%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:09:37 AM UTC 2026
% Result : Theorem 55.14s 30.08s
% Output : Refutation 61.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1139
% Syntax : Number of formulae : 2280 ( 724 unt; 0 typ; 0 def)
% Number of atoms : 6457 (1639 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 31717 ( 519 ~; 186 |; 718 &;27021 @)
% ( 268 <=>;3005 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 92 usr; 11 con; 0-3 aty)
% Number of variables : 4824 ( 0 ^;4787 !; 37 ?;4824 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_na_____decl,type,
v_na____: $i ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i > $i ).
thf(c_Groups_Otimes__class_Otimes_decl,type,
c_Groups_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(c_Int_Onumber__class_Onumber__of_decl,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(c_Int_OBit0_decl,type,
c_Int_OBit0: $i > $i ).
thf(c_Int_OBit1_decl,type,
c_Int_OBit1: $i > $i ).
thf(c_Int_OPls_decl,type,
c_Int_OPls: $i ).
thf(class_RealVector_Oreal__normed__algebra__1_decl,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(tc_RealDef_Oreal_decl,type,
tc_RealDef_Oreal: $i ).
thf(c_RealVector_Onorm__class_Onorm_decl,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(c_RealVector_Oof__real_decl,type,
c_RealVector_Oof__real: $i > $i > $i ).
thf(c_Groups_Oabs__class_Oabs_decl,type,
c_Groups_Oabs__class_Oabs: $i > $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(c_Groups_Oone__class_Oone_decl,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(class_Rings_Odivision__ring_decl,type,
class_Rings_Odivision__ring: $i > $o ).
thf(c_Rings_Oinverse__class_Odivide_decl,type,
c_Rings_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(class_RealVector_Oreal__normed__field_decl,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(c_Groups_Ozero__class_Ozero_decl,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(class_Rings_Olinordered__semiring__1__strict_decl,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(tc_Int_Oint_decl,type,
tc_Int_Oint: $i ).
thf(class_Fields_Ofield__inverse__zero_decl,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_Rings_Olinordered__semiring__1_decl,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_Groups_Oordered__ab__group__add__abs_decl,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
thf(class_Rings_Olinordered__ring_decl,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_Rings_Odivision__ring__inverse__zero_decl,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(class_Rings_Olinordered__ring__strict_decl,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Rings_Oordered__ring__abs_decl,type,
class_Rings_Oordered__ring__abs: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $i > $o ).
thf(v_b_decl,type,
v_b: $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_Rings_Oordered__ring_decl,type,
class_Rings_Oordered__ring: $i > $o ).
thf(class_Groups_Olinordered__ab__group__add_decl,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Fields_Olinordered__field_decl,type,
class_Fields_Olinordered__field: $i > $o ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Rings_Ocomm__semiring_decl,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(class_Rings_Oordered__semiring_decl,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(c_Int_OMin_decl,type,
c_Int_OMin: $i ).
thf(c_Parity_Oeven__odd__class_Oeven_decl,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(class_Rings_Oordered__cancel__semiring_decl,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(class_Rings_Olinordered__semidom_decl,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(class_Fields_Olinordered__field__inverse__zero_decl,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Rings_Ocomm__semiring__1_decl,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_decl,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Rings_Olinordered__idom_decl,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_NthRoot_Osqrt_decl,type,
c_NthRoot_Osqrt: $i > $i ).
thf(class_Groups_Oone_decl,type,
class_Groups_Oone: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_decl,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Fields_Ofield_decl,type,
class_Fields_Ofield: $i > $o ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(class_Rings_Omult__zero_decl,type,
class_Rings_Omult__zero: $i > $o ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_decl,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_decl,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_decl,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_decl,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_decl,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_decl,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Groups_Ozero_decl,type,
class_Groups_Ozero: $i > $o ).
thf(class_Rings_Oordered__comm__semiring_decl,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(class_Groups_Oab__semigroup__add_decl,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(class_Rings_Oring__1__no__zero__divisors_decl,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Groups_Ocomm__monoid__add_decl,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Int_Onumber_decl,type,
class_Int_Onumber: $i > $o ).
thf(class_Groups_Omonoid__mult_decl,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(c_Transcendental_Oarctan_decl,type,
c_Transcendental_Oarctan: $i > $i ).
thf(class_Int_Oring__char__0_decl,type,
class_Int_Oring__char__0: $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_decl,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(class_Rings_Ozero__neq__one_decl,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Rings_Olinordered__semiring_decl,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Rings_Olinordered__comm__semiring__strict_decl,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(class_Groups_Omonoid__add_decl,type,
class_Groups_Omonoid__add: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_decl,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_Complex_Oii_decl,type,
c_Complex_Oii: $i ).
thf(class_Groups_Oab__semigroup__mult_decl,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(class_Rings_Osemiring_decl,type,
class_Rings_Osemiring: $i > $o ).
thf(class_Rings_Osemiring__0_decl,type,
class_Rings_Osemiring__0: $i > $o ).
thf(class_Rings_Ono__zero__divisors_decl,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Rings_Osemiring__1_decl,type,
class_Rings_Osemiring__1: $i > $o ).
thf(c_Groups_Ominus__class_Ominus_decl,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(v_n_decl,type,
v_n: $i ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt_decl,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__zero__eq__number__of) ).
thf(2163,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
thf(1501,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(3944,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1091,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(5136,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(622,axiom,
c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).
thf(3399,plain,
c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(1140,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_csqrt) ).
thf(5320,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(776,axiom,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
thf(3927,plain,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(21,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
thf(1179,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__ge__zero) ).
thf(4166,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(75,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
thf(1322,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(168,axiom,
c_Int_OPls @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I6_J) ).
thf(1665,plain,
c_Int_OPls @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(918,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power3__eq__cube) ).
thf(4447,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ~ ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( B @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__odd__power) ).
thf(1879,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ~ ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(2889,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(29,axiom,
( ( v_b @ ( v_b @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Complex_Ocomplex @ c_RealVector_Oof__real ) @ ( tc_Complex_Ocomplex @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th0) ).
thf(1190,plain,
( ( v_b @ ( v_b @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Complex_Ocomplex @ c_RealVector_Oof__real ) @ ( tc_Complex_Ocomplex @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ c_NthRoot_Osqrt )
= ( A @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__power) ).
thf(2295,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ c_NthRoot_Osqrt )
= ( A @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(335,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
thf(2306,plain,
tc_Complex_Ocomplex @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(835,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__numeral__1) ).
thf(4101,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(919,axiom,
tc_Nat_Onat @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(4450,plain,
tc_Nat_Onat @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(2336,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(257,axiom,
tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
thf(2031,plain,
tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(1125,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(5260,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__idom )
=> ( ( C @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( D @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( D @ c_Groups_Oabs__class_Oabs ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( C @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono__even) ).
thf(3661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__idom )
=> ( ( C @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( D @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( D @ c_Groups_Oabs__class_Oabs ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( C @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zmod) ).
thf(1767,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i,E: $i] :
( ( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( E @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(735,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(3798,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(140,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1559,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(701,axiom,
! [A: $i] :
( ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__0__iff) ).
thf(3666,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(993,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).
thf(4729,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(621,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(3397,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(1899,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).
thf(3863,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(203,axiom,
tc_RealDef_Oreal @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
thf(1850,plain,
tc_RealDef_Oreal @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(366,axiom,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
thf(2427,plain,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(239,axiom,
~ ( c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I7_J) ).
thf(1982,plain,
~ ( c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).
thf(2280,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(1554,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Osemiring )
& ( D @ class_Int_Onumber ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).
thf(4339,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Osemiring )
& ( D @ class_Int_Onumber ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(755,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(3858,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(724,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
thf(3762,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(2062,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(464,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left__number__of) ).
thf(2776,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(416,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).
thf(2590,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(1043,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(4960,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
thf(3012,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
thf(2099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(886,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(4326,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(955,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
<=> ( ( ( A
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) )
& ( B
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ) )
| ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__eq__1__iff) ).
thf(4592,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) )
& ( B
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ) )
| ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( ( A
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) )
& ( B
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ) )
| ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(924,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(4479,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(1855,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(33,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
thf(1200,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(821,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber )
& ( B @ class_Groups_Omonoid__mult ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).
thf(4043,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber )
& ( B @ class_Groups_Omonoid__mult ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
thf(3534,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(987,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(4714,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
thf(2976,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(538,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I30_J) ).
thf(3072,plain,
! [A: $i] :
( ( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(1924,plain,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(309,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__zero) ).
thf(2210,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__power__le__0__imp__0) ).
thf(5168,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(4500,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(829,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
thf(4075,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield__inverse__zero ) )
=> ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral0) ).
thf(1290,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield__inverse__zero ) )
=> ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1132,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(5292,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(741,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(3813,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(391,axiom,
tc_Int_Oint @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(2495,plain,
tc_Int_Oint @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(615,axiom,
! [A: $i] :
( ( ( A @ class_Rings_Olinordered__idom )
& ( A @ class_Int_Onumber__ring ) )
=> ( ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Groups_Oabs__class_Oabs ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__one) ).
thf(3377,plain,
! [A: $i] :
( ( ( A @ class_Rings_Olinordered__idom )
& ( A @ class_Int_Onumber__ring ) )
=> ( ( c_Int_OMin @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Groups_Oabs__class_Oabs ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(3040,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(3153,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(3460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(504,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
thf(2947,plain,
! [A: $i] :
( ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).
thf(1569,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Olinordered__field )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less) ).
thf(1544,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Olinordered__field )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(250,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__one) ).
thf(2014,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1104,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
<=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(5173,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
thf(1971,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(624,axiom,
! [A: $i,B: $i] :
( ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__less__iff) ).
thf(3402,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1120,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(5237,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(179,axiom,
tc_RealDef_Oreal @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1692,plain,
tc_RealDef_Oreal @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1048,axiom,
tc_Nat_Onat @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(4973,plain,
tc_Nat_Onat @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(17,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
thf(1173,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
thf(1486,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( B @ class_Power_Opower )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
thf(1426,plain,
! [A: $i,B: $i] :
( ( B @ class_Power_Opower )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(530,axiom,
tc_Int_Oint @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(3049,plain,
tc_Int_Oint @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Ofield__inverse__zero ) )
=> ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A )
<=> ( ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).
thf(2686,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Ofield__inverse__zero ) )
=> ( ( ( ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) )
=> ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) )
& ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A )
=> ( ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(1164,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1139,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(5316,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(2434,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).
thf(1919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__eq) ).
thf(1342,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1000,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
thf(4762,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(412,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).
thf(2575,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1019,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(4839,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(967,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__zmod__mult__2) ).
thf(4647,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(3942,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(809,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(4011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1029,axiom,
! [A: $i,B: $i] :
( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt )
= A )
=> ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel2) ).
thf(4884,plain,
! [A: $i,B: $i] :
( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt )
= A )
=> ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(612,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(3365,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(815,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit1) ).
thf(4026,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(528,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(3044,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(4110,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(563,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(3175,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(968,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(4650,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Divides_Osemiring__div )
=> ( ( ( D @ ( E @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( ( D @ ( B @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__cong) ).
