fact_add__mult__distrib2, fact_eq__add__iff1, fact_less__not__refl3, arity_Complex__Ocomplex__Rings_Ozero__neq__one, fact_arith__simps_I32_J, fact_nat__diff__split__asm, fact_zle__antisym, fact_add__left__cancel, fact_neg__less__nonneg, fact_frac__eq__eq, fact_zmult__assoc, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_complex_Oinject, fact_add__number__of__diff1, arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, fact_power__less__imp__less__base, fact_less__eq__real__def, arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, fact_add__Bit1__Bit0, fact_add__right__cancel, fact_mult__strict__mono_H, fact_one__less__mult, fact_mult__Bit1, fact_nat__one__le__power, fact_mult__nonneg__nonneg, fact_add__less__cancel__left, fact_complex__minus, fact_zero__less__mult__pos2, fact_y0, fact_frac__le, fact_power__even__eq, arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, arity_Int__Oint__Rings_Oordered__semiring, arity_Complex__Ocomplex__Rings_Ocomm__semiring, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_real__sqrt__less__mono, fact_nat__add__left__cancel__le, fact_real__sqrt__two__ge__zero, fact_double__zero__sym, fact_divide__pos__pos, fact_power2__eq__square__number__of, fact_zminus__zadd__distrib, fact_le__diff__conv, fact_zmult__1, fact_one__neq__zero, fact_divide__neg__neg, fact_mult__left__mono, fact_less__Suc__eq__0__disj, fact_mult__imp__less__div__pos, fact_add__divide__eq__iff, fact_rel__simps_I47_J, fact_neg__0__equal__iff__equal, fact_left__minus, fact_diff__cancel, fact_divide__neg__pos, fact_divide__Numeral0, fact_rel__simps_I26_J, arity_Nat__Onat__Rings_Osemiring__1, arity_RealDef__Oreal__Fields_Olinordered__field, fact_right__minus, fact_real__less__half__sum, fact_power__decreasing, fact_le__add__iff1, arity_Complex__Ocomplex__Rings_Osemiring__1, fact_divide__nonneg__pos, fact_minus__numeral__code_I6_J, fact_le__Suc__eq, fact_real__minus__mult__self__le, fact_add__Pls, fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, fact_less__add__iff2, fact_add__strict__mono, fact_rel__simps_I7_J, fact_diff__divide__eq__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_power2__less__0, fact_frac__less, arity_RealDef__Oreal__Orderings_Olinorder, fact_mult__number__of__left, fact_nat__mult__le__cancel1, fact_le__add__diff__inverse2, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_Suc__mult__less__cancel1, fact_add__num__frac, fact_not__one__le__zero, fact_mult__cancel2, arity_RealDef__Oreal__Rings_Ocomm__semiring, fact_mult__2__right, arity_Int__Oint__Rings_Olinordered__semidom, fact_nat__number__of__mult__left, arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_rel__simps_I39_J, fact_nat__diff__add__eq2, fact_mult__neg__pos, arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult, fact_diff__int__def__symmetric, arity_Nat__Onat__Groups_Ocomm__monoid__add, fact_less__divide__eq__number__of, fact_less__antisym, fact_th_I1_J, fact_not__real__square__gt__zero, fact_Suc__le__eq, arity_Int__Oint__Groups_Ogroup__add, fact_add__diff__cancel, fact_eq__divide__eq__number__of1, arity_Nat__Onat__Rings_Ocomm__semiring, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_mult__less__le__imp__less, fact_nat__mult__assoc, fact_rel__simps_I40_J, fact_equation__minus__iff, fact_zero__less__power2, fact_equal__neg__zero, fact_diff__int__def, arity_Nat__Onat__Groups_Omonoid__add, fact_semiring__norm_I110_J, fact_rel__simps_I13_J, fact_lemma__real__divide