TSTP Solution File: SWW209+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW209+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:22:02 EDT 2023
% Result : Theorem 25.36s 6.85s
% Output : Refutation 26.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1206
% Syntax : Number of formulae : 2314 ( 667 unt; 100 typ; 0 def)
% Number of atoms : 5937 (1606 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 35583 ( 317 ~; 136 |; 525 &;31543 @)
% ( 257 <=>;2805 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 134 ( 134 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 100 usr; 8 con; 0-5 aty)
% Number of variables : 5085 ( 0 ^;5018 !; 67 ?;5085 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Fun_Ocomp_type,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(v_f_____type,type,
v_f____: $i ).
thf(v_ga_____type,type,
v_ga____: $i ).
thf(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(class_Groups_Oordered__ab__group__add_type,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i ).
thf(c_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(class_Rings_Oring__1_type,type,
class_Rings_Oring__1: $i > $o ).
thf(c_Int_Oring__1__class_Oof__int_type,type,
c_Int_Oring__1__class_Oof__int: $i > $i > $i ).
thf(class_Rings_Oordered__ring_type,type,
class_Rings_Oordered__ring: $i > $o ).
thf(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
thf(class_Rings_Olinordered__semiring__1__strict_type,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_Rings_Olinordered__semiring__1_type,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_type,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(class_Rings_Ocomm__ring__1_type,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).
thf(c_Int_Onat_type,type,
c_Int_Onat: $i ).
thf(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
thf(class_Rings_Oring__1__no__zero__divisors_type,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Rings_Oordered__semiring_type,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_RealDef_Oreal_type,type,
c_RealDef_Oreal: $i > $i ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(c_Power_Opower_Opower_type,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_type,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Rings_Omult__zero_type,type,
class_Rings_Omult__zero: $i > $o ).
thf(class_Groups_Ominus_type,type,
class_Groups_Ominus: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(class_Rings_Ocomm__semiring_type,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(c_SMT_Oz3div_type,type,
c_SMT_Oz3div: $i > $i > $i ).
thf(class_Rings_Oordered__cancel__semiring_type,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_RComplete_Onatceiling_type,type,
c_RComplete_Onatceiling: $i > $i ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Ono__zero__divisors_type,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_type,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_type,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_type,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(c_Transcendental_Oln_type,type,
c_Transcendental_Oln: $i > $i ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_type,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(class_Rings_Oordered__comm__semiring_type,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(class_Groups_Oab__semigroup__add_type,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Rings_Osemiring__1_type,type,
class_Rings_Osemiring__1: $i > $o ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Nat_Osemiring__char__0_type,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Fun_Oswap_type,type,
c_Fun_Oswap: $i > $i > $i > $i > $i > $i ).
thf(c_RComplete_Onatfloor_type,type,
c_RComplete_Onatfloor: $i > $i ).
thf(class_Rings_Olinordered__ring_type,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(c_Nat__Transfer_Otsub_type,type,
c_Nat__Transfer_Otsub: $i > $i > $i ).
thf(class_Groups_Oone_type,type,
class_Groups_Oone: $i > $o ).
thf(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_type,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__comm__semiring__strict_type,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(class_Rings_Olinordered__ring__strict_type,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(c_Orderings_Oorder__class_Ostrict__mono_type,type,
c_Orderings_Oorder__class_Ostrict__mono: $i > $i > $i > $o ).
thf(class_Groups_Omonoid__add_type,type,
class_Groups_Omonoid__add: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_type,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Osemiring_type,type,
class_Rings_Osemiring: $i > $o ).
thf(c_Nat_Ofunpow_type,type,
c_Nat_Ofunpow: $i > $i ).
thf(c_Nat_Ocompow_type,type,
c_Nat_Ocompow: $i > $i > $i ).
thf(class_Rings_Osemiring__0_type,type,
class_Rings_Osemiring__0: $i > $o ).
thf(class_RealVector_Ometric__space_type,type,
class_RealVector_Ometric__space: $i > $o ).
thf(c_SEQ_Oconvergent_type,type,
c_SEQ_Oconvergent: $i > $i > $o ).
thf(c_SEQ_OCauchy_type,type,
c_SEQ_OCauchy: $i > $i > $o ).
thf(class_SEQ_Ocomplete__space_type,type,
class_SEQ_Ocomplete__space: $i > $o ).
thf(class_Rings_Olinordered__semiring_type,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_type,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(c_Nat__Transfer_Otransfer__morphism_type,type,
c_Nat__Transfer_Otransfer__morphism: $i > $i > $i > $i > $o ).
thf(v_r_type,type,
v_r: $i ).
thf(c_Record_Oiso__tuple__update__accessor__cong__assist_type,type,
c_Record_Oiso__tuple__update__accessor__cong__assist: $i > $i > $i > $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat__aux_type,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(c_SEQ_Osubseq_type,type,
c_SEQ_Osubseq: $i > $o ).
thf(class_Lattices_Oab__semigroup__idem__mult_type,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(c_SEQ_Odecseq_type,type,
c_SEQ_Odecseq: $i > $i > $o ).
thf(c_SEQ_Oincseq_type,type,
c_SEQ_Oincseq: $i > $i > $o ).
thf(c_Int_Onat__aux_type,type,
c_Int_Onat__aux: $i > $i > $i ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(2094,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
thf(2612,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(237,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(1823,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1633,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
thf(3167,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
thf(3581,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(2595,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1077,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(4682,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1089,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(4728,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1549,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(1554,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(3021,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(80,axiom,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
thf(1322,plain,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(533,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2822,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(846,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(3873,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(1048,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
thf(4571,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
thf(3053,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(589,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(3008,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(322,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero__iff) ).
thf(2109,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(2031,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(3661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(1767,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
thf(3399,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(1995,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(863,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(3930,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(4169,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(820,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
thf(3798,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__less__0__iff) ).
thf(1559,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(890,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth) ).
thf(4022,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(199,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
thf(1729,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(4183,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(560,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2921,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(729,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Int_Onat @ B )
= A )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( B
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff) ).
thf(3477,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Int_Onat @ B )
= A )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( B
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( B
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ c_Int_Onat @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__natfloor) ).
thf(1818,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
thf(1295,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(882,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(3990,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(1924,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(683,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
thf(3317,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( c_Nat__Transfer_Otsub @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).
thf(2644,plain,
! [A: $i,B: $i] :
( ( c_Nat__Transfer_Otsub @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(734,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).
thf(3509,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(571,axiom,
! [A: $i,B: $i] :
( ( class_SEQ_Ocomplete__space @ B )
=> ( ( c_SEQ_OCauchy @ B @ A )
=> ( c_SEQ_Oconvergent @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cauchy__convergent) ).
thf(2953,plain,
! [A: $i,B: $i] :
( ( class_SEQ_Ocomplete__space @ B )
=> ( ( c_SEQ_OCauchy @ B @ A )
=> ( c_SEQ_Oconvergent @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(3108,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(4711,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(4326,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
=> ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
thf(1305,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1023,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ A ) @ ( hAPP @ c_Int_Onat @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mono__iff) ).
thf(4487,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ A ) @ ( hAPP @ c_Int_Onat @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ A ) @ ( hAPP @ c_Int_Onat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(405,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ c_Int_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).
thf(2363,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ c_Int_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1855,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
thf(1200,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1085,axiom,
! [A: $i,B: $i] :
( ( c_Int_Onat__aux @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__aux__def) ).
thf(4714,plain,
! [A: $i,B: $i] :
( ( c_Int_Onat__aux @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(386,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_RComplete_Onatfloor @ A ) ) ) @ ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
thf(2309,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_RComplete_Onatfloor @ A ) ) ) @ ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(579,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
thf(2976,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(2117,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(2104,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(907,axiom,
c_SEQ_Osubseq @ v_ga____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_g_I1_J) ).
thf(4075,plain,
c_SEQ_Osubseq @ v_ga____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(68,axiom,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(1290,plain,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
thf(2231,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(463,axiom,
class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
thf(2622,plain,
class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(825,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(3813,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(409,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(2381,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= A ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(412,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(2395,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(2908,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(305,axiom,
( ( c_RComplete_Onatceiling @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__one) ).
thf(2062,plain,
( ( c_RComplete_Onatceiling @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(1443,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(1808,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(476,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ C ) ) @ B ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean4) ).
thf(2659,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ C ) ) @ B ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) )
<=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(3417,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(1080,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(4697,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2248,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(3912,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
thf(3098,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__int) ).
thf(2671,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(1544,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
thf(2676,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(2014,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(318,axiom,
( ( hAPP @ c_Int_Onat @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1) ).
thf(2099,plain,
( ( hAPP @ c_Int_Onat @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(2282,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
thf(2114,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__algebra @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(15,axiom,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(1142,plain,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(1269,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(269,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(1971,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(224,axiom,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1793,plain,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(710,axiom,
class_Rings_Osemiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
thf(3402,plain,
class_Rings_Osemiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(704,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
thf(3382,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(1019,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(4479,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(1037,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(4532,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(28,axiom,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
thf(1173,plain,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(128,axiom,
class_Rings_Oordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
thf(1486,plain,
class_Rings_Oordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(592,axiom,
! [A: $i,B: $i] :
( ( class_Power_Opower @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
thf(3017,plain,
! [A: $i,B: $i] :
( ( class_Power_Opower @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( c_Fun_Oswap @ E @ G @ C @ B @ A ) )
= ( c_Fun_Oswap @ E @ F @ C @ B @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__swap) ).
thf(4739,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( c_Fun_Oswap @ E @ G @ C @ B @ A ) )
= ( c_Fun_Oswap @ E @ F @ C @ B @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
thf(2686,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
thf(1310,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(294,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
thf(2035,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(867,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).