thf(2168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Divides_Osemiring__div )
=> ( ( ( D @ ( E @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( ( D @ ( B @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(825,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(4058,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(867,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(4247,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).
thf(1640,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Ofield__inverse__zero ) )
=> ( ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
<=> ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).
thf(2901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Ofield__inverse__zero ) )
=> ( ( ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= B ) ) )
=> ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
& ( ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
=> ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).
thf(3313,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(915,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).
thf(4435,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(676,axiom,
tc_Complex_Ocomplex @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
thf(3577,plain,
tc_Complex_Ocomplex @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(290,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__0__iff) ).
thf(2146,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1050,axiom,
tc_Nat_Onat @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(4980,plain,
tc_Nat_Onat @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(45,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
thf(1222,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(764,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(3895,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(545,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).
thf(3103,plain,
! [A: $i,B: $i] :
( ( ( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__idom )
=> ( ~ ( C @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( C @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono__odd) ).
thf(3629,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__idom )
=> ( ~ ( C @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( C @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(1124,axiom,
! [A: $i] :
( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq__one__mod__two) ).
thf(5252,plain,
! [A: $i] :
( ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__sum__zero__iff) ).
thf(4618,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A )
<=> ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
thf(1613,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) )
& ( ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A )
=> ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(975,axiom,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
!= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).
thf(4665,plain,
( ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
!= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
thf(4610,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(2531,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(1062,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OMin @ ( tc_Complex_Ocomplex @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__i) ).
thf(5024,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OMin @ ( tc_Complex_Ocomplex @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Ofield__inverse__zero ) )
=> ( ( C
= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
<=> ( ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).
thf(2348,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Ofield__inverse__zero ) )
=> ( ( ( ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= B ) ) )
=> ( C
= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
& ( ( C
= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
=> ( ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).
thf(3350,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(802,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__mult__squared__eq) ).
thf(3994,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(1914,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(458,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2763,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2491,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
thf(1243,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).
thf(2227,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(146,axiom,
tc_Complex_Ocomplex @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
thf(1576,plain,
tc_Complex_Ocomplex @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
thf(3249,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(4371,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1008,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).
thf(4803,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(840,axiom,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__gt__one) ).
thf(4124,plain,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(716,axiom,
tc_Int_Oint @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(3730,plain,
tc_Int_Oint @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1073,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(5056,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(92,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
thf(1386,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1134,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(5301,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(552,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(3140,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(1475,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).
thf(2400,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(999,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__half__sum) ).
thf(4760,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(2067,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(129,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
thf(1529,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(680,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(3597,plain,
! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).
thf(1254,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__sum) ).
thf(4238,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(3263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(418,axiom,
tc_RealDef_Oreal @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
thf(2603,plain,
tc_RealDef_Oreal @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
thf(3644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(3116,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(529,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__minus1__right) ).
thf(3046,plain,
! [A: $i] :
( ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(910,axiom,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__gt__zero) ).
thf(4415,plain,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I2_J) ).
thf(3495,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(1107,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).
thf(5188,plain,
c_Int_OPls != c_Int_OMin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__comm__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(2501,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__comm__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1323,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(549,axiom,
tc_Complex_Ocomplex @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
thf(3125,plain,
tc_Complex_Ocomplex @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(5289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).
thf(2466,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(431,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(2654,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__divide) ).
thf(1628,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(447,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
thf(2735,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(475,axiom,
tc_Int_Oint @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
thf(2814,plain,
tc_Int_Oint @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
thf(4563,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(912,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(4422,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ( ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__add) ).
thf(1264,plain,
! [A: $i,B: $i] :
( ( ( ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(312,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__less__mono) ).
thf(2217,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
thf(1577,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(1455,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( C = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(3749,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(813,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).
thf(4023,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(110,axiom,
tc_Int_Oint @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
thf(1462,plain,
tc_Int_Oint @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(527,axiom,
tc_RealDef_Oreal @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
thf(3043,plain,
tc_RealDef_Oreal @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(452,axiom,
tc_Int_Oint @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
thf(2745,plain,
tc_Int_Oint @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(2571,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(1118,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
thf(5231,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(1922,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(618,axiom,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(3385,plain,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(1247,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(851,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(4179,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(1609,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(772,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Transcendental_Oarctan )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__zero__zero) ).
thf(3919,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Transcendental_Oarctan )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(542,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).
thf(3084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(644,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(3470,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(3951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
thf(1963,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(905,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).
thf(4390,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).
thf(1232,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
thf(1847,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I1_J) ).
thf(2857,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(894,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ? [B: $i] :
( A
= ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__nat__equiv__def2) ).
thf(4353,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ? [B: $i] :
( A
= ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Osemiring )
& ( D @ class_Int_Onumber ) )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).
thf(4862,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Osemiring )
& ( D @ class_Int_Onumber ) )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(73,axiom,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
thf(1319,plain,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(185,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__zero__cancel) ).
thf(1704,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(3734,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(517,axiom,
tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(3014,plain,
tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).
thf(3602,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(669,axiom,
tc_Complex_Ocomplex @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__1) ).
thf(3557,plain,
tc_Complex_Ocomplex @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(211,axiom,
tc_RealDef_Oreal @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
thf(1875,plain,
tc_RealDef_Oreal @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(879,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square) ).
thf(4302,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(933,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power2) ).
thf(4514,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(480,axiom,
tc_RealDef_Oreal @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
thf(2829,plain,
tc_RealDef_Oreal @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(731,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(3788,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(914,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).
thf(4432,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_NthRoot_Osqrt )
= ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__divide) ).
thf(2222,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_NthRoot_Osqrt )
= ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(1126,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__number__of__Bit1) ).
thf(5264,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Ozero__neq__one )
& ( C @ class_Rings_Ono__zero__divisors )
& ( C @ class_Rings_Omult__zero )
& ( C @ class_Power_Opower ) )
=> ( ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
thf(3431,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Ozero__neq__one )
& ( C @ class_Rings_Ono__zero__divisors )
& ( C @ class_Rings_Omult__zero )
& ( C @ class_Power_Opower ) )
=> ( ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(5013,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(465,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(2782,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__mult) ).
thf(4820,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1682,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(654,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(3525,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(794,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__0) ).
thf(3973,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(329,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(2291,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(3569,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(421,axiom,
tc_RealDef_Oreal @ class_Fields_Ofield,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
thf(2616,plain,
tc_RealDef_Oreal @ class_Fields_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(906,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).
thf(4396,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).
thf(1465,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
thf(3966,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(951,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).
thf(4583,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(1034,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(4903,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(949,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(4578,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(869,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).
thf(4258,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(88,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(1373,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(495,axiom,
tc_Int_Oint @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
thf(2893,plain,
tc_Int_Oint @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(162,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I9_J) ).
thf(1632,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(877,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(4297,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I4_J) ).
thf(3453,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( B != A )
& ( D != C ) )
<=> ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(2236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B != A )
& ( D != C ) ) )
& ( ( ( B != A )
& ( D != C ) )
=> ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(1334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).
thf(3527,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(799,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(3983,plain,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).
thf(2555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(774,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
thf(3923,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Divides_Osemiring__div )
=> ( ( ( D @ ( E @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( ( D @ ( B @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__cong) ).
thf(1960,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Divides_Osemiring__div )
=> ( ( ( D @ ( E @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( ( D @ ( B @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) )
= ( D @ ( A @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Divides_Odiv__class_Omod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(25,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
thf(1183,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(63,axiom,
tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
thf(1283,plain,
tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Olinordered__field )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__le) ).
thf(2073,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Olinordered__field )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(3068,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(720,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
thf(3739,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( ( ~ ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
thf(3712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( ( ~ ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).
thf(2371,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(285,axiom,
tc_Complex_Ocomplex @ class_Fields_Ofield,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
thf(2137,plain,
tc_Complex_Ocomplex @ class_Fields_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(610,axiom,
~ ( c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).
thf(3361,plain,
~ ( c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(34,axiom,
tc_Complex_Ocomplex @ class_Rings_Odivision__ring__inverse__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
thf(1201,plain,
tc_Complex_Ocomplex @ class_Rings_Odivision__ring__inverse__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1600,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(2586,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(826,axiom,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(4065,plain,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(1070,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).
thf(5045,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(3389,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(1074,axiom,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(5059,plain,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(199,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1843,plain,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I2_J) ).
thf(2058,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(997,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).
thf(4751,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(15,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(1169,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
thf(2367,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B
= ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(660,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__mono) ).
thf(3537,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1020,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(4842,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(2861,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(1116,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Int_OBit0 )
= ( A @ c_Int_OBit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).
thf(5220,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Int_OBit0 )
= ( A @ c_Int_OBit0 ) ) )
& ( ( ( B @ c_Int_OBit0 )
= ( A @ c_Int_OBit0 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(40,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
thf(1215,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).
thf(2190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(630,axiom,
tc_Complex_Ocomplex @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
thf(3421,plain,
tc_Complex_Ocomplex @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(2483,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(1082,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).
thf(5101,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(739,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(3808,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(3036,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(2799,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(2103,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(455,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I25_J) ).
thf(2750,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
thf(1405,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(3588,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1697,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(52,axiom,
tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(1242,plain,
tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(570,axiom,
tc_RealDef_Oreal @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
thf(3211,plain,
tc_RealDef_Oreal @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(2392,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(768,axiom,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
thf(3906,plain,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(1521,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(961,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).
thf(4628,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(859,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(4211,plain,
! [A: $i,B: $i] :
( ( B
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).
thf(1863,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) )
<=> ( ( C @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__2__times__iff) ).
thf(4700,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) )
=> ( C
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
& ( ( C
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) )
=> ( ( C @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(2011,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).
thf(1206,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1100,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(5157,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(856,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__odd__eq) ).
thf(4199,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(1044,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(4962,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(953,axiom,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__ge__zero) ).
thf(4589,plain,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(674,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
thf(3567,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
thf(1438,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring )
=> ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(4531,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring )
=> ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(7,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(1153,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(1470,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(427,axiom,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(2641,plain,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
thf(2660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(3984,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(429,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__lt__1__iff) ).
thf(2646,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I3_J) ).
thf(1338,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1094,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(5142,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).
thf(1311,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(3767,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
thf(2307,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(191,axiom,
tc_RealDef_Oreal @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
thf(1736,plain,
tc_RealDef_Oreal @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(392,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(2496,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).
thf(4312,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
thf(2790,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(3550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(463,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(2773,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1087,axiom,
! [A: $i,B: $i] :
( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= A )
=> ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ c_NthRoot_Osqrt )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__unique) ).
thf(5122,plain,
! [A: $i,B: $i] :
( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= A )
=> ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ c_NthRoot_Osqrt )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).
thf(3418,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(734,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus__one) ).
thf(3795,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(1112,axiom,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(5206,plain,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__eq) ).
thf(1387,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(2428,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
thf(2249,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(2541,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(2596,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(1037,axiom,
~ ( v_na____ @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o) ).