__sqrt__less, fact_diff__add__cancel, arity_Complex__Ocomplex__Rings_Oring, arity_Int__Oint__Groups_Oab__group__add, fact_divide__nonpos__pos, fact_power__Suc__less__one, fact_not__sum__squares__lt__zero, fact_real__mult__1, fact_less__eq__Suc__le, fact_divide__eq__eq, fact_mult__nonneg__nonpos2, fact_less__add__Suc2, fact_sum__power2__ge__zero, fact_less__imp__diff__less, arity_RealDef__Oreal__Rings_Oordered__cancel__semiring, fact_number__of__mult, fact_power__add, arity_RealDef__Oreal__Rings_Odivision__ring, fact_nat__mult__eq__cancel1, arity_Int__Oint__Rings_Oring__1__no__zero__divisors, fact_Suc__pred_H, fact_zmult__eq__1__iff, fact_add__special_I2_J, fact_rel__simps_I19_J, fact_rel__simps_I11_J, fact_zmult__commute, fact_less__eq__int__code_I15_J, fact_nat__mult__2, arity_RealDef__Oreal__Rings_Oring, fact_comm__mult__strict__left__mono, fact_minus__minus, fact_le__real__sqrt__sumsq, fact_rel__simps_I38_J, fact_minus__add__distrib, fact_real__sqrt__pow2__gt__zero, arity_Complex__Ocomplex__Groups_Ocomm__monoid__add, fact_divide__less__0__iff, fact_left__distrib__number__of, fact_real__sqrt__unique, fact__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Az_A_061_AComplex_Ax_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, arity_Complex__Ocomplex__Groups_Oone, fact_add__is__1, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, fact_less__minus__iff, fact_real__sum__squared__expand, fact_zero__less__power__nat__eq, fact_power_Opower_Opower__0, fact_power__Suc__less, fact_linorder__neqE__nat, fact_mult__less__mono2, arity_RealDef__Oreal__Rings_Osemiring, fact_rel__simps_I17_J, fact_number__of__Bit0, fact_diffs0__imp__equal, fact_diff__diff__left, fact_power__inject__exp, fact_nonzero__divide__eq__eq, fact_less__number__of__int__code, arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, fact_zero__is__num__zero, arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add, arity_Nat__Onat__Groups_Ozero, fact_Complex__eq__number__of, fact_rel__simps_I29_J, fact_real__mult__le__cancel__iff1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_nat__mult__less__cancel1, fact_power__eq__0__iff__number__of, fact_diff__Suc__diff__eq2, arity_Complex__Ocomplex__Rings_Odivision__ring, fact_power2__minus, arity_Nat__Onat__Groups_Ocomm__monoid__mult, fact_diff__add__assoc2, fact_bin__less__0__simps_I3_J, fact_power__divide, arity_Int__Oint__Int_Oring__char__0, fact_power__increasing__iff, fact_real__sqrt__sum__squares__eq__cancel2, arity_RealDef__Oreal__Int_Onumber__ring, fact_diff__special_I1_J, fact_less__eq__int__code_I13_J, fact_zadd__left__commute, fact_rel__simps_I43_J, fact_unique__quotient__lemma, fact_frac__less2, arity_Complex__Ocomplex__Rings_Oring__1, fact_diff__diff__right, fact_power__le__imp__le__exp, fact_power__one__right, fact_add__nonneg__pos, fact_mult__less__cancel__right__disj, arity_RealDef__Oreal__Groups_Oab__semigroup__add, fact_add__less__cancel__right, fact_Suc__mult__cancel1, fact_mult__strict__right__mono, fact_add__nonpos__nonpos, arity_Int__Oint__Groups_Omonoid__mult, arity_RealDef__Oreal__Rings_Olinordered__semiring__strict, fact_less__special_I2_J, fact_Pls__def, fact_Suc__le__lessD, arity_RealDef__Oreal__Rings_Oordered__ring, fact_add__increasing, fact_not__add__less1, fact_zero__le__power2, fact_zless__le, fact_number__of__reorient, arity_RealDef__Oreal__Int_Oring__char__0, fact_ext, fact_eq__0__number__of, arity_RealDef__Oreal__Groups_Oordered