thf(3942,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(2740,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(891,axiom,
! [A: $i] :
( ( c_RComplete_Onatfloor @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
thf(4026,plain,
! [A: $i] :
( ( c_RComplete_Onatfloor @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(4220,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
thf(1164,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= A )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
thf(1275,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(500,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(2712,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(970,axiom,
class_Divides_Osemiring__div @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
thf(4279,plain,
class_Divides_Osemiring__div @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
thf(3781,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(4058,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
thf(1640,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(681,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(3313,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(752,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(3577,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(332,axiom,
! [A: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
thf(2146,plain,
! [A: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(1788,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(1426,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
thf(3217,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(4090,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__eq__positive) ).
thf(1655,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( B
= ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1327,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( B
= ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(4564,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(1919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__eq) ).
thf(1988,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__less__iff) ).
thf(3414,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
thf(1342,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(625,axiom,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(3121,plain,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
thf(1507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(1222,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1099,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).
thf(4762,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(119,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ B ) ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zless) ).
thf(1458,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ B ) ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(701,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
thf(3370,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add) ).
thf(3350,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat__aux @ C @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
thf(3994,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat__aux @ C @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__add) ).
thf(4496,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(615,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(3088,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(869,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Nat_OSuc @ B )
!= A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(3947,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Nat_OSuc @ B )
!= A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(1921,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(1359,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(1386,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(426,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatfloor @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
thf(2516,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatfloor @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatfloor @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(2400,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
thf(1228,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1103,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(4775,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
thf(2957,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(3836,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(986,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(4343,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) @ ( c_Transcendental_Oln @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__realpow) ).
thf(3236,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) @ ( c_Transcendental_Oln @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(770,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(3634,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2046,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(53,axiom,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
thf(1243,plain,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(3915,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(438,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).
thf(2548,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(3249,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(4079,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
thf(1441,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(632,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(3140,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
thf(1724,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(4607,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less__dividend) ).
thf(1366,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(228,axiom,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
thf(1803,plain,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(849,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(3880,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(848,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(3878,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(1904,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(59,axiom,
class_Rings_Oidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
thf(1265,plain,
class_Rings_Oidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).
thf(1703,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(827,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
thf(3820,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(1709,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(558,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).
thf(2916,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(718,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(3425,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oswap @ E @ D @ C @ B @ A )
= ( c_Fun_Oswap @ E @ D @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__commute) ).
thf(3275,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oswap @ E @ D @ C @ B @ A )
= ( c_Fun_Oswap @ E @ D @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(1078,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ G @ E @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ C @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ C @ D ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(4692,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ ( hAPP @ ( c_Fun_Ocomp @ C @ G @ E @ B ) @ A ) )
= ( hAPP @ ( c_Fun_Ocomp @ C @ F @ E @ ( hAPP @ ( c_Fun_Ocomp @ G @ F @ C @ D ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
thf(1907,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
thf(2274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1105,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(4778,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(486,axiom,
class_Groups_Omonoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(2682,plain,
class_Groups_Omonoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(802,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(3744,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(697,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(3353,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(513,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
thf(2745,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(2703,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(4238,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(4539,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__int__split) ).
thf(3442,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(666,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
thf(3263,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(67,axiom,
! [A: $i] :
( ( class_Rings_Oring__1 @ A )
=> ( ( c_Int_Oring__1__class_Oof__int @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__1) ).
thf(1287,plain,
! [A: $i] :
( ( class_Rings_Oring__1 @ A )
=> ( ( c_Int_Oring__1__class_Oof__int @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
thf(1985,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(4422,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(628,axiom,
class_SEQ_Ocomplete__space @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__SEQ_Ocomplete__space) ).
thf(3131,plain,
class_SEQ_Ocomplete__space @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(72,axiom,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
thf(1298,plain,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(764,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oone @ B )
=> ( ( ( c_Groups_Oone__class_Oone @ B )
= A )
<=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(3617,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oone @ B )
=> ( ( ( ( c_Groups_Oone__class_Oone @ B )
= A )
=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Groups_Oone__class_Oone @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(1330,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(1860,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(352,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatceiling @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
thf(2217,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatceiling @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(1323,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(3653,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(77,axiom,
! [A: $i] :
( ( class_Power_Opower @ A )
=> ( ( c_Power_Opower__class_Opower @ A )
= ( c_Power_Opower_Opower @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Otimes__class_Otimes @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
thf(1313,plain,
! [A: $i] :
( ( class_Power_Opower @ A )
=> ( ( c_Power_Opower__class_Opower @ A )
= ( c_Power_Opower_Opower @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Otimes__class_Otimes @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(968,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(4275,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(987,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(4349,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ? [C: $i] :
( ( B
= ( c_Nat_OSuc @ C ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(714,axiom,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(3410,plain,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
thf(2185,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(1006,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(4428,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(10,axiom,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
thf(1132,plain,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(1800,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(2169,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Osemiring__1 @ B )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__Suc) ).
thf(1609,plain,
! [A: $i,B: $i] :
( ( class_Rings_Osemiring__1 @ B )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(680,axiom,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(3312,plain,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(1773,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != E )
=> ( ( c_Fun_Oswap @ C @ B @ F @ D @ ( c_Fun_Oswap @ C @ B @ D @ E @ ( c_Fun_Oswap @ C @ B @ F @ D @ A ) ) )
= ( c_Fun_Oswap @ C @ B @ F @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__triple) ).
thf(1963,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != E )
=> ( ( c_Fun_Oswap @ C @ B @ F @ D @ ( c_Fun_Oswap @ C @ B @ D @ E @ ( c_Fun_Oswap @ C @ B @ F @ D @ A ) ) )
= ( c_Fun_Oswap @ C @ B @ F @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(702,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(3374,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__realpow__diff) ).
thf(3385,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(4617,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(18,axiom,
class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
thf(1147,plain,
class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
thf(1247,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) )
& ( ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(2049,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(1070,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(4664,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).
thf(2767,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).
thf(1741,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(613,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0__le__iff) ).
thf(3084,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ ( c_RComplete_Onatceiling @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__mono) ).
thf(2635,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ ( c_RComplete_Onatceiling @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(726,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(3470,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(798,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(3734,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq) ).
thf(3014,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(289,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatfloor @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
thf(2024,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_RComplete_Onatfloor @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
<=> ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(4632,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
=> ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
& ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
& ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(994,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(4383,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(2301,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(749,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(3557,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(998,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(4400,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(976,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(4302,plain,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(842,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(3866,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(2533,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Int_Oring__1__class_Oof__int @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__of__nat__eq) ).
thf(1232,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Int_Oring__1__class_Oof__int @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(668,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(3268,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).
thf(2829,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_RComplete_Onatfloor @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
thf(3788,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_RComplete_Onatfloor @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_RComplete_Onatfloor @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(1056,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A )
& ! [D: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth__unique) ).
thf(4595,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
= A )
& ! [D: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ B )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(4411,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(685,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(3322,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(1450,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(707,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add) ).
thf(3393,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(675,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
<=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).
thf(3295,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ C ) ) ) ) )
& ( ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(550,axiom,
! [A: $i] :
( ( hAPP @ c_Int_Onat @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__int) ).
thf(2893,plain,
! [A: $i] :
( ( hAPP @ c_Int_Onat @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
thf(1136,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(738,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(3525,plain,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
thf(2291,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Orderings_Oorder @ C )
& ( class_Orderings_Oorder @ B ) )
=> ( ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ B @ D @ E )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ A @ D ) @ ( hAPP @ A @ E ) ) )
=> ( c_Orderings_Oorder__class_Ostrict__mono @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__monoI) ).
thf(4162,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Orderings_Oorder @ C )
& ( class_Orderings_Oorder @ B ) )
=> ( ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ B @ D @ E )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ A @ D ) @ ( hAPP @ A @ E ) ) )
=> ( c_Orderings_Oorder__class_Ostrict__mono @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).
thf(1302,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(1664,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1091,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(4733,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ C )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1) ).
thf(2259,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ C )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(638,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle) ).
thf(3163,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le) ).
thf(2650,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(727,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
thf(3473,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(793,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
thf(3702,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) )
<=> ( B
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div__lemma) ).
thf(1828,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) )
=> ( B
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) ) )
& ( ( B
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(877,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(3973,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(1978,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
thf(1677,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(435,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(2540,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(293,axiom,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
thf(2034,plain,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(862,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
<=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(3923,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) )
& ( ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(616,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__iff) ).
thf(3093,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(918,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(4115,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(155,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero) ).
thf(1581,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
thf(2777,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono2) ).
thf(4783,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(635,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(3152,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1043,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(4556,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(308,axiom,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
thf(2073,plain,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(576,axiom,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
thf(2964,plain,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(1087,axiom,
! [A: $i] :
( ( c_SEQ_Osubseq @ A )
<=> ! [B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__def) ).
thf(4718,plain,
! [A: $i] :
( ( ( c_SEQ_Osubseq @ A )
=> ! [B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) ) ) )
& ( ! [B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) ) )
=> ( c_SEQ_Osubseq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(1896,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(1447,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(732,axiom,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
thf(3505,plain,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
thf(3036,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(785,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6a) ).
thf(3676,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(856,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(3906,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(2718,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(1021,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(4483,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(3068,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__le__0__iff) ).
thf(1377,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
thf(2618,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_RComplete_Onatfloor @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).
thf(3189,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) ) @ ( c_RComplete_Onatfloor @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
thf(3739,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(989,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ! [E: $i] : ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ E ) @ ( hAPP @ C @ ( c_Nat_OSuc @ E ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lift__Suc__mono__less__iff) ).