thf(4920,plain,
~ ( v_na____ @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1027,axiom,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__num__one) ).
thf(4878,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(42,axiom,
tc_RealDef_Oreal @ class_Groups_Olinordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
thf(1217,plain,
tc_RealDef_Oreal @ class_Groups_Olinordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
thf(3022,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(1666,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(833,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(4091,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Ozero__neq__one )
& ( C @ class_Rings_Ono__zero__divisors )
& ( C @ class_Rings_Omult__zero )
& ( C @ class_Power_Opower ) )
=> ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff__number__of) ).
thf(3884,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Ozero__neq__one )
& ( C @ class_Rings_Ono__zero__divisors )
& ( C @ class_Rings_Omult__zero )
& ( C @ class_Power_Opower ) )
=> ( ( ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1006,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__no__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(4785,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__no__zero__divisors )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(551,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).
thf(3134,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(2032,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1018,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(4836,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(3664,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(3207,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(2705,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(2409,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).
thf(1223,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(986,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
thf(4712,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(713,axiom,
tc_Complex_Ocomplex @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
thf(3711,plain,
tc_Complex_Ocomplex @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__number__of__Bit0) ).
thf(4016,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(793,axiom,
tc_Complex_Ocomplex @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
thf(3972,plain,
tc_Complex_Ocomplex @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(956,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(4609,plain,
tc_Nat_Onat @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).
thf(1174,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(173,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 )
= ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
thf(1676,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 )
= ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(935,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(4521,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(842,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(4128,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(580,axiom,
tc_RealDef_Oreal @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
thf(3239,plain,
tc_RealDef_Oreal @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(874,axiom,
! [A: $i] :
( ( c_Int_OPls
= ( A @ c_Int_OBit0 ) )
<=> ( c_Int_OPls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).
thf(4284,plain,
! [A: $i] :
( ( ( c_Int_OPls = A )
=> ( c_Int_OPls
= ( A @ c_Int_OBit0 ) ) )
& ( ( c_Int_OPls
= ( A @ c_Int_OBit0 ) )
=> ( c_Int_OPls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(743,axiom,
! [A: $i] :
( ( v_na____ @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ? [B: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ) @ ( v_b @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IH) ).
thf(3816,plain,
! [A: $i] :
( ( v_na____ @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ? [B: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ) @ ( v_b @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B
= ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
<=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
thf(1883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= A )
=> ( B
= ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
& ( ( B
= ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(1560,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).
thf(3307,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_NthRoot_Osqrt )
= ( A @ c_NthRoot_Osqrt ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__iff) ).
thf(3191,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_NthRoot_Osqrt )
= ( A @ c_NthRoot_Osqrt ) ) )
& ( ( ( B @ c_NthRoot_Osqrt )
= ( A @ c_NthRoot_Osqrt ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(2332,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(943,axiom,
! [A: $i] :
( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= A )
<=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2__iff) ).
thf(4553,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= A ) )
& ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= A )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(1687,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) )
= ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) )
<=> ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
thf(2200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) )
= ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
& ( ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) )
= ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) )
=> ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(908,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(4402,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1110,axiom,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__power2) ).
thf(5201,plain,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oabs__class_Oabs ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).
thf(1195,plain,
! [A: $i] :
( ( A @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oabs__class_Oabs ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(694,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
thf(3647,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(1130,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(5285,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).
thf(3166,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A )
<=> ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
thf(2445,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) )
& ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= A )
=> ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(876,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__gt__half__sum) ).
thf(4295,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Ofield__inverse__zero ) )
=> ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
<=> ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).
thf(3269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Ofield__inverse__zero ) )
=> ( ( ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
=> ( ( ( B
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
thf(3618,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(370,axiom,
tc_Int_Oint @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(2433,plain,
tc_Int_Oint @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(384,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I26_J) ).
thf(2477,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(991,axiom,
! [A: $i,B: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge__zero) ).
thf(4725,plain,
! [A: $i,B: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(1968,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(4757,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(649,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(3499,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).
thf(3065,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(677,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).
thf(3578,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(20,axiom,
tc_RealDef_Oreal @ class_Rings_Odivision__ring__inverse__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
thf(1178,plain,
tc_RealDef_Oreal @ class_Rings_Odivision__ring__inverse__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(664,axiom,
c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of2) ).
thf(3546,plain,
c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1067,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(5038,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(995,axiom,
( ( c_Complex_Oii @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes ) ) )
= ( c_Int_OMin @ ( tc_Complex_Ocomplex @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_i__squared) ).
thf(4746,plain,
( ( c_Complex_Oii @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes ) ) )
= ( c_Int_OMin @ ( tc_Complex_Ocomplex @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(3050,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(775,axiom,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3926,plain,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(348,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).
thf(2344,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(836,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(4104,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(779,axiom,
tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
thf(3931,plain,
tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(625,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(3408,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).
thf(3731,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(791,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(3968,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(976,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I3_J) ).
thf(4668,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(932,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).
thf(4512,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(2895,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(1328,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(823,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(4048,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(710,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
thf(3704,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(789,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
thf(3963,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(2537,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).
thf(3632,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(539,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
thf(3078,plain,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(579,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(3237,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(426,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).
thf(2638,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(514,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
<=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(3001,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( A
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ c_Groups_Oone__class_Oone )
= A ) )
& ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(1012,axiom,
! [A: $i] :
( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2) ).
thf(4817,plain,
! [A: $i] :
( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(708,axiom,
! [A: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
thf(3699,plain,
! [A: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(1592,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(2300,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(2498,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(770,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
thf(3909,plain,
! [A: $i] :
( ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(685,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).
thf(3615,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(1234,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__even__abs__number__of) ).
thf(1541,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(2157,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit0) ).
thf(2840,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(2115,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1072,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__abs) ).
thf(5053,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(1095,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).
thf(5145,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(196,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1762,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(585,axiom,
tc_Complex_Ocomplex @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
thf(3254,plain,
tc_Complex_Ocomplex @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(3413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(204,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
thf(1851,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(1259,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(548,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(3122,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(1049,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__Suc) ).
thf(4974,plain,
! [A: $i] :
( ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(757,axiom,
tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
thf(3862,plain,
tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(963,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).
thf(4636,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(1587,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(619,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1) ).
thf(3386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(2631,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(1567,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(10,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
thf(1160,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(227,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).
thf(1942,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
thf(2323,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1052,axiom,
! [A: $i] :
( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).
thf(4983,plain,
! [A: $i] :
( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
= ( C @ c_Groups_Oone__class_Oone ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
thf(3441,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Odivision__ring )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
= ( C @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
= ( C @ c_Groups_Oone__class_Oone ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(942,axiom,
! [A: $i] :
( ( ( A @ c_Int_OBit0 )
= c_Int_OPls )
<=> ( A = c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
thf(4545,plain,
! [A: $i] :
( ( ( A = c_Int_OPls )
=> ( ( A @ c_Int_OBit0 )
= c_Int_OPls ) )
& ( ( ( A @ c_Int_OBit0 )
= c_Int_OPls )
=> ( A = c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
thf(2666,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(3935,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).
thf(2023,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(3326,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__mult__ge__zero) ).
thf(5031,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(553,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(3143,plain,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(1083,axiom,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
thf(5107,plain,
! [A: $i] :
( c_Int_OPls
!= ( A @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(2830,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(24,axiom,
tc_Complex_Ocomplex @ class_Fields_Ofield__inverse__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
thf(1182,plain,
tc_Complex_Ocomplex @ class_Fields_Ofield__inverse__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__1__iff) ).
thf(1414,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
thf(2053,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(304,axiom,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
thf(2196,plain,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(2038,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( ( C = A )
| ( D = B ) )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(1446,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(405,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(2551,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__one__even__power) ).
thf(2085,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(509,axiom,
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
thf(2978,plain,
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(381,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(2472,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(2317,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(594,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq__number__of) ).
thf(3294,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(507,axiom,
! [A: $i] :
( ( ( A @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
<=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__1__iff) ).
thf(2968,plain,
! [A: $i] :
( ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
=> ( ( A @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Olinordered__ring )
& ( C @ class_Groups_Omonoid__mult ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( B @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__even__power) ).
thf(3656,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Olinordered__ring )
& ( C @ class_Groups_Omonoid__mult ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( B @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(283,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(2125,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__algebra__1 )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).
thf(1150,plain,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__algebra__1 )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
thf(2487,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(1047,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmod__mult__2) ).
thf(4970,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
thf(1984,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1852,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
thf(3333,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(911,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(4416,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
thf(1297,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(3126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(438,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(2681,plain,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).
thf(3541,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).
thf(1451,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1097,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).
thf(5149,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).
thf(3354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(499,axiom,
tc_RealDef_Oreal @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
thf(2900,plain,
tc_RealDef_Oreal @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(48,axiom,
tc_Int_Oint @ class_Rings_Oordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(1231,plain,
tc_Int_Oint @ class_Rings_Oordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1119,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2) ).
thf(5234,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(3770,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(1552,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).
thf(2851,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
thf(1192,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).
thf(1932,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(866,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
thf(4244,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(2581,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(377,axiom,
tc_Int_Oint @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
thf(2465,plain,
tc_Int_Oint @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ( ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__add) ).
thf(2505,plain,
! [A: $i,B: $i] :
( ( ( ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(744,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(3819,plain,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).
thf(3222,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(246,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__one) ).
thf(2006,plain,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__zero__eq) ).
thf(3937,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(988,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2__right) ).
thf(4717,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(1429,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(3247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(2766,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(1033,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(4902,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(54,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
thf(1246,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1 )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(1979,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1 )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1063,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(5026,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(287,axiom,
( c_Int_OPls
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
thf(2140,plain,
( c_Int_OPls
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(456,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
thf(2756,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(558,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(3162,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(568,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I8_J) ).
thf(3201,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).
thf(1759,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(3215,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(895,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(4361,plain,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(555,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt )
= ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__mult) ).
thf(3147,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ c_NthRoot_Osqrt )
= ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(51,axiom,
tc_RealDef_Oreal @ class_Fields_Olinordered__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
thf(1241,plain,
tc_RealDef_Oreal @ class_Fields_Olinordered__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
thf(3624,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(566,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(3183,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(923,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(4476,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__field )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
= ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__norm__divide) ).
thf(1170,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__field )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
= ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_RealVector_Oreal__normed__algebra__1 )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__number__of) ).
thf(1187,plain,
! [A: $i,B: $i] :
( ( ( B @ class_RealVector_Oreal__normed__algebra__1 )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(4036,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(2529,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(746,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(3824,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(2634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__conj) ).
thf(1434,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
thf(1857,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(853,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(4184,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(736,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).
thf(3802,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(1099,axiom,
! [A: $i,B: $i] :
( ( B @ c_Int_OBit0 )
!= ( A @ c_Int_OBit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).
thf(5153,plain,
! [A: $i,B: $i] :
( ( B @ c_Int_OBit0 )
!= ( A @ c_Int_OBit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(35,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
thf(1202,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(893,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(4352,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(966,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(4644,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
thf(3225,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(1005,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(4782,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(831,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero) ).