__ab__group__add, fact_mult__le__cancel__left__pos, fact_eq__diff__iff, fact_zero__less__double__add__iff__zero__less__single__add, arity_Complex__Ocomplex__Rings_Ocomm__ring__1, fact_times__divide__eq__right, fact_zero__le__power, fact_Suc__neq__Zero, fact_eq__divide__imp, fact_le__divide__eq, fact_real__mult__less__iff1, fact_nat__le__add__iff2, arity_RealDef__Oreal__Rings_Olinordered__ring__strict, fact_Suc__inject, arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors, fact_less__diff__conv, fact_divide__right__mono__neg, fact_crossproduct__noteq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, arity_Nat__Onat__Rings_Olinordered__semiring, fact_zle__trans, fact_le__imp__neg__le, fact_calculation, fact_zless__imp__add1__zle, fact_arith__simps_I30_J, fact_less__add__iff1, fact_four__x__squared, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_nat__power__less__imp__less, fact_nat__lt__two__imp__zero__or__one, fact_number__of2, fact_power__strict__increasing__iff, fact_divide__le__0__iff, fact_Bit0__Pls, fact_diff__bin__simps_I9_J, fact_diff__less__Suc, fact_add__eq__self__zero, fact_rel__simps_I14_J, fact_le__divide__eq__number__of1, fact_real__sqrt__two__gt__zero, arity_Nat__Onat__Orderings_Olinorder, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_mult__zero__right, fact_zminus__0, fact_mult__le__0__iff, fact_sum__power2__le__zero__iff, fact_le__iff__diff__le__0, fact_power__less__imp__less__exp, fact_divide__self__if, fact_mult__is__0, fact_Suc__diff__1, fact_add__special_I3_J, fact_nat__add__left__cancel, fact_mult__le__cancel2, fact_numeral__1__eq__1, fact_real__average__minus__second, arity_Int__Oint__Rings_Omult__zero, fact_minus__Pls, fact_real__le__antisym, fact_real__sqrt__pow2__iff, fact_mult__le__mono, fact_one__add__one__is__two, fact_n__not__Suc__n, fact_nat__le__linear, fact_nat__less__add__iff1, fact_power__diff, arity_Int__Oint__Rings_Oring, fact_divide__zero, arity_Nat__Onat__Rings_Omult__zero, arity_RealDef__Oreal__Groups_Ocomm__monoid__add, fact_power2__le__imp__le, fact_less__minus__self__iff, fact_add__strict__left__mono, fact_nat__0__less__mult__iff, fact_rel__simps_I3_J, fact_rel__simps_I33_J, fact_real__sqrt__gt__zero, arity_RealDef__Oreal__Rings_Ocomm__semiring__1, fact_diff__eq__diff__less, fact_add__mult__distrib, fact_le__add__diff, fact_real__sqrt__gt__1__iff, fact_diff__bin__simps_I1_J, fact_real__sqrt__not__eq__zero, arity_Int__Oint__Groups_Oordered__comm__monoid__add, fact_th_I2_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_le__divide__eq__number__of, fact_add__Suc, fact_diff__add__assoc, fact_zero__le__even__power_H, fact_minus1__divide, fact_sum__squares__gt__zero__iff, fact_nat__le__add__iff1, fact_mult__less__cancel1, fact_real__sum__of__halves, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_diff__divide__distrib, fact_less__2__cases, arity_RealDef__Oreal__Rings_Ono__zero__divisors, fact_add__gr__0, arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict, fact_zdiff__zmult__distrib2, fact_add__diff__assoc2, fact_mult__divide__mult__cancel__right, fact_minus__unique, fact_diff__bin__simps_I6_J, fact_diff__less__mono2, fact_divide__zero__left, arity_Nat__Onat__Rings_Oordered__cancel__semiring, fact_int__0__neq__1, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, fact_Suc__eq__plus1__left, fact_Zero__not__Suc, arity_RealDef__Oreal__Rings_Olinordered__semiring__1, arity_Complex__Ocomplex__Rings_Ono__zero__divisors, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le, fact_mult__strict__mono, fact_power__0, fact_zero__less__one, fact_power__0__left, fact_real__diff__def, fact_mult__2, fact_diff__mult__distrib, fact_real__divide__square__eq, fact_power__Suc, fact_power__m1__even, fact_add__less__imp__less__right, fact_le__Suc__ex__iff, arity_RealDef__Oreal__Rings_Oring__no__zero__divisors, fact_zdiff__zmult__distrib, fact_diff__less__mono, fact_Suc__leD, fact_neg__equal__zero, fact_power__mult, fact_add__number__of__eq, fact_add__minus__cancel, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_zero__less__divide__iff, fact_rel__simps_I9_J, fact_add_Ocomm__neutral, fact_pos__divide__less__eq, arity_Nat__Onat__Rings_Oordered__semiring, fact_mult__Suc, fact_Bit0__def, fact_less__trans__Suc, fact_arctan__minus, fact_le__minus__self__iff, fact_complex_Osize_I1_J, fact_rel__simps_I50_J, fact_diff__frac__eq, fact_power3__eq__cube, fact_trans__le__add2, fact_power__eq__if, fact_mult__right__le__one__le, fact_arctan__monotone_H, fact_less__number__of, fact_diff__bin__simps_I3_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_mult__zero__left, arity_Int__Oint__Groups_Oordered__ab__semigroup__add, fact_left__add__mult__distrib, fact_add__scale__eq__noteq, fact_Nat_Odiff__diff__eq, fact_complex__i__not__one, fact_power__minus1__even, fact_le__refl, fact_nat__add__assoc, fact_rel__simps_I20_J, fact_eq__add__iff2, fact_zadd__zmult__distrib2, fact_mult__imp__div__pos__le, fact_less__not__refl2, fact_real__sqrt__lt__0__iff, fact_mult__Bit0, fact_le__add1, fact_mult__cancel1, fact_rel__simps_I8_J, fact_le__special_I3_J, fact_real__sqrt__sum__squares__triangle__ineq, fact_rel__simps_I4_J, arity_RealDef__Oreal__Groups_Oone, fact_Suc__mult__le__cancel1, fact_minus__Min, fact_One__nat__def, fact_mult__diff__mult, fact_add__less__imp__less__left, arity_Int__Oint__Rings_Oordered__ring, fact_power_Opower_Opower__Suc, fact_complex__diff, fact_ab__diff__minus, fact_le__imp__less__Suc, fact_right__diff__distrib__number__of, fact_real__sqrt__minus, fact_mult__minus1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, arity_Int__Oint__Rings_Olinordered__semiring, fact_real__sqrt__power, fact_nonzero__minus__divide__divide, fact_numeral__3__eq__3, fact_less__add__Suc1, fact_ab__left__minus, fact_add__neg__neg, fact_minus__diff__eq, fact_comm__semiring__class_Odistrib, fact_add__number__of__left, fact_semiring__norm_I113_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_power2__i, fact_square__eq__iff, fact_nonzero__minus__divide__right, fact_add__is__0, fact_rel__simps_I10_J, fact_eq__number__of, fact_nat__diff__add__eq1, fact_divide__diff__eq__iff, fact_real__sqrt__pow2, fact_rel__simps_I46_J, fact_rel__simps_I16_J, fact_realpow__num__eq__if, fact_eq__number__of__0, fact_times__divide__times__eq, fact_Deriv_Oadd__diff__add, fact_mult__right__mono, fact_nat__less__add__iff2, fact_diff__minus__eq__add, fact_power__mono, fact_power2__sum, fact_mult__le__mono1, fact_diff__self__eq__0, fact_add__eq__0__iff, fact_rel__simps_I24_J, fact_neg__equal__iff__equal, fact_realpow__two__disj, arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, fact_diff__add__0, fact_divide__le__eq__number__of1, fact_mult__nonpos__nonneg, fact_add__pos__pos, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_diff__cancel2, fact_add__0, fact_rel__simps_I37_J, fact_add__nonneg__nonneg, fact_nat__eq__add__iff1, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, arity_RealDef__Oreal__Power_Opower, fact_Suc__eq__plus1, arity_RealDef__Oreal__Groups_Oab__group__add, fact_power__m1__odd, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, arity_Int__Oint__Rings_Olinordered__idom, arity_Int__Oint__Rings_Ocomm__semiring__1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_self__quotient__aux2, arity_RealDef__Oreal__Rings_Olinordered__semidom, fact_real__sqrt__lt__1__iff, fact_Suc__diff__le, fact_Zero__neq__Suc, fact_nat__mult__2__right, fact_less__eq__int__code_I16_J, fact_power2__eq__1__iff, arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, fact_less__special_I3_J, fact_rel__simps_I28_J, fact_power__mult__distrib, fact_sum__power2__gt__zero__iff, arity_Int__Oint__Rings_Oordered__comm__semiring, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_square__eq__1__iff, fact_Suc__pred, arity_Int__Oint__Groups_Oab__semigroup__add, fact_divide__less__eq, arity_Int__Oint__Groups_Oone, fact_real__sqrt__zero, arity_Nat__Onat__Groups_Oab__semigroup__add, fact_arith__simps_I31_J, 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_power__Suc__0, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_n__less__n__mult__m, fact_xy, fact_less__not__refl, fact_double__add__le__zero__iff__single__add__le__zero, fact_mult__less__cancel__left__neg, fact_less__1__mult, fact_Int_OMin__def, fact_le0, fact_power__one, 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, 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, arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero, fact_less__add__one, fact_int__one__le__iff__zero__less, fact_mult__less__imp__less__right, fact_zero__neq__one, fact_number__of1, fact_divide__strict__left__mono, fact_real__sqrt__eq__zero__cancel, fact_one__power2, fact_diff__Suc__1, fact_add__less__le__mono, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_real__two__squares__add__zero__iff, fact_power__less__power__Suc, fact_real__sqrt__sum__squares__eq__cancel, arity_Nat__Onat__Int_Onumber, fact_double__number__of__Bit0, arity_Nat__Onat__Rings_Olinordered__semiring__strict, fact_power__eq__imp__eq__base, fact_less__Suc__eq, fact_nat__add__commute, arity_Int__Oint__Rings_Ono__zero__divisors, fact_diff__eq__diff__less__eq, fact_less__int__code_I15_J, fact_Suc__less__eq, fact_mult__neg__neg, fact_add__leE, fact_arctan__half, arity_Int__Oint__Rings_Oring__1, fact_right__minus__eq, arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, fact_neg__0__le__iff__le, arity_RealDef__Oreal__Rings_Osemiring__1, fact_Complex__eq__0, fact_zdiv__mono2__lemma, fact_rel__simps_I23_J, fact_zmult__zminus, arity_RealDef__Oreal__Rings_Oring__1, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, fact_complex__i__not__number__of, fact_rel__simps_I42_J, fact_real__sqrt__ge__zero, fact_rel__simps_I45_J, fact_divide__minus1, fact_zero__less__Suc, fact_rel__simps_I2_J, fact_less__divide__eq, fact_mult_Ocomm__neutral, fact_real__add__left__mono, fact_real__mult__order, arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_add__nonpos__neg, fact_real__sqrt__eq__iff, arity_RealDef__Oreal__Rings_Oordered__semiring, fact_le__SucE, fact_le__less__Suc__eq, fact_nat__power__eq__Suc__0__iff, fact_nat__mult__commute, fact_divide__Numeral1, fact_add1__zle__eq, fact_real__sqrt__ge__0__iff, 