thf(4364,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ! [E: $i] : ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ E ) @ ( hAPP @ C @ ( c_Nat_OSuc @ E ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
thf(1622,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__mult) ).
thf(2979,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Transcendental_Oln @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
thf(3756,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(4536,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(2242,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_SMT_Oz3div @ A @ B )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_SMT_Oz3div @ A @ B )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_z3div__def) ).
thf(1345,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_SMT_Oz3div @ A @ B )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_SMT_Oz3div @ A @ B )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(2965,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1033,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(4519,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(1083,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ~ ! [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( A
!= ( c_Nat_OSuc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessE) ).
thf(4707,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ~ ! [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( A
!= ( c_Nat_OSuc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ C ) ) @ B ) @ ( c_Fun_Ocomp @ C @ C @ D @ A ) )
= ( c_Fun_Ocomp @ C @ C @ D @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__funpow) ).
thf(3870,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ C ) ) @ B ) @ ( c_Fun_Ocomp @ C @ C @ D @ A ) )
= ( c_Fun_Ocomp @ C @ C @ D @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__eq) ).
thf(1697,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(52,axiom,
class_Rings_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(1242,plain,
class_Rings_Oidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
<=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(3559,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
=> ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
| ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(4285,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
thf(3184,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1017,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(4475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(2586,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) )
& ( ( C
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(581,axiom,
class_Orderings_Oord @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
thf(2982,plain,
class_Orderings_Oord @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1082,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
thf(4700,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(283,axiom,
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__one) ).
thf(2011,plain,
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(724,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
thf(3459,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(756,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(3591,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(185,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Nat_OSuc @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).
thf(1691,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Nat_OSuc @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(111,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
thf(1438,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(641,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(3169,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(837,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(3852,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(2164,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
thf(2905,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(170,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(1636,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(819,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(3795,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(786,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(3679,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(1604,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(561,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(2922,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(3011,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(39,axiom,
class_Rings_Oordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(1206,plain,
class_Rings_Oordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(908,axiom,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__1) ).
thf(4076,plain,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(991,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
thf(4370,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(1049,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ G @ F @ E @ D )
=> ( ( ( hAPP @ C @ ( hAPP @ D @ B ) )
= ( hAPP @ D @ B ) )
=> ( ( hAPP @ ( hAPP @ E @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ G @ A ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ E @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_update__accessor__noop__compE) ).
thf(4576,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ G @ F @ E @ D )
=> ( ( ( hAPP @ C @ ( hAPP @ D @ B ) )
= ( hAPP @ D @ B ) )
=> ( ( hAPP @ ( hAPP @ E @ ( hAPP @ ( c_Fun_Ocomp @ G @ G @ G @ A ) @ C ) ) @ B )
= ( hAPP @ ( hAPP @ E @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(385,axiom,
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).
thf(2307,plain,
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__mult) ).
thf(4031,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(202,axiom,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc) ).
thf(1736,plain,
! [A: $i] :
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(3261,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(1014,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(4466,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(456,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(2601,plain,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(843,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(3867,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(1123,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,axiom,
class_Rings_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(1217,plain,
class_Rings_Oring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(963,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ! [B: $i] :
? [C: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean3) ).
thf(4252,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ! [B: $i] :
? [C: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1666,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(1487,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(3239,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(3134,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(972,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(4284,plain,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(1069,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(4661,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
thf(4044,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(498,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(2705,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(370,axiom,
class_Rings_Olinordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(2264,plain,
class_Rings_Olinordered__idom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
& ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zdiv) ).
thf(2409,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
& ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ! [D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ E ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
& ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(508,axiom,
class_Rings_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(2733,plain,
class_Rings_Osemiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
thf(2805,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
thf(1355,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(2277,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
thf(1174,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(180,axiom,
class_Rings_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1676,plain,
class_Rings_Omult__zero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(656,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power) ).
thf(3233,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(566,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(2937,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(1107,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(4785,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(1027,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(4499,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(3207,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(787,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( B
= ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(3682,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( B
= ( c_Nat_OSuc @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( B
= ( c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
thf(3339,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__power) ).
thf(3778,plain,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) )
=> ( ( c_RComplete_Onatfloor @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
thf(3307,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(1837,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(4053,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(542,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(2872,plain,
class_Orderings_Oorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(1104,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ ( c_Nat_OSuc @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(4776,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ ( c_Nat_OSuc @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(3894,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(1096,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(4746,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3535,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).
thf(2327,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1003,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(4417,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).
thf(2344,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ D ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
thf(1281,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
thf(3033,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ B @ ( hAPP @ c_Int_Onat @ A ) ) )
<=> ( ! [C: $i] :
( ( A
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__nat) ).
thf(3191,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ B @ ( hAPP @ c_Int_Onat @ A ) ) )
=> ( ! [C: $i] :
( ( A
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
& ( ( ! [C: $i] :
( ( A
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(971,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ I @ H @ G @ F ) @ E )
= ( hAPP @ ( c_Fun_Ocomp @ D @ H @ G @ C ) @ B ) )
=> ( ( hAPP @ F @ ( hAPP @ E @ A ) )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(4280,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ I @ H @ G @ F ) @ E )
= ( hAPP @ ( c_Fun_Ocomp @ D @ H @ G @ C ) @ B ) )
=> ( ( hAPP @ F @ ( hAPP @ E @ A ) )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(2873,plain,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(4192,plain,
! [A: $i,B: $i] :
( ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(3810,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(711,axiom,
class_Nat_Osemiring__char__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Nat_Osemiring__char__0) ).
thf(3403,plain,
class_Nat_Osemiring__char__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1088,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(4725,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult2) ).
thf(2663,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
thf(2332,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(2826,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1__strict @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ A ) )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(3137,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1__strict @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ A ) )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(606,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
thf(3065,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(748,axiom,
class_Power_Opower @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(3556,plain,
class_Power_Opower @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Int_Oring__1__class_Oof__int @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ ( hAPP @ c_Int_Onat @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Int_Oring__1__class_Oof__int @ B @ A )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__of__nat) ).
thf(1195,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Int_Oring__1__class_Oof__int @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ ( hAPP @ c_Int_Onat @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Int_Oring__1__class_Oof__int @ B @ A )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(350,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(2211,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(781,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
thf(3667,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(2228,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).
thf(3647,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(323,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__zle__int) ).
thf(2112,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).
thf(1291,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1076,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(4680,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
thf(3799,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2245,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(1983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(4668,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(229,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).
thf(1804,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) )
<=> ( ( D = B )
| ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(2841,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) )
=> ( ( D = B )
| ( C = A ) ) )
& ( ( ( D = B )
| ( C = A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(403,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(2359,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(491,axiom,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
thf(2692,plain,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(4525,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(620,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(3102,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(873,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(3963,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(3078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
thf(1755,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(4109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
thf(2268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
thf(1402,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(797,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
thf(3731,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(3105,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(158,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
thf(1592,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(381,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
thf(2300,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(813,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
thf(3784,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__add) ).
thf(3909,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( hAPP @ ( c_Fun_Ocomp @ D @ D @ D @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(1541,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
thf(3831,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
thf(1143,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ A )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).
thf(1762,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ A )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(664,axiom,
! [A: $i] :
( ! [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) )
<=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat) ).
thf(3254,plain,
! [A: $i] :
( ( ! [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) ) )
& ( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(57,axiom,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
thf(1259,plain,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(3122,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
thf(2990,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(1794,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(488,axiom,
class_RealVector_Ometric__space @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Ometric__space) ).
thf(2685,plain,
class_RealVector_Ometric__space @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
thf(1111,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
thf(2709,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
thf(1878,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(2631,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
thf(1719,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(2537,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(769,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(3632,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).
thf(3746,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ C ) ) ) )
& ( ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(777,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(3650,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(889,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(4012,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(643,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
thf(3176,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(614,axiom,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
thf(3087,plain,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Int_Oring__1__class_Oof__int @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__mult) ).
thf(1182,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Int_Oring__1__class_Oof__int @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(995,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(4389,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).
thf(4545,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1000,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
thf(4406,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(115,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
thf(1446,plain,
class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).
thf(2666,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(251,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(1889,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1036,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(4530,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
thf(3775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(544,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Ometric__space @ B )
=> ( ( c_SEQ_Oconvergent @ B @ A )
=> ( c_SEQ_OCauchy @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convergent__Cauchy) ).
thf(2877,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Ometric__space @ B )
=> ( ( c_SEQ_Oconvergent @ B @ A )
=> ( c_SEQ_OCauchy @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(4582,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(3179,plain,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(713,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(3407,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(650,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
thf(3210,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(2561,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).
thf(4772,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(1739,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(121,axiom,
! [A: $i] :
( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
thf(1461,plain,
! [A: $i] :
( ( ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(1005,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(4425,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(979,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Oincseq @ B @ A )
<=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incseq__def) ).
thf(4315,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( ( c_SEQ_Oincseq @ B @ A )
=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) ) )
=> ( c_SEQ_Oincseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(1424,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(720,axiom,
c_Nat__Transfer_Otransfer__morphism @ tc_Int_Oint @ tc_Nat_Onat @ c_Int_Onat @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__morphism__nat__int) ).
thf(3441,plain,
c_Nat__Transfer_Otransfer__morphism @ tc_Int_Oint @ tc_Nat_Onat @ c_Int_Onat @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(1097,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(4750,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(345,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__eq__of__nat) ).
thf(2196,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(2240,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1095,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(4744,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
thf(1700,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1066,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).