thf(4081,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(181,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(1695,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1001,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(4765,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(3999,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(1286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(1114,axiom,
! [A: $i,B: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge2) ).
thf(5209,plain,
! [A: $i,B: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
thf(1663,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(3508,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).
thf(1167,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(301,axiom,
tc_RealDef_Oreal @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
thf(2189,plain,
tc_RealDef_Oreal @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(3422,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(513,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__lt__0__iff) ).
thf(2995,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(751,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 )
= ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
thf(3841,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
= ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(2617,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1088,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__2__cases) ).
thf(5126,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(2662,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Transcendental_Oarctan @ ( B @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__monotone) ).
thf(1732,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Transcendental_Oarctan @ ( B @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(4572,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(2144,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(711,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).
thf(3707,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring__inverse__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(2413,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(436,axiom,
tc_RealDef_Oreal @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
thf(2677,plain,
tc_RealDef_Oreal @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(526,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(3042,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1117,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(5230,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(3375,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(5016,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(496,axiom,
tc_RealDef_Oreal @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
thf(2894,plain,
tc_RealDef_Oreal @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(3343,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(922,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(4470,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(904,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(4380,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(609,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(3358,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).
thf(2275,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(1092,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(5138,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(958,axiom,
! [A: $i,B: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__squared__expand) ).
thf(4613,plain,
! [A: $i,B: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__idom )
=> ( ( C @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).
thf(2253,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__idom )
=> ( ( C @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(3257,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Oabs__class_Oabs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).
thf(1219,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Oabs__class_Oabs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I1_J) ).
thf(3491,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(117,axiom,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
thf(1483,plain,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(540,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(3079,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(4438,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(161,axiom,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
thf(1631,plain,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(1069,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(5043,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(820,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(4041,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(665,axiom,
tc_RealDef_Oreal @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
thf(3547,plain,
tc_RealDef_Oreal @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(537,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
thf(3070,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(4309,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring__abs )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
thf(1652,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring__abs )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(3900,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(887,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(4328,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(231,axiom,
tc_RealDef_Oreal @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
thf(1965,plain,
tc_RealDef_Oreal @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(954,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power2) ).
thf(4590,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(1061,axiom,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(5022,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(659,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3536,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).
thf(1154,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Odivision__ring )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
thf(3234,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__sqrt__hcomplex__capprox) ).
thf(2048,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(315,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(2225,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).
thf(3504,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(926,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
thf(4494,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(586,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(3255,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(740,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
thf(3811,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(581,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(3240,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
thf(5065,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Transcendental_Oarctan @ ( B @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__monotone_H) ).
thf(2849,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Transcendental_Oarctan @ ( B @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1086,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(5121,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(645,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(3472,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(3266,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).
thf(2674,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(2016,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(817,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).
thf(4032,plain,
! [A: $i] :
( ( A @ c_Int_OBit0 )
!= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(984,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(4709,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(474,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(2806,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(512,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(2991,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(1081,axiom,
! [A: $i,B: $i] :
( ( B @ c_Int_OBit1 )
!= ( A @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).
thf(5097,plain,
! [A: $i,B: $i] :
( ( B @ c_Int_OBit1 )
!= ( A @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
thf(3458,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(2827,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(681,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(3599,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(2161,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).
thf(3773,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1079,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(5086,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(1096,axiom,
tc_Nat_Onat @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(5148,plain,
tc_Nat_Onat @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(3832,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(1023,axiom,
! [A: $i] :
( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ? [B: $i] :
( A
= ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nat__equiv__def2) ).
thf(4854,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc ) )
=> ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ? [B: $i] :
( A
= ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(628,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(3416,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(57,axiom,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
thf(1258,plain,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(595,axiom,
tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
thf(3304,plain,
tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(382,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
thf(2474,plain,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
thf(3532,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(937,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1) ).
thf(4526,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(4537,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(303,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oabs__class_Oabs ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).
thf(2193,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oabs__class_Oabs ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(1068,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(5039,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(170,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
thf(1669,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
thf(3118,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(1066,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(5033,plain,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(1707,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(2293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(1371,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1057,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(5011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__conj) ).
thf(3726,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(602,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).
thf(3330,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(449,axiom,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I2_J) ).
thf(2738,plain,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1129,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).
thf(5282,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(699,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
thf(3663,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(374,axiom,
tc_Int_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(2442,plain,
tc_Int_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1113,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(5207,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(5314,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
thf(2055,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(1638,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1030,axiom,
( v_na____
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n) ).
thf(4887,plain,
( v_na____
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).
thf(2573,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(83,axiom,
tc_Complex_Ocomplex @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
thf(1356,plain,
tc_Complex_Ocomplex @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(2311,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(1035,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(4914,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
thf(1589,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(642,axiom,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(3468,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(4586,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(472,axiom,
tc_Int_Oint @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(2802,plain,
tc_Int_Oint @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1002,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of1) ).
thf(4773,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
thf(1209,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(282,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__1__iff) ).
thf(2119,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).
thf(3352,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(862,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(4228,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A = B )
=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(691,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
thf(3631,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I4_J) ).
thf(1408,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(3251,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(899,axiom,
! [A: $i,B: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge1) ).
thf(4369,plain,
! [A: $i,B: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= A )
=> ( B
= ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
thf(2642,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odivision__ring )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= A )
=> ( B
= ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(742,axiom,
tc_Int_Oint @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
thf(3815,plain,
tc_Int_Oint @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(272,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
thf(2084,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2214,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(353,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I13_J) ).
thf(2383,plain,
! [A: $i] :
( ( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( c_Int_OMin @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).
thf(3764,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).
thf(2415,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(524,axiom,
( ( c_Complex_Oii @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes ) ) )
= ( c_Int_OMin @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Complex_Ocomplex @ c_RealVector_Oof__real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_i__mult__eq) ).
thf(3038,plain,
( ( c_Complex_Oii @ ( c_Complex_Oii @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes ) ) )
= ( c_Int_OMin @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Complex_Ocomplex @ c_RealVector_Oof__real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(880,axiom,
tc_Nat_Onat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(4305,plain,
tc_Nat_Onat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(705,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
thf(3683,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(1017,axiom,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__0) ).
thf(4828,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(1603,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(505,axiom,
tc_Int_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(2955,plain,
tc_Int_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).
thf(2246,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
thf(1722,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(3,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
thf(1144,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(712,axiom,
tc_Complex_Ocomplex @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
thf(3710,plain,
tc_Complex_Ocomplex @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(1042,axiom,
( ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).
thf(4958,plain,
( ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__triangle__ineq) ).
thf(4616,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(828,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).
thf(4073,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(1080,axiom,
! [A: $i,B: $i] :
( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt )
= B )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel) ).
thf(5093,plain,
! [A: $i,B: $i] :
( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt )
= B )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(845,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ c_Nat_OSuc )
!= A )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(4154,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ c_Nat_OSuc )
!= A )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
thf(4374,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(565,axiom,
tc_Int_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(3182,plain,
tc_Int_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(2871,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(1376,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(930,axiom,
tc_Nat_Onat @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(4509,plain,
tc_Nat_Onat @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(305,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
thf(2197,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(837,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).
thf(4107,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(2182,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(451,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(2742,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).
thf(2314,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(947,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(4569,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I3_J) ).
thf(2111,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Olinordered__idom )
& ( B @ class_Int_Onumber__ring ) )
=> ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(243,axiom,
tc_RealDef_Oreal @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
thf(1993,plain,
tc_RealDef_Oreal @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__even__eq) ).
thf(4264,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(780,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(3932,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(457,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).
thf(2757,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(796,axiom,
tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(3977,plain,
tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(792,axiom,
tc_RealDef_Oreal @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
thf(3971,plain,
tc_RealDef_Oreal @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(138,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
thf(1556,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(556,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(3150,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).
thf(3893,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(574,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(3219,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).
thf(2824,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(4694,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(533,axiom,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__mult__self__sum__ge__zero) ).
thf(3055,plain,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(1557,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(559,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(3165,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(4208,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(852,axiom,
! [A: $i] :
( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls) ).
thf(4181,plain,
! [A: $i] :
( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(467,axiom,
tc_Int_Oint @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(2785,plain,
tc_Int_Oint @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(3451,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral1) ).
thf(4652,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Ofield ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__zero__eq__number__of) ).
thf(2874,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
thf(1293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).
thf(2278,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(406,axiom,
! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
thf(2553,plain,
! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1055,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(5007,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(502,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(2928,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(19,axiom,
tc_RealDef_Oreal @ class_Fields_Ofield__inverse__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
thf(1177,plain,
tc_RealDef_Oreal @ class_Fields_Ofield__inverse__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(1381,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(183,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(1699,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(460,axiom,
tc_Int_Oint @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
thf(2765,plain,
tc_Int_Oint @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(104,axiom,
tc_Complex_Ocomplex @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1445,plain,
tc_Complex_Ocomplex @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(771,axiom,
! [A: $i] :
( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__pos) ).
thf(3917,plain,
! [A: $i] :
( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(600,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
thf(3325,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(2535,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(1364,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(4965,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono) ).
thf(3539,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(462,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).
thf(2770,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(270,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).
thf(2075,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(1198,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(989,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).
thf(4720,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
thf(2212,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(2171,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3759,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(750,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(3838,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq) ).
thf(3687,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).
thf(5248,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
thf(3806,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
thf(2064,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(896,axiom,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(4362,plain,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(3674,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1016,axiom,
tc_Nat_Onat @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(4827,plain,
tc_Nat_Onat @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
thf(2288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(788,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(3953,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(2797,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(611,axiom,
! [A: $i,B: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cos__x__y__le__one) ).
thf(3363,plain,
! [A: $i,B: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(3310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__div__pos) ).
thf(1496,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(1133,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
thf(5299,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).
thf(2303,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield )
=> ( ( D
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C
!= ( E @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(927,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
thf(4497,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
= ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(873,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
thf(4282,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1093,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
thf(5139,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(4890,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).
thf(1973,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(925,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ c_Nat_OSuc ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(4481,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ c_Nat_OSuc ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ c_Nat_OSuc ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(2867,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__eq) ).
thf(3380,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self1) ).
thf(1562,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(761,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_NthRoot_Osqrt )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__not__eq__zero) ).
thf(3881,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_NthRoot_Osqrt )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).
thf(3009,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq) ).
thf(1948,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
& ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(909,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(4405,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) ) )
& ( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
thf(1203,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Ofield__inverse__zero )
=> ( ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1026,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(4868,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(1011,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(4813,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(2652,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(938,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).
thf(4529,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(1277,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(554,axiom,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
thf(3146,plain,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).
thf(3975,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
thf(3921,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( B @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__even__abs) ).
thf(1472,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( B @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(950,axiom,
! [A: $i] : ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_two__realpow__ge__one) ).
thf(4581,plain,
! [A: $i] : ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(23,axiom,
tc_RealDef_Oreal @ class_Rings_Odivision__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
thf(1181,plain,
tc_RealDef_Oreal @ class_Rings_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(166,axiom,
tc_Int_Oint @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1662,plain,
tc_Int_Oint @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(917,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).