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, arity_RealDef__Oreal__Int_Onumber, fact_neg__divide__less__eq, fact_diff__eq__diff__eq, fact_minus__le__self__iff, fact_less__int__code_I16_J, fact_add__strict__increasing, fact_number__of__Bit1, fact_real__sqrt__mult, fact_le__special_I4_J, fact_neq0__conv, fact_mult__left__mono__neg, fact_le__antisym, fact_zadd__0__right, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, fact_complex__one__def, fact_zero__less__mult__pos, fact_mult__Suc__right, fact_add__2__eq__Suc, fact_Suc__n__not__n, fact_nat__numeral__1__eq__1, fact_add__frac__num, fact_minus__equation__iff, fact_half, 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_real__sqrt__less__iff, fact_bin__less__0__simps_I1_J, fact_trans__le__add1, fact_add__divide__distrib, fact_divide__less__eq__number__of, fact_lemma__MVT, fact_diff__le__mono, arity_Complex__Ocomplex__Rings_Omult__zero, fact_zmult__1__right, fact_double__eq__0__iff, fact_le__0__eq, fact_less__iff__Suc__add, fact_real__0__le__add__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_mult__less__cancel2, fact_zle__add1__eq__le, fact_mult__1__right, fact_add__le__imp__le__right, fact_real__mult__less__mono2, fact_less__Suc0, fact_rel__simps_I32_J, arity_Nat__Onat__Rings_Osemiring, fact_real__average__minus__first, fact_zero__less__two, fact_real__sqrt__le__mono, fact_diff__is__0__eq, fact_number__of__Pls, fact_sum__squares__eq__zero__iff, fact_le__add__diff__inverse, fact_nat__zero__less__power__iff, arity_Int__Oint__Rings_Ocomm__ring__1, fact_add__le__mono, fact_add__diff__inverse, fact_convex__bound__le, fact_divide__nonneg__neg, fact_mult__minus1__right, arity_Int__Oint__Groups_Olinordered__ab__group__add, fact_nat__mult__eq__cancel__disj, 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, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_power__gt1, fact_no__zero__divisors, fact_le__square, fact_zadd__zmult__distrib, arity_RealDef__Oreal__Groups_Ogroup__add, fact_zadd__zminus__inverse2, 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, arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, fact_realpow__square__minus__le, fact_power__0__Suc, fact_nat__less__le, fact_less__iff__diff__less__0, fact_mult__eq__if, 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, fact_real__le__linear, arity_Complex__Ocomplex__Power_Opower, fact_power__odd__eq, fact_diff__bin__simps_I5_J, fact_nonzero__eq__divide__eq, fact_realpow__Suc__le__self, 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_less__diff__iff, fact_odd__less__0, fact_ab__semigroup__add__class_Oadd__ac_I1_J, fact_real__sqrt__sum__squares__ge__zero, arity_Int__Oint__Groups_Omonoid__add, fact_less__half__sum, fact_add__Suc__shift, fact_diff__bin__simps_I4_J, arity_Complex__Ocomplex__Groups_Ozero, fact_power__le__imp__le__base, fact_mult__1, fact_rel__simps_I22_J, fact_less__special_I1_J, fact_le__special_I2_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, arity_Complex__Ocomplex__Int_Onumber, fact_eq__number__of__Pls__Min, fact_less__SucI, fact_Suc__not__Zero, 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_zdiv__mono2__neg__lemma, fact_even__power__le__0__imp__0, fact_divide__self, fact_nonzero__power__divide, fact_odd__power__less__zero, fact_diff__special_I2_J
% 95.16/24.33 % No. of inferences in proof: 2352
% 95.16/24.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23812 ms resp. 23083 ms w/o parsing
% 95.85/24.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 95.85/24.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------