thf(4648,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(719,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ B ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Nat_OSuc @ D ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div_H) ).
thf(3428,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ B ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Nat_OSuc @ D ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
| ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) ) @ B ) )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Nat_OSuc @ D ) ) )
& ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
thf(1810,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(2551,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
<=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
thf(1207,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) )
& ( ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(3671,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(163,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(1612,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1061,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(4621,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(941,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).
thf(4180,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(2317,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
thf(1155,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(4736,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(659,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
!= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
thf(3242,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
!= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(3611,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(2125,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
thf(1478,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(808,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(3770,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(1552,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__eq__zle) ).
thf(2505,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(920,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__int) ).
thf(4120,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(956,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(4231,plain,
class_Groups_Omonoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(767,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(3628,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(193,axiom,
class_Nat_Osemiring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
thf(1715,plain,
class_Nat_Osemiring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(930,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(4152,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(1393,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
thf(2285,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A )
= ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
thf(1114,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(815,axiom,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
thf(3787,plain,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(118,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero) ).
thf(1456,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(4508,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1) ).
thf(2487,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( hAPP @ c_Int_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ A ) @ ( hAPP @ c_Int_Onat @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__distrib) ).
thf(2598,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( hAPP @ c_Int_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ A ) @ ( hAPP @ c_Int_Onat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(60,axiom,
class_Rings_Oring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(1266,plain,
class_Rings_Oring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(905,axiom,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(4068,plain,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(47,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
thf(1231,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
thf(2153,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(2900,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(961,axiom,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(4244,plain,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1020,axiom,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(4482,plain,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(1192,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(2006,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
thf(2497,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(445,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(2566,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(864,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(3937,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1086,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(4717,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(1429,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ D @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
thf(3967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ D @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(661,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
thf(3247,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(4135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(3692,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
thf(1599,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(494,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
thf(2697,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(906,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(4069,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).
thf(3005,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__mult) ).
thf(3920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(700,axiom,
! [A: $i] :
( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
<=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).
thf(3364,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) ) )
& ( ! [B: $i] : ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(2140,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(4086,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(3215,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ( hAPP @ K @ ( hAPP @ J @ I ) )
= ( hAPP @ H @ ( hAPP @ G @ F ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ C @ K ) @ J ) @ I )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ B @ D @ A @ H ) @ G ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(4361,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ( hAPP @ K @ ( hAPP @ J @ I ) )
= ( hAPP @ H @ ( hAPP @ G @ F ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ E @ D @ C @ K ) @ J ) @ I )
= ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ B @ D @ A @ H ) @ G ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).
thf(1525,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(3454,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(1333,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1038,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(4535,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(654,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(3225,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(974,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(4288,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1100,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(4765,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(838,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(3856,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(1712,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).
thf(1170,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(525,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__less__0__conv) ).
thf(2793,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
thf(1167,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
thf(2995,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(430,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
thf(2529,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(200,axiom,
class_Rings_Olinordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1732,plain,
class_Rings_Olinordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(467,axiom,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(2634,plain,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(515,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__add__one__self__le__self) ).
thf(2749,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
thf(1857,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(277,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(1991,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(524,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(2788,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(79,axiom,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1318,plain,
! [A: $i] :
( A
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(3624,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1063,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__nat__conj) ).
thf(4625,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(348,axiom,
class_Orderings_Olinorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
thf(2208,plain,
class_Orderings_Olinorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(910,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(4081,plain,
! [A: $i,B: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(298,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(2043,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(645,axiom,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
thf(3183,plain,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(575,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(2963,plain,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(2368,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(772,axiom,
class_Rings_Osemiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
thf(3639,plain,
class_Rings_Osemiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(557,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2915,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(137,axiom,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
thf(1515,plain,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(895,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
thf(4036,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(477,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
thf(2662,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(32,axiom,
class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
thf(1185,plain,
class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ A )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(2235,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ A )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(17,axiom,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
thf(1146,plain,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(2391,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(2556,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(1483,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) ) @ ( hAPP @ c_Int_Onat @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__distrib__neg) ).
thf(1927,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) ) @ ( hAPP @ c_Int_Onat @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
thf(1374,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(12,axiom,
class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
thf(1135,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(506,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ A )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__int) ).
thf(2729,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ A )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A )
<=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
thf(1648,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A )
=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) )
& ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(4613,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2253,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(3042,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(451,axiom,
class_Power_Opower @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
thf(2585,plain,
class_Power_Opower @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(1055,axiom,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(4594,plain,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(760,axiom,
c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(3607,plain,
c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1008,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(4438,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Nat_OSuc @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth2) ).
thf(2941,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
& ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ ( c_Nat_OSuc @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(997,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(4393,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ) )
& ( ? [C: $i] :
( A
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(3289,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(291,axiom,
! [A: $i] :
( ( hAPP @ c_Int_Onat @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zminus__int) ).
thf(2028,plain,
! [A: $i] :
( ( hAPP @ c_Int_Onat @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(834,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatfloor @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__neg) ).
thf(3839,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatfloor @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(3523,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Oone__class_Oone @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
thf(2734,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(2524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(3396,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
thf(3343,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__if) ).
thf(3158,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(801,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__geq) ).
thf(3741,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
= ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
thf(3319,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oordered__ring @ F )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(771,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(3636,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(2188,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(1620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(670,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(3272,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
= ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(413,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
thf(2398,plain,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(759,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1 @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ A ) )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(3604,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1 @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) ) @ A ) )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) ) @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).
thf(1256,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(2134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(897,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).
thf(4041,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Ometric__space @ C )
=> ( ( c_SEQ_OCauchy @ C @ B )
=> ( ( c_SEQ_Osubseq @ A )
=> ( c_SEQ_OCauchy @ C @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ C @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cauchy__subseq__Cauchy) ).
thf(4144,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Ometric__space @ C )
=> ( ( c_SEQ_OCauchy @ C @ B )
=> ( ( c_SEQ_Osubseq @ A )
=> ( c_SEQ_OCauchy @ C @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ C @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(4341,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(967,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(4268,plain,
! [A: $i] :
( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(505,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__self) ).
thf(2727,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(220,axiom,
class_Groups_Oone @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
thf(1784,plain,
class_Groups_Oone @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(1389,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__self) ).
thf(3081,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
thf(3758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(3945,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(667,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
thf(3266,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(482,axiom,
class_Divides_Osemiring__div @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
thf(2674,plain,
class_Divides_Osemiring__div @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(2016,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1013,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(4465,plain,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ F @ E @ D @ C )
=> ( ( ( hAPP @ B @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ A ) )
=> ( ( hAPP @ ( hAPP @ D @ B ) @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_update__accessor__noopE) ).
thf(3900,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ F @ E @ D @ C )
=> ( ( ( hAPP @ B @ ( hAPP @ C @ A ) )
= ( hAPP @ C @ A ) )
=> ( ( hAPP @ ( hAPP @ D @ B ) @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ H @ G @ F @ E ) @ D )
= ( hAPP @ ( c_Fun_Ocomp @ C @ G @ F @ B ) @ A ) )
=> ! [I: $i] :
( ( hAPP @ E @ ( hAPP @ D @ I ) )
= ( hAPP @ B @ ( hAPP @ A @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(4590,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ H @ G @ F @ E ) @ D )
= ( hAPP @ ( c_Fun_Ocomp @ C @ G @ F @ B ) @ A ) )
=> ! [I: $i] :
( ( hAPP @ E @ ( hAPP @ D @ I ) )
= ( hAPP @ B @ ( hAPP @ A @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(712,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
thf(3404,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(844,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(3868,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Int_Oring__1__class_Oof__int @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__add) ).
thf(1139,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Int_Oring__1__class_Oof__int @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1022,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(4485,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(874,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
thf(3964,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(944,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__power) ).
thf(4186,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Osemiring__1 @ C )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
thf(3051,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
thf(2738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(676,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hAPP @ c_Int_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__div__distrib) ).
thf(3302,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hAPP @ c_Int_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(742,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(3532,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).
thf(2193,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(595,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(3023,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
& ( ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(179,axiom,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ c_Int_Onat @ A ) )
= A ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__nat__eq) ).
thf(1669,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ c_Int_Onat @ A ) )
= A ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
thf(2891,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(796,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).
thf(3726,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(4149,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(937,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(4171,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(958,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(4236,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(780,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(3663,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(586,axiom,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
thf(3002,plain,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(201,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).
thf(1733,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( ( D = C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(3594,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( ( D = C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Int_Oring__1__class_Oof__int @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__power) ).
thf(1239,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Int_Oring__1__class_Oof__int @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(3700,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(901,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(4060,plain,
class_Orderings_Opreorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(2166,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(213,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(1765,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(3579,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(698,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__le__0__conv) ).
thf(3355,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(4245,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
thf(2510,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).
thf(2521,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).
thf(2721,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(2679,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(3251,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__diff) ).
thf(2214,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(230,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(1806,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
thf(2774,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E @ A )
=> ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div) ).
thf(1933,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E @ A )
=> ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) ) )
& ( ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ! [D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ E @ A )
=> ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
thf(2955,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(926,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).
thf(4139,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(568,axiom,
! [A: $i] :
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
thf(2945,plain,
! [A: $i] :
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(4154,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(731,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__int) ).
thf(3500,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
thf(1439,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(268,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero__imp__gt__one) ).
thf(1969,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oln @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
thf(2079,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(2311,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(768,axiom,
class_Orderings_Opreorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
thf(3631,plain,
class_Orderings_Opreorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(1853,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(636,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power__div__base) ).