thf(4441,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(420,axiom,
! [A: $i,B: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
thf(2614,plain,
! [A: $i,B: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(2096,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1032,axiom,
tc_Nat_Onat @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
thf(4901,plain,
tc_Nat_Onat @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(13,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(1166,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(2107,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(702,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
thf(3672,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__eq__number__of) ).
thf(1420,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(798,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__real__divide__sqrt__less) ).
thf(3981,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
thf(2503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(875,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
thf(4292,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(1509,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(242,axiom,
( v_b
!= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_b) ).
thf(1990,plain,
( v_b
!= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(946,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
thf(4566,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(2684,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(981,axiom,
! [A: $i] :
( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).
thf(4688,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra__1 )
=> ( ( A @ ( B @ c_RealVector_Oof__real ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__of__real) ).
thf(1145,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra__1 )
=> ( ( A @ ( B @ c_RealVector_Oof__real ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(484,axiom,
! [A: $i] :
( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
thf(2846,plain,
! [A: $i] :
( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(1010,axiom,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(4812,plain,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(135,axiom,
tc_RealDef_Oreal @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
thf(1551,plain,
tc_RealDef_Oreal @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1053,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
thf(4986,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
<=> ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(4168,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(2298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(719,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(3737,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(2397,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1123,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
thf(5250,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(541,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(3082,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(572,axiom,
tc_RealDef_Oreal @ class_Fields_Olinordered__field__inverse__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
thf(3214,plain,
tc_RealDef_Oreal @ class_Fields_Olinordered__field__inverse__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(3904,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(1038,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(4922,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(786,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
thf(3949,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(477,axiom,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).
thf(2821,plain,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).
thf(3786,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(1531,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
thf(2567,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(868,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(4255,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
thf(1547,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(1748,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).
thf(2863,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(1598,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
thf(1611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1084,axiom,
! [A: $i] :
( ( c_Int_OMin
= ( A @ c_Int_OBit1 ) )
<=> ( c_Int_OMin = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
thf(5111,plain,
! [A: $i] :
( ( ( c_Int_OMin = A )
=> ( c_Int_OMin
= ( A @ c_Int_OBit1 ) ) )
& ( ( c_Int_OMin
= ( A @ c_Int_OBit1 ) )
=> ( c_Int_OMin = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1039,axiom,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(4939,plain,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(4366,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1__strict )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(3260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1__strict )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1041,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ? [B: $i] :
( A
= ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__mult__two__ex) ).
thf(4950,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ? [B: $i] :
( A
= ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1103,axiom,
! [A: $i,B: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__abs2) ).
thf(5171,plain,
! [A: $i,B: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(4534,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(2732,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(641,axiom,
! [A: $i] :
( ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__1__iff) ).
thf(3462,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(437,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).
thf(2678,plain,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(2518,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(1368,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(934,axiom,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).
thf(4517,plain,
! [A: $i] :
( c_Int_OMin
!= ( A @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
thf(2175,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(444,axiom,
( ( v_na____ @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ? [A: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( v_na____ @ ( A @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ) @ ( v_b @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).
thf(2720,plain,
( ( v_na____ @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ? [A: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( v_na____ @ ( A @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ) @ ( v_b @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(902,axiom,
tc_Nat_Onat @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(4377,plain,
tc_Nat_Onat @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(3608,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(47,axiom,
tc_Int_Oint @ class_Rings_Oordered__ring__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
thf(1230,plain,
tc_Int_Oint @ class_Rings_Oordered__ring__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).
thf(2569,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(501,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(2920,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(27,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__ring__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
thf(1186,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__ring__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(806,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_four__x__squared) ).
thf(4003,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(2219,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(43,axiom,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
thf(1218,plain,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
thf(3019,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zmod) ).
thf(2747,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
thf(1499,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(635,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
thf(3448,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(884,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(4314,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(944,axiom,
! [A: $i] :
( ( ( A @ class_Int_Onumber__ring )
& ( A @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half) ).
thf(4561,plain,
! [A: $i] :
( ( ( A @ class_Int_Onumber__ring )
& ( A @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(891,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(4346,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
thf(3305,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(1432,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) )
& ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__zero__eq) ).
thf(3475,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) )
& ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( ( B
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) )
& ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
thf(3026,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(695,axiom,
tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(3655,plain,
tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(60,axiom,
~ ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I20_J) ).
thf(1262,plain,
~ ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
thf(1317,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(1763,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(1901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(663,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__zero) ).
thf(3544,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(747,axiom,
tc_RealDef_Oreal @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
thf(3828,plain,
tc_RealDef_Oreal @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(1098,axiom,
tc_Nat_Onat @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(5152,plain,
tc_Nat_Onat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(387,axiom,
tc_RealDef_Oreal @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
thf(2486,plain,
tc_RealDef_Oreal @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(865,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
thf(4241,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(3847,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1679,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(672,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(3564,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(1075,axiom,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__power2) ).
thf(5062,plain,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(1106,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(5186,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(2468,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(2411,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(202,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).
thf(1849,plain,
tc_Complex_Ocomplex @ class_Int_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).
thf(3829,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(1,conjecture,
? [A: $i] :
( v_na____
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( v_na____
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1141,plain,
~ ? [A: $i] :
( v_na____
= ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(1702,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1121,axiom,
! [A: $i] :
( ( ( A @ c_Int_OBit1 )
= c_Int_OMin )
<=> ( A = c_Int_OMin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).
thf(5240,plain,
! [A: $i] :
( ( ( A = c_Int_OMin )
=> ( ( A @ c_Int_OBit1 )
= c_Int_OMin ) )
& ( ( ( A @ c_Int_OBit1 )
= c_Int_OMin )
=> ( A = c_Int_OMin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
thf(1284,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(2320,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(822,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(4046,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(1007,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__nat__number__of) ).
thf(4795,plain,
! [A: $i,B: $i] :
( ( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(977,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
thf(4671,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(861,axiom,
! [A: $i,B: $i] :
( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) )
& ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) ) ) )
& ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nat__number__of) ).
thf(4217,plain,
! [A: $i,B: $i] :
( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) )
& ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) ) ) )
& ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(931,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(4510,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(996,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(4748,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__eq) ).
thf(2843,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(863,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(4235,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(4202,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(962,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(4634,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(171,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(1670,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(521,axiom,
~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__1__nat) ).
thf(3024,plain,
~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(834,axiom,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__0__number__of) ).
thf(4093,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(2722,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(871,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(4267,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(256,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
thf(2030,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(889,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ c_Int_OBit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit0) ).
thf(4342,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ c_Int_OBit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(706,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).
thf(3684,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(3288,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
thf(4639,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(3400,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(785,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).
thf(3946,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(1022,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Pls) ).
thf(4851,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(22,axiom,
tc_Complex_Ocomplex @ class_Rings_Odivision__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
thf(1180,plain,
tc_Complex_Ocomplex @ class_Rings_Odivision__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).
thf(1966,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(176,axiom,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__real__sqrt__sumsq) ).
thf(1685,plain,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(848,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(4165,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
thf(3171,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(807,axiom,
! [A: $i] :
( A
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(4006,plain,
! [A: $i] :
( A
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).
thf(2342,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(1453,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
thf(3929,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(561,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).
thf(3168,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(1940,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(678,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(3584,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(969,axiom,
tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(4651,plain,
tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(687,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).
thf(3620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(843,axiom,
! [A: $i] :
( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ? [B: $i] :
( A
= ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__Suc__mult__two__ex) ).
thf(4138,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc ) )
=> ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ? [B: $i] :
( A
= ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(638,axiom,
tc_RealDef_Oreal @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
thf(3457,plain,
tc_RealDef_Oreal @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(3565,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(992,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
thf(4727,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__1) ).
thf(2088,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ozero) ).
thf(1157,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(972,axiom,
! [A: $i] :
( ( A @ c_Transcendental_Oarctan )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__half) ).
thf(4656,plain,
! [A: $i] :
( ( A @ c_Transcendental_Oarctan )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(337,axiom,
tc_Complex_Ocomplex @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
thf(2310,plain,
tc_Complex_Ocomplex @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).
thf(1844,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1054,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(4997,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(3548,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(349,axiom,
tc_RealDef_Oreal @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
thf(2347,plain,
tc_RealDef_Oreal @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(1412,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(994,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber )
=> ( ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= A )
<=> ( A
= ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__reorient) ).
thf(4738,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Int_Onumber )
=> ( ( ( A
= ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
=> ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= A ) )
& ( ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= A )
=> ( A
= ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(1004,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(4780,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(777,axiom,
c_Int_OPls @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I23_J) ).
thf(3928,plain,
c_Int_OPls @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(854,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__product__nat) ).
thf(4185,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(41,axiom,
tc_Int_Oint @ class_Rings_Olinordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1216,plain,
tc_Int_Oint @ class_Rings_Olinordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(308,axiom,
tc_RealDef_Oreal @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
thf(2209,plain,
tc_RealDef_Oreal @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(830,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).
thf(4078,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1137,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__0__number__of) ).
thf(5308,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(190,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(1734,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1077,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Int_OBit1 )
= ( A @ c_Int_OBit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).
thf(5068,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Int_OBit1 )
= ( A @ c_Int_OBit1 ) ) )
& ( ( ( B @ c_Int_OBit1 )
= ( A @ c_Int_OBit1 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1105,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2__gt__zero) ).
thf(5184,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
thf(2443,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__power__nat) ).
thf(2707,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(985,axiom,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).
thf(4710,plain,
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).
thf(2406,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(921,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__one__imp__sqr__less__one) ).
thf(4468,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(3383,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(613,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I28_J) ).
thf(3369,plain,
! [A: $i] :
( ( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Orderings_Olinorder )
& ( C @ class_Int_Onumber ) )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ~ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).
thf(2026,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Orderings_Olinorder )
& ( C @ class_Int_Onumber ) )
=> ( ( ~ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(369,axiom,
~ ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I3_J) ).
thf(2431,plain,
~ ( c_Int_OMin @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( B
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).
thf(4823,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( B
= ( c_Int_OMin @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(398,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(2526,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(291,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
thf(2152,plain,
! [A: $i] :
( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(354,axiom,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__one) ).
thf(2389,plain,
( c_Complex_Oii
!= ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(1009,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).
thf(4806,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(1127,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__pos__lt__two__imp__zero__or__one) ).
thf(5272,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(328,axiom,
tc_Int_Oint @ class_Rings_Olinordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(2290,plain,
tc_Int_Oint @ class_Rings_Olinordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(979,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(4681,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1108,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
thf(5191,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
= ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(1090,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(5132,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__sign) ).
thf(2004,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(801,axiom,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).
thf(3991,plain,
! [A: $i] :
( ( A @ class_Int_Onumber__ring )
=> ( ( A @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(650,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2) ).
thf(3501,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( B @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( B @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(1056,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(5010,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(459,axiom,
c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I24_J) ).
thf(2764,plain,
c_Int_OMin @ ( c_Int_OMin @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(808,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(4010,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(3516,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__iff) ).