thf(3155,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(826,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
thf(3815,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(2637,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
thf(3551,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
thf(1117,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(2097,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(669,axiom,
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
thf(3270,plain,
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
thf(2378,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
thf(2896,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(723,axiom,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(3456,plain,
! [A: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(3219,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(1471,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
<=> ! [E: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(2812,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
=> ! [E: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) ) )
& ( ! [E: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(887,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(4009,plain,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1047,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_ga____ @ A ) @ ( hAPP @ v_ga____ @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) ).
thf(4569,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_ga____ @ A ) @ ( hAPP @ v_ga____ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Orderings_Oorder @ E )
& ( class_Orderings_Oorder @ D ) )
=> ( ( c_Orderings_Oorder__class_Ostrict__mono @ D @ E @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__monoD) ).
thf(4064,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Orderings_Oorder @ E )
& ( class_Orderings_Oorder @ D ) )
=> ( ( c_Orderings_Oorder__class_Ostrict__mono @ D @ E @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(4731,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(1010,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(4452,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(3165,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(89,axiom,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
thf(1344,plain,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
<=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
thf(1177,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(2329,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(1688,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).
thf(1339,plain,
! [A: $i,B: $i] :
( ( class_Divides_Osemiring__div @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(4445,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_RComplete_Onatfloor @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor) ).
thf(2610,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_RComplete_Onatfloor @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(388,axiom,
class_Rings_Osemiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(2314,plain,
class_Rings_Osemiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(399,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(2343,plain,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1011,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(4462,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(3073,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(879,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(3977,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(82,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).
thf(1325,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(3614,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
thf(1149,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1068,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(4652,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(436,axiom,
! [A: $i] :
( ( c_Int_Oring__1__class_Oof__int @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__int__eq) ).
thf(2542,plain,
! [A: $i] :
( ( c_Int_Oring__1__class_Oof__int @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(120,axiom,
class_Groups_Ozero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
thf(1460,plain,
class_Groups_Ozero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__le__cancel__iff) ).
thf(2647,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) ) @ ( c_Transcendental_Oln @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(851,axiom,
class_Groups_Ominus @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(3893,plain,
class_Groups_Ominus @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1820,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
thf(1396,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(537,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ B )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self1) ).
thf(2835,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ B )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(301,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
thf(2051,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
thf(2620,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(3110,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(860,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(3917,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(2064,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Oring @ F )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C )
= A ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C )
= A )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
= ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(871,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(3953,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(735,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
thf(3512,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(519,axiom,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
thf(2770,plain,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(2075,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(4232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(401,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(2350,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(992,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(4373,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).
thf(1643,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(564,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(2931,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__le__iff) ).
thf(2288,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(362,axiom,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
thf(2244,plain,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Nat__Transfer_Otsub @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
thf(1775,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Nat__Transfer_Otsub @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
thf(2592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(687,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hAPP @ c_Int_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__0) ).
thf(3325,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hAPP @ c_Int_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(633,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
thf(3142,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(2535,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(2101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oswap @ D @ C @ B @ B @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__self) ).
thf(1726,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Oswap @ D @ C @ B @ B @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(578,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(2967,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( B
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( A
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
thf(1496,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(383,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).
thf(2303,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(3348,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).
thf(2156,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(186,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(1694,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(492,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2693,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(949,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Int_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__nat__eq__int__zless) ).
thf(4209,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Int_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(270,axiom,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(1973,plain,
! [A: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
!= ( c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( c_SEQ_Osubseq @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_seq__suble) ).
thf(4473,plain,
! [A: $i,B: $i] :
( ( c_SEQ_Osubseq @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
thf(1562,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ B ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(168,axiom,
! [A: $i] :
( ( ( hAPP @ c_Int_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__iff) ).
thf(1626,plain,
! [A: $i] :
( ( ( ( hAPP @ c_Int_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( hAPP @ c_Int_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
thf(1203,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__le__iff) ).
thf(2271,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
thf(2652,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(107,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1420,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(296,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__zero__iff) ).
thf(2037,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__comm__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(4319,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__comm__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(1509,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(4113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(672,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B )
= A )
<=> ( ( B
= ( hAPP @ c_Int_Onat @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__iff) ).
thf(3278,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B )
= A )
=> ( ( B
= ( hAPP @ c_Int_Onat @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) )
& ( ( ( B
= ( hAPP @ c_Int_Onat @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(674,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(3292,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(836,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__int) ).
thf(3849,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
thf(2054,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(948,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(4207,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(999,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(4405,plain,
class_Groups_Ozero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(1583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(1758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(25,axiom,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
thf(1166,plain,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(4177,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).
thf(2927,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(3975,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
thf(3048,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1046,axiom,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0) ).
thf(4566,plain,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(935,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(4168,plain,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
thf(2582,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__eq__zless) ).
thf(2715,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(2375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(1743,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1074,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( A
!= ( c_Nat_OSuc @ B ) )
=> ~ ! [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( A
!= ( c_Nat_OSuc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessE) ).
thf(4673,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( A
!= ( c_Nat_OSuc @ B ) )
=> ~ ! [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( A
!= ( c_Nat_OSuc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
thf(3833,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(507,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
thf(2732,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(503,axiom,
class_Rings_Osemiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
thf(2720,plain,
class_Rings_Osemiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(2888,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(2882,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(2689,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(1547,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
thf(1748,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(799,axiom,
( ( c_RComplete_Onatceiling @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).
thf(3737,plain,
( ( c_RComplete_Onatceiling @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
thf(1770,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(3376,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
thf(3640,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(1516,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono) ).
thf(3315,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(835,axiom,
! [A: $i] :
( ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ B ) ) )
<=> ? [B: $i] : ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).
thf(3842,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ B ) ) )
=> ? [B: $i] : ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) ) )
& ( ? [B: $i] : ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1024,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
thf(4490,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
<=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
thf(3112,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) )
& ( ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__zle__neg) ).
thf(1566,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
thf(2143,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oring @ E )
=> ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(855,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
thf(3904,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(1368,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(655,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
thf(3228,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(4469,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(1780,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B ) @ A ) )
& ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A ) @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(1753,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(2407,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(814,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3786,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(61,axiom,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(1267,plain,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(761,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(3608,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).
thf(2850,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
thf(2747,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(3642,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(677,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(3305,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).
thf(4222,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(1785,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
thf(1679,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B )
= A ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B )
= A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(642,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero__imp__ge__one) ).
thf(3174,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Int_Oring__1__class_Oof__int @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ C @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__diff) ).
thf(1218,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Int_Oring__1__class_Oof__int @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ C @ ( c_Int_Oring__1__class_Oof__int @ C @ B ) @ ( c_Int_Oring__1__class_Oof__int @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(1336,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(4409,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
thf(2569,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(1007,axiom,
c_SEQ_Osubseq @ v_f____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f_I1_J) ).
thf(4437,plain,
c_SEQ_Osubseq @ v_f____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oswap @ E @ D @ C @ B @ ( c_Fun_Oswap @ E @ D @ C @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__nilpotent) ).
thf(1716,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Fun_Oswap @ E @ D @ C @ B @ ( c_Fun_Oswap @ E @ D @ C @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(866,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ! [E: $i] : ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ E ) @ ( hAPP @ C @ ( c_Nat_OSuc @ E ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lift__Suc__mono__less) ).
thf(3940,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ! [E: $i] : ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ E ) @ ( hAPP @ C @ ( c_Nat_OSuc @ E ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0__less__iff) ).
thf(1813,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(788,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
thf(3691,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
thf(3334,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(817,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__zero) ).
thf(3791,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2700,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
thf(1186,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(728,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(3475,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1101,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(4768,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(1262,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(49,axiom,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
thf(1235,plain,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__comm__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(3823,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__comm__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(398,axiom,
! [A: $i] :
( ? [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) )
<=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat) ).
thf(2337,plain,
! [A: $i] :
( ( ? [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) ) )
& ( ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ ( hAPP @ c_Int_Onat @ B ) ) ) )
=> ? [B: $i] : ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(3801,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
thf(2219,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(1980,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1901,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(745,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__def) ).
thf(3544,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( c_Nat__Transfer_Otsub @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(830,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ c_Int_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__distrib) ).
thf(3828,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ c_Int_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(923,axiom,
class_Rings_Omult__zero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(4132,plain,
class_Rings_Omult__zero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(392,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__1) ).
thf(2322,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
thf(1538,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(437,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ? [B: $i] :
( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negD) ).
thf(2545,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ? [B: $i] :
( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(554,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(2903,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(422,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(2500,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
thf(1898,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1062,axiom,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(4624,plain,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(391,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle__0) ).
thf(2320,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(449,axiom,
! [A: $i] :
( ( c_Nat_Ofunpow @ A )
= ( c_Nat_Ocompow @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__code__def) ).
thf(2579,plain,
! [A: $i] :
( ( c_Nat_Ofunpow @ A )
= ( c_Nat_Ocompow @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(706,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
thf(3388,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(4093,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ! [D: $i] :
( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
=> ( hBOOL @ ( hAPP @ C @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(954,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( A
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).
thf(4225,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ? [B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( A
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(608,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
thf(3071,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(736,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(3520,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
= ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(4516,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( c_SEQ_Odecseq @ B @ A )
<=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) ) @ ( hAPP @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decseq__def) ).
thf(4257,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( ( ( c_SEQ_Odecseq @ B @ A )
=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) ) @ ( hAPP @ A @ C ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) ) @ ( hAPP @ A @ C ) ) ) )
=> ( c_SEQ_Odecseq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(996,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(4392,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(951,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).
thf(4217,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(483,axiom,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(2675,plain,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ ( c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(2056,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ ( c_Nat_OSuc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(93,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
thf(1358,plain,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(569,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(2948,plain,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatfloor @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__eq) ).
thf(3697,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatfloor @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(538,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(2838,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__subtract) ).
thf(2558,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) )
=> ( ( c_RComplete_Onatfloor @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(876,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(3970,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).
thf(4133,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
thf(2992,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(1536,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(44,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
thf(1221,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
thf(1284,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(2279,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Nat_Osemiring__char__0 @ C )
=> ( ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).
thf(4510,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Nat_Osemiring__char__0 @ C )
=> ( ( ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
thf(2357,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(947,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(4202,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
thf(1585,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
& ( ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1079,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(4695,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__nat) ).
thf(1797,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).
thf(1881,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
thf(2807,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(284,axiom,
class_Groups_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(2013,plain,
class_Groups_Omonoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(969,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(4278,plain,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(314,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ c_Int_Onat @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__le) ).
thf(2088,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ c_Int_Onat @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(1053,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(4587,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(267,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__zle__0__negative) ).
thf(1966,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(493,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2696,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(934,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).
thf(4165,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(574,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
thf(2960,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).
thf(1412,plain,
! [A: $i,B: $i] :
( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1044,axiom,
! [A: $i] :
( ( c_SEQ_Osubseq @ A )
<=> ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__Suc__iff) ).
thf(4559,plain,
! [A: $i] :
( ( ( c_SEQ_Osubseq @ A )
=> ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) ) )
& ( ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) )
=> ( c_SEQ_Osubseq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( D != C )
& ( B != A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(3056,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( D != C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) )
=> ( ( D != C )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(475,axiom,
class_Orderings_Opreorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
thf(2658,plain,
class_Orderings_Opreorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(902,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(4061,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(1998,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(1067,axiom,
class_Power_Opower @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(4651,plain,
class_Power_Opower @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
thf(1839,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__int__eq) ).
thf(3584,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(465,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(2626,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(1316,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1081,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(4698,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__int) ).
thf(1685,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(547,axiom,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(2885,plain,
! [A: $i] :
( ( c_Nat_OSuc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(311,axiom,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
thf(2078,plain,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
<=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(1913,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
=> ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) )
& ( ( B
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(393,axiom,
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
thf(2325,plain,
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(943,axiom,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(4185,plain,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(41,axiom,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
thf(1216,plain,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(349,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
thf(2209,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
thf(1126,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(795,axiom,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
thf(3725,plain,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(2490,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
thf(1189,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__ring__1 @ C )
=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(2305,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(559,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(2919,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
thf(1575,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(4463,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1108,plain,
~ ! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat @ v_f____ ) @ v_ga____ ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1075,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(4678,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(3039,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(1646,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(171,axiom,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
thf(1639,plain,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(4666,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(431,axiom,
class_Orderings_Oorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
thf(2532,plain,
class_Orderings_Oorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) @ B )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self2) ).
thf(1745,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Divides_Osemiring__div @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Divides_Odiv__class_Odiv @ C @ ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) @ B )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(290,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__def) ).
thf(2026,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat )
= ( c_Nat_Osemiring__1__class_Oof__nat @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(984,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(4338,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(3331,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(4261,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(840,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(3864,plain,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(196,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6) ).
thf(1721,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ? [B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(410,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(2389,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(1476,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
thf(2853,plain,
! [A: $i,B: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(2251,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(829,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
thf(3825,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(913,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(4089,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(440,axiom,
( ( c_Transcendental_Oln @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__one) ).
thf(2554,plain,
( ( c_Transcendental_Oln @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(587,axiom,
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0) ).
thf(3003,plain,
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(54,axiom,
! [A: $i] :
( ( class_Rings_Oring__1 @ A )
=> ( ( c_Int_Oring__1__class_Oof__int @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0) ).
thf(1244,plain,
! [A: $i] :
( ( class_Rings_Oring__1 @ A )
=> ( ( c_Int_Oring__1__class_Oof__int @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__cancel__iff) ).
thf(2764,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Transcendental_Oln @ B ) @ ( c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).
thf(4010,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1025,axiom,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(4495,plain,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(3859,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( A != B )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(2526,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( A != B )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(1035,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(4527,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(2934,plain,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(369,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
thf(2262,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
thf(2009,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
thf(2081,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(686,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3324,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C )
= B )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(4321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ G @ F @ E @ D ) @ C )
= B )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1777,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ D ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ D ) @ ( hAPP @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(4759,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ D ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ D ) @ ( hAPP @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
thf(2198,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(818,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
thf(3793,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).
thf(1607,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
thf(1513,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(2120,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(389,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(2315,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(790,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(3694,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(2786,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(1057,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).
thf(4602,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(2796,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(975,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(4293,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(939,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
thf(4175,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(3497,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(950,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(4214,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(758,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Transcendental_Oln @ B )
= ( c_Transcendental_Oln @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__inj__iff) ).
thf(3598,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( ( c_Transcendental_Oln @ B )
= ( c_Transcendental_Oln @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Transcendental_Oln @ B )
= ( c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(70,axiom,
class_Rings_Oring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
thf(1294,plain,
class_Rings_Oring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(2576,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1018,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(4478,plain,
class_Groups_Oone @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(741,axiom,
! [A: $i,B: $i] :
( ( class_SEQ_Ocomplete__space @ B )
=> ( ( c_SEQ_OCauchy @ B @ A )
<=> ( c_SEQ_Oconvergent @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cauchy__convergent__iff) ).
thf(3529,plain,
! [A: $i,B: $i] :
( ( class_SEQ_Ocomplete__space @ B )
=> ( ( ( c_SEQ_OCauchy @ B @ A )
=> ( c_SEQ_Oconvergent @ B @ A ) )
& ( ( c_SEQ_Oconvergent @ B @ A )
=> ( c_SEQ_OCauchy @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1706,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(404,axiom,
class_Orderings_Oord @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(2362,plain,
class_Orderings_Oord @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Oone__class_Oone @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
thf(2162,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ ( c_Groups_Oone__class_Oone @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(355,axiom,
class_Groups_Ominus @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
thf(2230,plain,
class_Groups_Ominus @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int) ).
thf(1893,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) )
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(295,axiom,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
thf(2036,plain,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(775,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
thf(3645,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
thf(2623,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B = A )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(3761,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( B = A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(1161,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(1614,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_SEQ_Ocomplete__space @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( ( c_SEQ_Osubseq @ A )
=> ( c_SEQ_Oconvergent @ C @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ C @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convergent__subseq__convergent) ).
thf(4039,plain,
! [A: $i,B: $i,C: $i] :
( ( class_SEQ_Ocomplete__space @ C )
=> ( ( c_SEQ_Oconvergent @ C @ B )
=> ( ( c_SEQ_Osubseq @ A )
=> ( c_SEQ_Oconvergent @ C @ ( hAPP @ ( c_Fun_Ocomp @ tc_Nat_Onat @ C @ tc_Nat_Onat @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(135,axiom,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1512,plain,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(2683,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(794,axiom,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ c_Int_Onat @ A ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( A
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).
thf(3705,plain,
! [A: $i,B: $i] :
( ( ( B
= ( hAPP @ c_Int_Onat @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( A
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( A
= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
=> ( B
= ( hAPP @ c_Int_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__subtract) ).
thf(1578,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ A ) )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1073,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(4670,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
& ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(2255,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ? [C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
& ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(3997,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(4254,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(357,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(2233,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(619,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(3100,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(570,axiom,
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__1) ).
thf(2951,plain,
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
thf(1876,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(629,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(3132,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(210,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1757,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1050,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Osemiring__1 @ D )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ B @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
thf(4579,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Osemiring__1 @ D )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ ( c_Nat_OSuc @ B ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ B @ ( hAPP @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(990,axiom,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(4367,plain,
! [A: $i,B: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(883,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(3992,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int__left) ).
thf(2003,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(563,axiom,
class_Groups_Oone @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(2930,plain,
class_Groups_Oone @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(4125,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(11,axiom,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
thf(1133,plain,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(582,axiom,
! [A: $i] :
( ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
thf(2983,plain,
! [A: $i] :
( ( ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(841,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(3865,plain,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(167,axiom,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
thf(1625,plain,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(881,axiom,
! [A: $i] :
( ( c_RComplete_Onatceiling @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
thf(3987,plain,
! [A: $i] :
( ( c_RComplete_Onatceiling @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( B
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(2604,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( ( B
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(725,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__nat__nat__iff) ).
thf(3464,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Int_Onat @ B )
= ( hAPP @ c_Int_Onat @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
thf(1380,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Power_Opower @ C )
=> ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) )
& ( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
thf(2815,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(510,axiom,
( ( c_RComplete_Onatfloor @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__zero) ).
thf(2736,plain,
( ( c_RComplete_Onatfloor @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(1527,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(691,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(3337,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(19,axiom,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
thf(1148,plain,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(4146,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ A )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ D @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).
thf(2751,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
=> ( ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ A )
& ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ D @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(2334,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(847,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Orderings_Oorder @ E )
& ( class_Orderings_Olinorder @ D ) )
=> ( ( c_Orderings_Oorder__class_Ostrict__mono @ D @ E @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__mono__less) ).
thf(3875,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Orderings_Oorder @ E )
& ( class_Orderings_Olinorder @ D ) )
=> ( ( c_Orderings_Oorder__class_Ostrict__mono @ D @ E @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ C @ B ) @ ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(886,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_f____ @ A ) @ ( hAPP @ v_f____ @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) ).
thf(4007,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ v_f____ @ A ) @ ( hAPP @ v_f____ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
thf(2091,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(1891,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(1473,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(297,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__neg) ).