thf(1523,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_NthRoot_Osqrt @ ( B @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(920,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(4451,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Oadd) ).
thf(2394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__field )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(506,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
thf(2956,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(860,axiom,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ c_NthRoot_Osqrt )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs) ).
thf(4214,plain,
! [A: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ c_NthRoot_Osqrt )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(752,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(3844,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(878,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).
thf(4299,plain,
c_Int_OMin != c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(656,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
thf(3529,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(704,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).
thf(3677,plain,
! [A: $i] :
( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).
thf(1513,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(2009,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(1861,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(1689,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(797,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__m1__even) ).
thf(3978,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(1135,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(5304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(2081,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(564,axiom,
tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
thf(3181,plain,
tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).
thf(2475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(468,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(2786,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(733,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).
thf(3793,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).
thf(1212,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1085,axiom,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
thf(5119,plain,
( ( c_Int_OPls @ c_Int_OBit0 )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(1115,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__number__of) ).
thf(5211,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__left) ).
thf(2739,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Int_Onumber__ring )
=> ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(390,axiom,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(2494,plain,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(1994,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(881,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(4306,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Int_Oring__char__0 )
& ( C @ class_Int_Onumber__ring ) )
=> ( ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of) ).
thf(5194,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Int_Oring__char__0 )
& ( C @ class_Int_Onumber__ring ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) )
& ( ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
= ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(668,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__iff) ).
thf(3552,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(814,axiom,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos2) ).
thf(4025,plain,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(2019,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_RealVector_Oreal__normed__field )
& ( C @ class_Fields_Ofield__inverse__zero ) )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__divide) ).
thf(1161,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_RealVector_Oreal__normed__field )
& ( C @ class_Fields_Ofield__inverse__zero ) )
=> ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(365,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
thf(2421,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(1036,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).
thf(4917,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(125,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1512,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
thf(2233,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(133,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
thf(1546,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
thf(1625,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).
thf(3100,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(419,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(2604,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(1876,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2050,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(643,axiom,
tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__zero__nat) ).
thf(3469,plain,
tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(218,axiom,
! [A: $i] :
( ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I11_J) ).
thf(1908,plain,
! [A: $i] :
( ( ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( c_Int_OMin @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OMin @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(2142,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(697,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__eq) ).
thf(3658,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__eq__number__of) ).
thf(2930,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ~ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(841,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(4125,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(1071,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(5051,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1028,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(4880,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(819,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).
thf(4039,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(82,axiom,
! [A: $i] :
( ( ( A @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__0__iff) ).
thf(1348,plain,
! [A: $i] :
( ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ c_NthRoot_Osqrt )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(4014,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(1089,axiom,
( v_n
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I2_J) ).
thf(5129,plain,
( v_n
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(4399,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(980,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(4687,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
thf(3860,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(729,axiom,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(3785,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
thf(2155,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(903,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(4378,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
<=> ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
thf(2255,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= B ) ) )
=> ( C
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
& ( ( C
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
=> ( ( ( A
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(577,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
thf(3232,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(593,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(3291,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(3997,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(769,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(3907,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(2983,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(3865,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(1078,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(5078,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(4523,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(476,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).
thf(2815,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
thf(2736,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( E
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B != A )
& ( D = C ) )
=> ( ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(1986,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( E
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B != A )
& ( D = C ) )
=> ( ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(247,axiom,
tc_Int_Oint @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(2008,plain,
tc_Int_Oint @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).
thf(1303,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(3790,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).
thf(3337,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra__1 )
=> ( A @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
thf(1148,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra__1 )
=> ( A @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
thf(1673,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(1757,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(974,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__less) ).
thf(4663,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
thf(3822,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Olinordered__idom )
& ( C @ class_Int_Onumber__ring ) )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of) ).
thf(3015,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Olinordered__idom )
& ( C @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( A @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(4029,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( A @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(670,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
thf(3558,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(3804,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(760,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).
thf(3875,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(754,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
thf(3850,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(2417,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).
thf(1710,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(2091,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(4865,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__sign) ).
thf(2340,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono) ).
thf(2021,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
thf(2783,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
thf(1859,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
& ( ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).
thf(4146,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
& ( ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(765,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(3897,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1003,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__m1__odd) ).
thf(4777,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(4051,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(1101,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
thf(5159,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(892,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).
thf(4350,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(4981,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).
thf(2334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(3560,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).
thf(4968,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(453,axiom,
tc_Int_Oint @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(2746,plain,
tc_Int_Oint @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(846,axiom,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
thf(4157,plain,
! [A: $i] :
( ( A @ c_Int_OBit1 )
!= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(1693,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1060,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(5019,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(832,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(4083,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
& ( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).
thf(2714,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).
thf(1891,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field__inverse__zero )
=> ( ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(855,axiom,
! [A: $i] :
( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).
thf(4193,plain,
! [A: $i] :
( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).
thf(2619,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Int_Onumber )
& ( D @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
& ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(3424,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(885,axiom,
! [A: $i,B: $i] :
( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) )
& ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).
thf(4318,plain,
! [A: $i,B: $i] :
( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) )
& ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(2549,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
thf(2159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(59,axiom,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(1261,plain,
tc_Complex_Ocomplex @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(4118,plain,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(236,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
thf(1976,plain,
tc_Complex_Ocomplex @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(973,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).
thf(4659,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Int_Onumber__ring )
& ( B @ class_Fields_Olinordered__field__inverse__zero ) )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(890,axiom,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(4345,plain,
c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
thf(4363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
thf(1930,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power2) ).
thf(5275,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
thf(2127,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1021,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(4848,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1111,axiom,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__Min) ).
thf(5204,plain,
( ( c_Int_OMin @ c_Int_OBit1 )
= c_Int_OMin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(1977,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(368,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(2430,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
thf(3701,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(3057,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(2803,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(498,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__zero) ).
thf(2898,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__comm__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(3411,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__comm__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(386,axiom,
tc_Complex_Ocomplex @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
thf(2485,plain,
tc_Complex_Ocomplex @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Olinordered__field )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less2) ).
thf(1384,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Fields_Olinordered__field )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(683,axiom,
! [A: $i] :
~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
thf(3605,plain,
! [A: $i] :
~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
thf(1357,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B = A )
=> ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ) )
& ( ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
= ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(929,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit1) ).
thf(4506,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__one__odd__power) ).
thf(2583,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(4066,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(812,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(4019,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(1299,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(4271,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Olinordered__idom )
& ( C @ class_Int_Onumber__ring ) )
=> ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of) ).
thf(1621,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Olinordered__idom )
& ( C @ class_Int_Onumber__ring ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).
thf(2138,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Fields_Olinordered__field )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(978,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__eq__power2) ).
thf(4674,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(722,axiom,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__one__even__odd__power) ).
thf(3753,plain,
! [A: $i,B: $i] :
( ( B @ class_Int_Onumber__ring )
=> ( ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( A @ ( c_Int_OMin @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1015,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(4826,plain,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(971,axiom,
tc_Nat_Onat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
thf(4655,plain,
tc_Nat_Onat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(1064,axiom,
! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(5029,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(1320,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(965,axiom,
! [A: $i,B: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__abs1) ).
thf(4642,plain,
! [A: $i,B: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_NthRoot_Osqrt @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(1184,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
thf(2436,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self2) ).
thf(3052,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(1449,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(805,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(4002,plain,
tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Oof__real ) @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Oof__real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__power) ).
thf(1331,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Oof__real ) @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Oof__real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1606,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1136,axiom,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(5307,plain,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
thf(3626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Fields_Ofield__inverse__zero )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
= ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
thf(3212,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(990,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
thf(4723,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc )
= ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
<=> ( ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
& ~ ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
& ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__sum__nat) ).
thf(1737,plain,
! [A: $i,B: $i] :
( ( ( ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
& ~ ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
& ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
=> ( ( ~ ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
& ~ ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) )
| ( ( A @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) )
& ( B @ ( tc_Nat_Onat @ c_Parity_Oeven__odd__class_Oeven ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(543,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
thf(3096,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(2206,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(1463,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
thf(1565,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(490,axiom,
tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
thf(2866,plain,
tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(847,axiom,
! [A: $i] :
( c_Complex_Oii
!= ( A @ ( tc_Complex_Ocomplex @ c_Int_Onumber__class_Onumber__of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__number__of) ).
thf(4161,plain,
! [A: $i] :
( c_Complex_Oii
!= ( A @ ( tc_Complex_Ocomplex @ c_Int_Onumber__class_Onumber__of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(373,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(2438,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(120,axiom,
! [A: $i] :
( ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__0__iff) ).
thf(1490,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_NthRoot_Osqrt @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(913,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
thf(4423,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
thf(1917,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(1468,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(2470,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(1040,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(4940,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).