thf(2040,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_RComplete_Onatceiling @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(480,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(2668,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(3309,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(3982,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(3145,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(892,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(4029,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(3328,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(977,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(4303,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(853,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(3897,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
thf(1816,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(130,axiom,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
thf(1495,plain,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1064,axiom,
class_Rings_Osemiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(4631,plain,
class_Rings_Osemiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Orderings_Oorder @ E )
& ( class_Orderings_Olinorder @ D ) )
=> ( ( c_Orderings_Oorder__class_Ostrict__mono @ D @ E @ C )
=> ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__mono__eq) ).
thf(3804,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Orderings_Oorder @ E )
& ( class_Orderings_Olinorder @ D ) )
=> ( ( c_Orderings_Oorder__class_Ostrict__mono @ D @ E @ C )
=> ( ( ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(932,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(4157,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(2070,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(2572,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(596,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
thf(3030,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(894,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(4034,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ D @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).
thf(3045,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ D @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(733,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
thf(3506,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2) ).
thf(3673,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Divides_Osemiring__div @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Divides_Odiv__class_Odiv @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ ( c_Divides_Odiv__class_Odiv @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(2021,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(1930,plain,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(238,axiom,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1827,plain,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(62,axiom,
class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
thf(1268,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
thf(1152,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
thf(3772,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(955,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(4229,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(744,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__eq__zero__iff) ).
thf(3538,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( ( c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(3886,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(865,axiom,
class_Nat_Osemiring__char__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
thf(3939,plain,
class_Nat_Osemiring__char__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(249,axiom,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
thf(1880,plain,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
thf(1299,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C ) @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(3076,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1028,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
thf(4501,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).
thf(1120,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
thf(3341,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
thf(1236,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(2502,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
thf(2127,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Orderings_Oorder @ E )
& ( class_Orderings_Olinorder @ D ) )
=> ( ( c_Orderings_Oorder__class_Ostrict__mono @ D @ E @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__mono__less__eq) ).
thf(2159,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( class_Orderings_Oorder @ E )
& ( class_Orderings_Olinorder @ D ) )
=> ( ( c_Orderings_Oorder__class_Ostrict__mono @ D @ E @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ B ) ) @ ( hAPP @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(699,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zless__0) ).
thf(3362,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( c_Nat_OSuc @ A ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(530,axiom,
( ( c_RComplete_Onatfloor @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__one) ).
thf(2810,plain,
( ( c_RComplete_Onatfloor @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1352,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(627,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( c_Nat__Transfer_Otsub @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).
thf(3128,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ c_Int_Onat @ B ) @ ( hAPP @ c_Int_Onat @ A ) )
= ( hAPP @ c_Int_Onat @ ( c_Nat__Transfer_Otsub @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(922,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__implies__Suc) ).
thf(4129,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ? [B: $i] :
( A
= ( c_Nat_OSuc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(271,axiom,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(1977,plain,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Int_Oring__1__class_Oof__int @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__minus) ).
thf(1129,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Int_Oring__1__class_Oof__int @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Oring__1__class_Oof__int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
thf(2803,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ D ) @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(4242,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(552,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(2898,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(993,axiom,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(4382,plain,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).
thf(3411,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(2485,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
thf(2265,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(4118,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(4506,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(904,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(4066,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(3245,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(593,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(3020,plain,
class_Orderings_Olinorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(417,axiom,
class_Groups_Ozero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(2484,plain,
class_Groups_Ozero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(495,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(2699,plain,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(1505,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(104,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
thf(1399,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A ) )
=> ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(912,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(4088,plain,
class_Orderings_Oorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).
thf(3950,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_Fun_Ocomp @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(1052,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(4584,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(309,axiom,
class_Groups_Ominus @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).
thf(2074,plain,
class_Groups_Ominus @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(151,axiom,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1565,plain,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1042,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(4547,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(460,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero__iff) ).
thf(2615,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(4189,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(343,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(2191,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(1468,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(938,axiom,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(4174,plain,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(3575,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(2177,plain,
! [A: $i,B: $i] :
( ( ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Nat_OSuc @ B )
= ( c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
thf(3753,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
thf(3526,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult2__eq) ).
thf(3960,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(740,axiom,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ v_r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp) ).
thf(3528,plain,
hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ v_r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( c_Fun_Ocomp @ C @ C @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow_Osimps_I2_J) ).
thf(4335,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ ( c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( c_Fun_Ocomp @ C @ C @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Nat_Ocompow @ C @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
thf(2879,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(2640,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(444,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
thf(2563,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ B ) ) @ ( hAPP @ ( c_RealDef_Oreal @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(3626,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
thf(3096,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(2206,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__mult) ).
thf(2018,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(2832,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
thf(1848,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
thf(2059,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(359,axiom,
( ( hAPP @ c_Int_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0) ).
thf(2238,plain,
( ( hAPP @ c_Int_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(1094,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(4742,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(978,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(4313,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(2106,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(747,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__distrib) ).