thf(2980,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(5365,plain,
$false,
inference(e,[status(thm)],[2163,1501,3944,5136,3399,5320,3927,1179,4166,1322,1665,4447,1879,2889,1190,2295,2306,4101,4450,2336,2031,5260,3661,1767,3798,1559,3666,4729,3397,1899,3863,1850,2427,1982,2280,1554,4339,3858,3762,2062,2776,2590,4960,3012,2099,4326,4592,4479,1855,1200,4043,3534,4714,2976,3072,1924,2210,5168,4500,4075,1290,5292,3813,2495,3377,3040,3153,3460,2947,1569,1544,2014,5173,1971,3402,5237,1692,4973,1173,1486,1426,3049,2686,1164,5316,2434,1919,1342,4762,2575,4839,4647,3942,4011,4884,3365,4026,3044,4110,3175,4650,2168,4058,4247,1640,2901,3313,4435,3577,2146,4980,1222,3895,3103,3629,5252,4618,1613,4665,4610,2531,5024,2348,3350,3994,1914,2763,2491,1243,2227,1576,3249,4371,4803,4124,3730,5056,1386,5301,3140,1475,2400,4760,2067,1529,3597,1254,4238,3263,2603,3644,3116,3046,4415,3495,5188,2501,1323,3125,5289,2466,2654,1628,2735,2814,4563,4422,1264,2217,1577,1455,3749,4023,1462,3043,2745,2571,5231,1922,3385,1247,4179,1609,3919,3084,3470,3951,1963,4390,1232,1847,2857,4353,4862,1319,1704,3734,3014,3602,3557,1875,4302,4514,2829,3788,4432,2222,5264,3431,5013,2782,4820,1682,3525,3973,2291,3569,2616,4396,1465,3966,4583,4903,4578,4258,1373,2893,1632,4297,3453,2236,1334,3527,3983,2555,3923,1960,1183,1283,2073,3068,3739,3712,2371,2137,3361,1201,1600,2586,4065,5045,3389,5059,1843,2058,4751,1169,2367,3537,4842,2861,5220,1215,2190,3421,2483,5101,3808,3036,2799,2286,2103,2750,1405,3588,1697,1242,3211,2392,3906,1521,4628,4211,1863,4700,2011,1206,5157,4199,4962,4589,3567,1438,4531,1153,1470,2641,2660,3984,2646,1338,5142,1311,3767,2307,1736,2496,4312,2790,3550,2773,5122,3418,3795,5206,1387,2428,2249,2541,2596,4920,4878,1217,3022,1666,4091,3884,4785,3134,2032,4836,3664,3207,2705,2409,1223,4712,3711,4016,3972,4609,1174,1676,4521,4128,3239,4284,3816,1883,1560,3307,3191,2332,4553,1687,2200,4402,5201,1195,3647,5285,3166,2445,4295,3269,3618,2433,2477,4725,1968,4757,3499,3065,3578,1178,3546,5038,4746,3050,3926,2344,4104,3931,3408,3731,3968,4668,4512,2895,1328,4048,3704,3963,2537,3632,3078,3237,2638,3001,4817,3699,1592,2300,2498,3909,3615,1234,1541,2157,2840,2115,5053,5145,1762,3254,3413,1851,1259,3122,4974,3862,4636,1587,3386,2631,1567,1160,1942,2323,4983,3441,4545,2666,3935,2023,3326,5031,3143,5107,2830,1182,1414,2053,2196,2038,1446,2551,2085,2978,2472,2317,3294,2968,3656,2125,1150,2487,4970,1984,1852,3333,4416,1297,3126,2681,3541,1451,5149,3354,2900,1231,5234,3770,1552,2851,1192,1932,4244,2581,2465,2505,3819,3222,2006,3937,4717,1429,3247,2766,4902,1246,1979,5026,2140,2756,3162,3201,1759,3215,4361,3147,1241,3624,3183,4476,1170,1187,4036,2529,3824,2634,1434,1857,4184,3802,5153,1202,4352,4644,3225,4782,4081,1695,4765,3999,1286,5209,1663,3508,1167,2189,3422,2995,3841,2617,5126,2662,1732,4572,2144,3707,2413,2677,3042,5230,3375,5016,2894,3343,4470,4380,3358,2275,5138,4613,2253,3257,1219,3491,1483,3079,4438,1631,5043,4041,3547,3070,4309,1652,3900,4328,1965,4590,5022,3536,1154,3234,2048,2225,3504,4494,3255,3811,3240,5065,2849,5121,3472,3266,2674,2016,4032,4709,2806,2991,5097,3458,2827,3599,2161,3773,5086,5148,3832,4854,3416,1258,3304,2474,3532,4526,4537,2193,5039,1669,3118,5033,1707,2293,1371,5011,3726,3330,2738,5282,3663,2442,5207,5314,2055,1638,4887,2573,1356,2311,4914,1589,3468,4586,2802,4773,1209,2119,3352,4228,3631,1408,3251,4369,2642,3815,2084,2214,2383,3764,2415,3038,4305,3683,4828,1603,2955,2246,1722,1144,3710,4958,4616,4073,5093,4154,4374,3182,2871,1376,4509,2197,4107,2182,2742,2314,4569,2111,1993,4264,3932,2757,3977,3971,1556,3150,3893,3219,2824,4694,3055,1557,3165,4208,4181,2785,3451,4652,2874,1293,2278,2553,5007,2928,1177,1381,1699,2765,1445,3917,3325,2535,1364,4965,3539,2770,2075,1198,4720,2212,2171,3759,3838,3687,5248,3806,2064,4362,3674,4827,2288,3953,2797,3363,3310,1496,5299,2303,4497,4282,5139,4890,1973,4481,2069,2867,3380,1562,3881,3009,1948,4405,1203,4868,4813,2652,4529,1277,3146,3975,3921,1472,4581,1181,1662,4441,2614,2096,4901,1166,2107,3672,1420,3981,2503,4292,1509,1990,4566,2684,4688,1145,2846,4812,1551,4986,4168,2298,3737,2397,5250,3082,3214,3904,4922,3949,2821,3786,1531,2567,4255,1547,1748,2863,1598,1611,5111,4939,4366,3260,4950,5171,4534,2732,3462,2678,2518,1368,4517,2175,2720,4377,3608,1230,1484,2569,2920,1186,4003,2219,1218,3019,2747,1499,3448,4314,4561,4346,3305,1432,3475,3026,3655,1262,1317,1763,1901,3544,3828,5152,2486,4241,3847,1679,3564,5062,5186,2468,2411,1849,3829,1141,1702,5240,1284,2320,4046,4795,4671,4217,4510,4748,2843,4235,4202,4634,1670,3024,4093,2722,4267,2030,4342,3684,3288,4639,3400,3946,4851,1180,1966,1685,4165,3171,4006,2342,1453,3929,3168,1940,3584,4651,3620,4138,3457,3565,4727,2088,1157,4656,2310,1844,4997,3548,2347,1412,4738,4780,3928,4185,1216,2209,4078,5308,1734,5068,5184,2443,2707,4710,2406,4468,3383,3369,2026,2431,4823,2526,2152,2389,4806,5272,2290,4681,5191,5132,2004,3991,3501,5010,2764,4010,3516,1523,4451,2394,2956,4214,3844,4299,3529,3677,1513,2009,1861,1689,3978,5304,2081,3181,2475,2786,3793,1212,5119,5211,2739,2494,1994,4306,5194,3552,4025,2019,1161,2421,4917,1512,2233,1546,1625,3100,2604,1876,2050,3469,1908,2142,3658,2930,4125,5051,4880,4039,1348,4014,5129,4399,4687,3860,3785,2155,4378,2255,3232,3291,3997,3907,2983,3865,5078,4523,2815,2736,1986,2008,1303,3790,3337,1148,1673,1757,4663,3822,3015,4029,3558,3804,3875,3850,2417,1710,2091,4865,2340,2021,2783,1859,4146,3897,4777,4051,5159,4350,4981,2334,3560,4968,2746,4157,1693,5019,4083,2714,1891,4193,2619,3424,4318,2549,2159,1261,4118,1976,4659,4345,4363,1930,5275,2127,4848,5204,1977,2430,3701,3057,2803,2898,3411,2485,1384,3605,1357,4506,2583,4066,4019,1299,4271,1621,2138,4674,3753,4826,4655,5029,1320,4642,1184,2436,3052,1449,4002,1331,1606,5307,3626,3212,4723,1737,3096,2206,1463,1565,2866,4161,2438,1490,4423,1917,1468,2470,4940,2980]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/15.50 % CPULimit : 300
% 0.12/15.50 % WCLimit : 300
% 0.12/15.50 % DateTime : Sat Sep 26 15:28:15 UTC 2026
% 0.12/15.51 % CPUTime :
% 0.12/15.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.31/16.28 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.49/16.99 % [INFO] Parsing done (705ms).
% 3.49/17.01 % [INFO] Running in sequential loop mode.
% 4.95/17.58 % [INFO] eprover registered as external prover.
% 4.95/17.59 % [INFO] Scanning for conjecture ...
% 6.06/17.95 % [INFO] Found a conjecture (or negated_conjecture) and 1185 axioms. Running axiom selection ...
% 8.31/18.49 % [INFO] Axiom selection finished. Selected 1138 axioms (removed 47 axioms).
% 11.22/19.34 % [INFO] Problem is first-order (TPTP FOF).
% 11.67/19.42 % [INFO] Type checking passed.
% 11.67/19.43 % [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 ...
% 55.14/30.04 % External prover 'e' found a proof!
% 55.14/30.04 % [INFO] Killing All external provers ...
% 55.14/30.04 % Time passed: 14335ms (effective reasoning time: 13025ms)
% 55.14/30.04 % 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)>
% 55.14/30.08 % Axioms used in derivation (1138): fact_le__SucI, fact_numeral__2__eq__2, fact_nat_Osimps_I3_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_zero__power2, fact_arctan__monotone, fact_real__sqrt__ge__abs1, fact_zle__refl, fact_neg__divide__le__eq, fact_zmod__minus1__right, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_pos2, fact_zero__le__divide__iff, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_right__inverse__eq, fact_xt1_I1_J, fact_less__eq__int__code_I14_J, fact_abs__of__pos, fact_real__le__refl, fact_real__sqrt__sum__squares__mult__squared__eq, fact_odd__pos, fact_not__sum__power2__lt__zero, arity_fun__Orderings_Oorder, fact_Numeral1__eq1__nat, fact_power__abs, fact_real__less__def, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_mult__right__le__imp__le, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, 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, arity_RealDef__Oreal__Orderings_Oord, 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_mult__less__cancel__left__disj, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_semiring__norm_I112_J, fact_realpow__two__sum__zero__iff, fact_zmod__number__of__Bit1, fact_le__eq__less__or__eq, fact_xt1_I4_J, 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, fact_abs__ge__self, arity_RealDef__Oreal__Rings_Oordered__comm__semiring, fact_nat__add__left__commute, fact_real__mult__left__cancel, fact_mult__nonpos__nonpos, fact_order__le__less__trans, 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_mult__nat__number__of, arity_Int__Oint__Rings_Olinordered__semiring__strict, fact_less__int__code_I14_J, fact_add__nat__number__of, 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_add__leD1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_abs__div__pos, fact_zero__less__power, fact_add__less__mono, fact_mult__0, arity_Nat__Onat__Orderings_Oorder, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_mult__right__less__imp__less, fact_mod__mult__cong, fact_le__imp__0__less, fact_abs__eq__mult, fact_split__mult__neg__le, fact_real__gt__half__sum, fact_zpower__zmod, 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_linorder__not__le, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_mult__le__less__imp__less, fact_zadd__commute, arity_Nat__Onat__Groups_Omonoid__mult, fact_power__increasing, fact_real__sqrt__one, fact_order__less__asym_H, fact_le__number__of__eq__not__less, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, fact_linorder__antisym__conv2, fact_zmult2__lemma__aux4, fact_mult__mono, fact_gr0__conv__Suc, fact_linorder__neqE, arity_RealDef__Oreal__Groups_Omonoid__add, fact_real__sqrt__divide, fact_field__power__not__zero, arity_Complex__Ocomplex__Int_Onumber__ring, fact_mult__le__mono2, fact_zero__le__odd__power, fact_Suc__le__mono, fact_order__eq__refl, fact_mod__mult__eq, arity_Nat__Onat__Rings_Ozero__neq__one, fact_nat__number__of__Pls, fact_power__le__zero__eq__number__of, fact_real__sqrt__sum__squares__ge2, fact_zero__le__zpower__abs, fact_add__right__imp__eq, fact_rel__simps_I25_J, fact_nat__add__right__cancel, fact_leI, fact_mod__pos__pos__trivial, fact_less__special_I4_J, fact_int__pos__lt__two__imp__zero__or__one, fact_power2__eq__imp__eq, fact_rel__simps_I31_J, fact_mult__eq__self__implies__10, fact_le__neq__implies__less, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, fact_add__pos__nonneg, fact_power2__eq__square, fact_neg__one__even__power, fact_zero__le__one, fact_zero__less__power__eq__number__of, arity_Int__Oint__Orderings_Oord, fact_zero__less__power__nat__eq__number__of, fact_Bit1__def, fact_int__0__less__1, fact_pos__le__divide__eq, fact_real__sqrt__sum__squares__mult__ge__zero, fact_mult__imp__le__div__pos, fact_mult__left__le__imp__le, fact_divide__pos__neg, fact_real__sqrt__two__gt__one, fact_mult__numeral__1__right, fact_zle__linear, fact_nat__add__left__cancel__less, fact_add__Bit0__Bit1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_linorder__antisym__conv3, fact_add__strict__increasing2, fact_order__less__imp__not__eq, fact_n, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_linorder__neqE__linordered__idom, arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, fact_odd__1__nat, fact_mod__by__1, fact_sum__power2__eq__zero__iff, fact_divide__right__mono, fact_rel__simps_I5_J, fact_add__le__imp__le__left, fact_mod__mult__self1, arity_RealDef__Oreal__Fields_Ofield__inverse__zero, fact_add__nonneg__eq__0__iff, 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, fact_even__power__nat, arity_Int__Oint__Rings_Olinordered__semiring__1__strict, fact_mult__le__cancel__left__neg, fact_sum__squares__ge__zero, fact_add__increasing2, fact_zero__le__mult__iff, arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero, fact_linorder__antisym__conv1, arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, arity_Int__Oint__Groups_Ozero, fact_divide__le__eq, fact_gr0I, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, arity_Int__Oint__Rings_Olinordered__ring, fact_add__0__iff, fact_le__funD, fact_abs__add__one__gt__zero, fact_neg__mod__sign, fact_real__sqrt__eq__0__iff, 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_mod__pos__neg__trivial, 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__mono, fact_complex__of__real__power, fact_add__right__mono, fact_Divides_Otransfer__nat__int__function__closures_I2_J, fact_le__nat__number__of, fact_less__int__code_I13_J, fact_le__fun__def, fact_divide__eq__imp, fact_one__less__power, fact_mod__mult__left__eq, arity_Nat__Onat__Rings_Osemiring__0, fact_rabs__ratiotest__lemma, fact_less__eq__number__of__int__code, fact_nat__mult__1__right, fact_divide__strict__left__mono__neg, fact_linorder__less__linear, arity_Complex__Ocomplex__Rings_Osemiring__0, fact_order__less__imp__not__less, fact_number__of__add, fact_divide__le__eq__number__of, fact_add__numeral__0__right, fact_zero__le__power__abs, fact_ord__less__eq__trans, fact_add__numeral__0, fact_rel__simps_I15_J, arity_RealDef__Oreal__Rings_Olinordered__idom, fact_le__iff__add, fact_one__reorient, fact_le__number__of, fact_rel__simps_I44_J, arity_Nat__Onat__Rings_Oordered__comm__semiring, fact_power__eq__0__iff, fact_half__gt__zero__iff, fact_less__divide__eq__number__of1, fact_divide__add__eq__iff, fact_xt1_I9_J, fact_less__add__eq__less, fact_pos__zmod__mult__2, fact_Bit1__Min, fact_add__lessD1, fact_add__le__mono1, fact_IH, fact_less__eq__nat_Osimps_I1_J, 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, arity_Int__Oint__Rings_Oring__no__zero__divisors, fact_less__0__number__of, fact_mod__add__self1, arity_RealDef__Oreal__Groups_Ocancel__semigroup__add, fact_real__sqrt__ge__abs2, fact_add__0__right, fact_zadd__zless__mono, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_mult__less__mono1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_split__mult__pos__le, 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fact_mult__right__le__one__le, fact_even__Suc, fact_real__sqrt__sum__squares__triangle__ineq, fact_rel__simps_I4_J, arity_RealDef__Oreal__Groups_Oone, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_linorder__not__less, fact_Suc__mult__le__cancel1, fact_add__neg__neg, fact_rel__simps_I16_J, arity_Int__Oint__Rings_Oordered__ring, fact_mod__mult__mult2, fact_neg__zmod__mult__2, fact_divide_Oadd, fact_le__imp__less__Suc, fact_mult__right__mono, fact_xt1_I2_J, arity_Int__Oint__Rings_Olinordered__semiring, fact_real__sqrt__power, fact_numeral__3__eq__3, fact_abs__zero, fact_less__add__Suc1, fact_less__fun__def, fact_One__nat__def, 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_zero__less__abs__iff, fact_abs__add__abs, fact_add__is__0, fact_rel__simps_I10_J, fact_eq__number__of, fact_real__sqrt__pow2, fact_rel__simps_I46_J, fact_add__less__imp__less__left, fact_pos__mod__conj, fact_eq__number__of__0, fact_times__divide__times__eq, fact_neg__one__even__odd__power, fact_power__even__abs, fact_power__mono, fact_power2__sum, fact_mult__le__mono1, fact_rel__simps_I24_J, arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, fact_divide__le__eq__number__of1, fact_real__sqrt__lt__1__iff, fact_add__pos__pos, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_add__0, fact_rel__simps_I37_J, fact_add__nonneg__nonneg, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, arity_RealDef__Oreal__Power_Opower, fact_Suc__eq__plus1, fact_power__m1__odd, fact_cos__x__y__le__one, 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, arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, fact_mult__nonpos__nonneg, fact_zmod__simps_I2_J, fact_Zero__neq__Suc, fact_nat__mult__2__right, fact_less__eq__int__code_I16_J, fact_order__eq__iff, arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, fact_less__special_I3_J, arity_Nat__Onat__Groups_Oab__semigroup__add, fact_add__left__mono, fact_less__1__mult, arity_Int__Oint__Rings_Oordered__comm__semiring, fact_mult__pos__pos, fact_comm__mult__left__mono, arity_Int__Oint__Groups_Oab__semigroup__add, fact_power__less__zero__eq, arity_Int__Oint__Groups_Oone, fact_real__sqrt__zero, 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_rel__simps_I28_J, fact_zmult2__lemma__aux1, fact_power__Suc__0, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_n__less__n__mult__m, fact_less__not__refl, fact_double__add__le__zero__iff__single__add__le__zero, fact_mult__less__cancel__left__neg, fact_real__sqrt__abs, fact_power__mult__distrib, fact_sum__power2__gt__zero__iff, fact_ord__eq__less__trans, fact_le0, fact_power__one, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, arity_Int__Oint__Orderings_Oorder, 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_divide__eq__eq__number__of1, fact_plus__numeral__code_I9_J, fact_divide__less__eq, fact_zmod__simps_I1_J, fact_gr__implies__not0, fact_mult__strict__right__mono__neg, fact_abs__triangle__ineq, 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_less__int__code_I15_J, fact_divide__strict__left__mono, fact_real__sqrt__eq__zero__cancel, arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, arity_RealDef__Oreal__Rings_Osemiring__1, fact_one__power2, 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_power__mono__odd, fact_Suc__less__eq, fact_mult__neg__neg, fact_add__leE, fact_arctan__half, fact_zdiv__mono2__lemma, fact_power__even__abs__number__of, fact_rel__simps_I23_J, 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_zero__less__Suc, fact_zero__le__power__iff, 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_nat__power__eq__Suc__0__iff, fact_nat__mult__commute, fact_divide__Numeral1, fact_divmod__int__rel__mod__eq, fact_add1__zle__eq, fact_real__sqrt__ge__0__iff, fact_eq__imp__le, fact_power__le__zero__eq, fact_rel__simps_I2_J, arity_Complex__Ocomplex__Int_Oring__char__0, fact_even__sum__nat, arity_Int__Oint__Rings_Olinordered__semiring__1, fact_plus__nat_Oadd__0, arity_RealDef__Oreal__Int_Onumber, fact_neg__divide__less__eq, fact_order__le__imp__less__or__eq, fact_less__int__code_I16_J, fact_add__strict__increasing, fact_number__of__Bit1, fact_real__sqrt__mult, fact_le__less__Suc__eq, fact_real__norm__def, fact_add__frac__num, fact_mult__left__mono__neg, fact_le__antisym, fact_zless__linear, fact_zadd__0__right, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, fact_abs__mult__pos, fact_zero__less__mult__pos, fact_le__special_I4_J, fact_nonzero__abs__divide, fact_order__antisym__conv, fact_neq0__conv, fact_add__2__eq__Suc, fact_Suc__n__not__n, fact_nat__numeral__1__eq__1, fact_half, fact_divide__strict__right__mono, fact_mult__0__right, 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, arity_Complex__Ocomplex__Rings_Omult__zero, fact_zmult__1__right, fact_double__eq__0__iff, fact_le__0__eq, fact_assms_I2_J, fact_mult__Suc__right, fact_order__less__trans, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_mult__less__cancel2, fact_zle__add1__eq__le, fact_mod__0, fact_mult__1__right, fact_i__squared, fact_number__of__Pls, fact_add__le__imp__le__right, fact_order__less__irrefl, fact_add__le__mono, fact_less__Suc0, fact_divide__nonneg__neg, arity_Nat__Onat__Rings_Osemiring, fact_mult__less__imp__less__left, fact_order__less__imp__le, fact_less__iff__Suc__add, fact_zero__less__two, fact_real__sqrt__le__mono, fact_abs__mult__self, fact_real__mult__less__mono2, fact_sum__squares__eq__zero__iff, fact_zabs__less__one__iff, fact_nat__zero__less__power__iff, fact_mod__add__right__eq, fact_order__le__less, fact_rel__simps_I32_J, fact_abs__power__minus__one, fact_convex__bound__le, 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_add__imp__eq, arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_power__gt1, fact_no__zero__divisors, fact_le__square, fact_zadd__zmult__distrib, fact_nonzero__norm__divide, fact_power__odd__eq, fact_double__add__less__zero__iff__single__add__less__zero, arity_RealDef__Oreal__Groups_Olinordered__ab__group__add, arity_Nat__Onat__Groups_Oone, fact_mod__mult__self2, fact_odd__Suc__mult__two__ex, arity_RealDef__Oreal__Groups_Oab__semigroup__mult, arity_Int__Oint__Rings_Ozero__neq__one, arity_RealDef__Oreal__Fields_Ofield, fact_half__gt__zero, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_power__0__Suc, fact_nat__less__le, fact_less__SucE, fact_gt__half__sum, fact_le__cube, fact_zless__add1__eq, fact_linorder__cases, fact_xt1_I11_J, fact_odd__nat__equiv__def2, 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_ord__eq__le__trans, fact_nonzero__eq__divide__eq, fact_realpow__Suc__le__self, fact_odd__less__0, fact_even__add, 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_xt1_I7_J, fact_power__le__imp__le__base, fact_mult__1, fact_even__product__nat, fact_mod__add__eq, 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, arity_Int__Oint__Orderings_Opreorder, fact_odd__power__less__zero, fact_eq__number__of__Pls__Min, fact_less__SucI, fact_Suc__not__Zero, fact_i__mult__eq, fact_order__trans, arity_Complex__Ocomplex__Groups_Ozero, fact_add__2__eq__Suc_H, fact_not__square__less__zero, fact_Suc__lessI, fact_add__Suc__right, 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
% 55.14/30.08 % No. of inferences in proof: 2280
% 55.14/30.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14335 ms resp. 13025 ms w/o parsing
% 61.16/31.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 61.29/31.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------