thf(3553,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ B ) )
=> ( ( hAPP @ c_Int_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ c_Int_Onat @ B ) ) @ ( hAPP @ c_Int_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
thf(3669,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(2771,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(4871,plain,
$false,
inference(e,[status(thm)],[2094,2612,1823,1633,3167,3581,2595,4682,4728,1549,1554,3021,1322,2822,3873,4571,3053,3008,2109,2031,3661,1767,3399,1995,3930,4169,3798,1559,4022,1729,4183,2921,3477,1818,1295,3990,1924,3317,2644,3509,2953,3108,4711,4326,1305,4487,2363,1855,1200,4714,2309,2976,2117,2104,4075,1290,2231,2622,3813,2381,2395,2908,2062,1443,1808,2659,3417,4697,2248,3912,3098,2671,1544,2676,2014,2099,2282,2114,1142,1269,1971,1793,3402,3382,4479,4532,1173,1486,3017,4739,2686,1310,2035,3942,2740,4026,4220,1164,1275,2712,4279,3781,4058,1640,3313,3577,2146,1788,1426,3217,4090,1655,1327,4564,1919,1988,3414,1342,3121,1507,1222,4762,1458,3370,3350,3994,4496,3088,3947,1921,1359,1386,2516,2400,1228,4775,2957,3836,4343,3236,3634,2046,1243,3915,2548,3249,4079,1441,3140,1724,4607,1366,1803,3880,3878,1904,1265,1703,3820,1709,2916,3425,3275,4692,1907,2274,4778,2682,3744,3353,2745,2703,4238,4539,3442,3263,1287,1985,4422,3131,1298,3617,1330,1860,2217,1323,3653,1313,4275,4349,3410,2185,4428,1132,1800,2169,1609,3312,1773,1963,3374,3385,4617,1147,1247,2049,4664,2767,1741,3084,2635,3470,3734,3014,2024,4632,4383,2301,3557,4400,4302,3866,2533,1232,3268,2829,3788,4595,4411,3322,1450,3393,3295,2893,1136,3525,2291,4162,1302,1664,4733,2259,3163,2650,3473,3702,1828,3973,1978,1677,2540,2034,3923,3093,4115,1581,2777,4783,3152,4556,2073,2964,4718,1896,1447,3505,3036,3676,3906,2718,4483,3068,1377,2618,3189,3739,4364,1622,2979,3756,4536,2242,1345,2965,4519,4707,3870,1697,1242,3559,4285,3184,4475,2586,2982,4700,2011,3459,3591,1691,1438,3169,3852,2164,2905,1636,3795,3679,1604,2922,3011,1206,4076,4370,4576,2307,4031,1736,3261,4466,2601,3867,1123,1217,4252,1666,1487,3239,3134,4284,4661,4044,2705,2264,2409,2733,2805,1355,2277,1174,1676,3233,2937,4785,4499,3207,3682,3339,3778,3307,1837,4053,2872,4776,3894,4746,3535,2327,4417,2344,1281,3033,3191,4280,2873,4192,3810,3403,4725,2663,2332,2826,3137,3065,3556,1195,2211,3667,2228,3647,2112,1291,4680,3799,2245,1983,4668,1804,2841,2359,2692,4525,3102,3963,3078,1755,4109,2268,1402,3731,3105,1592,2300,3784,3909,1541,3831,1143,1762,3254,1259,3122,2990,1794,2685,1111,2709,1878,2631,1719,2537,3632,3746,3650,4012,3176,3087,1182,4389,4545,4406,1446,2666,1889,4530,3775,2877,4582,3179,3407,3210,2561,4772,1739,1461,4425,4315,1424,3441,4750,2196,2240,4744,1700,4648,3428,1810,1791,2551,1207,3671,1612,4621,4180,2317,1155,4736,3242,3611,2125,1478,3770,1552,2505,4120,4231,3628,1715,4152,1393,2285,1114,3787,1456,4508,2487,2598,1266,4068,1231,2153,2900,4244,4482,1192,2006,2497,2566,3937,4717,1429,3967,3247,4135,3692,1599,2697,4069,3005,3920,3364,2140,4086,3215,4361,1525,3454,1333,4535,3225,4288,4765,3856,1712,1170,2793,1167,2995,2529,1732,2634,2749,1857,1991,2788,1318,3624,4625,2208,4081,2043,3183,2963,2368,3639,2915,1515,4036,2662,1185,2235,1146,2391,2556,1483,1927,1374,1135,2729,1648,4613,2253,3042,2585,4594,3607,4438,2941,4393,3289,2028,3839,3523,2734,2524,3396,3343,3158,3741,3319,3636,2188,1620,3272,2398,3604,1256,2134,4041,4144,4341,4268,2727,1784,1389,3081,3758,3945,3266,2674,2016,4465,3900,4590,3404,3868,1139,4485,3964,4186,3051,2738,3302,3532,2193,3023,1669,2891,3726,4149,4171,4236,3663,3002,1733,3594,1239,3700,4060,2166,1765,3579,3355,4245,2510,2521,2721,2679,3251,2214,1806,2774,1933,2955,4139,2945,4154,3500,1439,1969,2079,2311,3631,1853,3155,3815,2637,3551,1117,2097,3270,2378,2896,3456,3219,1471,2812,4009,4569,4064,4731,4452,3165,1344,1177,2329,1688,1339,4445,2610,2314,2343,4462,3073,3977,1325,3614,1149,4652,2542,1460,2647,3893,1820,1396,2835,2051,2620,3110,3917,2064,3953,3512,2770,2075,4232,2350,4373,1643,2931,2288,2244,1775,2592,3325,3142,2535,2101,1726,2967,1496,2303,3348,2156,1694,2693,4209,1973,4473,1562,1626,1203,2271,2652,1420,2037,4319,1509,4113,3278,3292,3849,2054,4207,4405,1583,1758,1166,4177,2927,3975,3048,4566,4168,2582,2715,2375,1743,4673,3833,2732,2720,2888,2882,2689,1547,1748,3737,1770,3376,3640,1516,3315,3842,4490,3112,1566,2143,3904,1368,3228,4469,1780,1753,2407,3786,1267,3608,2850,2747,3642,3305,4222,1785,1679,3174,1218,1336,4409,2569,4437,1716,3940,1813,3691,3334,3791,2700,1186,3475,4768,1262,1235,3823,2337,3801,2219,1980,1901,3544,3828,4132,2322,1538,2545,2903,2500,1898,4624,2320,2579,3388,4093,4225,3071,3520,4516,4257,4392,4217,2675,2056,1358,2948,3697,2838,2558,3970,4133,2992,1536,1221,1284,2279,4510,2357,4202,1585,4695,1797,1881,2807,2013,4278,2088,4587,1966,2696,4165,2960,1412,4559,3056,2658,4061,1998,4651,1839,3584,2626,1316,4698,1685,2885,2078,1913,2325,4185,1216,2209,1126,3725,2490,1189,2305,2919,1575,4463,1108,4678,3039,1646,1639,4666,2532,1745,2026,4338,3331,4261,3864,1721,2389,1476,2853,2251,3825,4089,2554,3003,1244,2764,4010,4495,3859,2526,4527,2934,2262,2009,2081,3324,4321,1777,4759,2198,3793,1607,1513,2120,2315,3694,2786,4602,2796,4293,4175,3497,4214,3598,1294,2576,4478,3529,1706,2362,2162,2230,1893,2036,3645,2623,3761,1161,1614,4039,1512,2683,3705,1578,4670,2255,3997,4254,2233,3100,2951,1876,3132,1757,4579,4367,3992,2003,2930,4125,1133,2983,3865,1625,3987,2604,3464,1380,2815,2736,1527,3337,1148,4146,2751,2334,3875,4007,2091,1891,1473,2040,2668,3309,3982,3145,4029,3328,4303,3897,1816,1495,4631,3804,4157,2070,2572,3030,4034,3045,3506,3673,2021,1930,1827,1268,1152,3772,4229,3538,3886,3939,1880,1299,3076,4501,1120,3341,1236,2502,2127,2159,3362,2810,1352,3128,4129,1977,1129,2803,4242,2898,4382,3411,2485,2265,4118,4506,4066,3245,3020,2484,2699,1505,1399,4088,3950,4584,2074,1565,4547,2615,4189,2191,1468,4174,3575,2177,3753,3526,3960,3528,4335,2879,2640,2563,3626,3096,2206,2018,2832,1848,2059,2238,4742,4313,2106,3553,3669,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW209+1 : TPTP v8.1.2. Released v5.2.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 22:05:28 EDT 2023
% 0.20/0.36 % CPUTime :
% 0.81/0.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.84/1.05 % [INFO] Parsing done (285ms).
% 1.84/1.06 % [INFO] Running in sequential loop mode.
% 2.41/1.26 % [INFO] eprover registered as external prover.
% 2.41/1.26 % [INFO] cvc4 registered as external prover.
% 2.41/1.26 % [INFO] Scanning for conjecture ...
% 2.83/1.40 % [INFO] Found a conjecture and 1160 axioms. Running axiom selection ...
% 3.64/1.61 % [INFO] Axiom selection finished. Selected 1105 axioms (removed 55 axioms).
% 4.91/1.96 % [INFO] Problem is first-order (TPTP FOF).
% 5.15/1.99 % [INFO] Type checking passed.
% 5.15/1.99 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 25.35/6.84 % External prover 'e' found a proof!
% 25.35/6.84 % [INFO] Killing All external provers ...
% 25.36/6.84 % Time passed: 6378ms (effective reasoning time: 5784ms)
% 25.36/6.84 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 25.36/6.85 % Axioms used in derivation (1105): fact_all__nat, arity_fun__Orderings_Oorder, fact_nat_Osimps_I3_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, arity_Int__Oint__Rings_Ocomm__semiring, fact_natfloor__power, fact_zle__refl, fact_transfer__nat__int__numerals_I1_J, fact_minus__mult__left, fact_neg__le__0__iff__le, fact_add__le__less__mono, fact_zadd__int, fact_mult__strict__left__mono__neg, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_real__squared__diff__one__factored, fact_int__mult, fact_xt1_I1_J, fact_div__mult__mult1, fact_le__SucI, fact_real__le__refl, fact_int__0, fact_of__int__minus, fact_le__imp__diff__is__add, 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_power__strict__decreasing, fact_natfloor__real__of__nat, 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_natfloor__add, fact_mult__1__left, fact_diff__0__eq__0, fact_nat__power__eq, fact_of__nat__add, fact_mult__less__cancel__left__disj, fact_diff__add__inverse, fact_Suc__lessE, fact_of__int__power, fact_power__inject__base, fact_le__eq__less__or__eq, fact_xt1_I4_J, fact_termination__basic__simps_I5_J, fact_odd__nonzero, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_mult__nonneg__nonpos, fact_q__pos__lemma, 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_lift__Suc__mono__less, fact_transfer__morphism__nat__int, fact_zdiv__eq__0__iff, fact_power__power__power, fact_real__of__nat__zero, fact_mult__left_Ominus, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_of__int__int__eq, fact_zero__less__int__conv, fact_one__is__add, fact_diff__le__mono2, arity_Int__Oint__Rings_Olinordered__semiring__strict, fact_minus__mult__right, fact_real__of__nat__diff, fact_transfer__int__nat__quantifiers_I2_J, fact_zminus__zminus, fact_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_add__leD1, fact_split__mult__neg__le, fact_zmult__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_zero__less__power, fact_add__less__mono, fact_mult__eq__0__iff, fact_zpower__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_Suc__nat__eq__nat__zadd1, fact_zless__nat__conj, arity_RealDef__Oreal__Groups_Ominus, arity_Nat__Onat__Orderings_Oorder, fact_mult__right__less__imp__less, fact_n__less__m__mult__n, fact_ln__eq__zero__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_of__int__add, arity_Int__Oint__Rings_Osemiring__1, fact_ln__inj__iff, 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, fact_zless__int, fact_natceiling__le, fact_ln__less__cancel__iff, arity_Nat__Onat__Groups_Omonoid__mult, fact_power__increasing, fact_diff__Suc__less, fact_transfer__int__nat__numerals_I2_J, fact_real__add__le__0__iff, fact_mult__0, fact_real__0__less__add__iff, fact_convergent__subseq__convergent, fact_int__eq__iff, fact_order__less__asym_H, fact_not__zle__0__negative, arity_Nat__Onat__Rings_Ozero__neq__one, fact_div__nonpos__pos__le0, fact_linorder__antisym__conv2, fact_zero__less__diff, fact_diff__diff__cancel, fact_mult__mono, fact_gr0__conv__Suc, fact_leI, fact_field__power__not__zero, fact_natceiling__le__eq__one, arity_RealDef__Oreal__Rings_Oidom, fact_Suc__le__mono, fact_zero__le__natfloor, fact_order__eq__refl, fact_add__right__imp__eq, fact_realpow__two__diff, fact_funpow__add, fact_nat__add__right__cancel, fact_neg__le__iff__le, fact_linorder__neqE, fact_o__eq__elim, arity_RealDef__Oreal__Groups_Omonoid__add, fact_neg__0__less__iff__less, fact_div__le__dividend, fact_mult__le__mono2, fact_Suc__diff__diff, fact_le__neq__implies__less, fact_mult__left__le__imp__le, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, fact_add__pos__nonneg, fact_transfer__nat__int__numerals_I2_J, fact_zero__le__one, arity_Int__Oint__Orderings_Oord, fact_nat__add__left__cancel__less, fact_int__0__less__1, fact_le__minus__iff, fact_o__apply, fact_lift__Suc__mono__less__iff, fact_mult_Oadd__right, fact_mult_Ominus__right, fact_swap__triple, fact_le__add__iff2, fact_mult__eq__self__implies__10, fact_of__int__1, fact_zle__linear, fact_nat__add__distrib, arity_RealDef__Oreal__Rings_Ocomm__ring__1, 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_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_of__nat__less__imp__less, fact_linorder__neqE__linordered__idom, fact_lemma__realpow__diff, fact_ex__nat, fact_neg__less__0__iff__less, fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J, fact_mult__strict__left__mono, fact_zero__le__mult__iff, arity_Int__Oint__Groups_Ozero, fact_swap__commute, fact_real__of__nat__zero__iff, fact_seq__suble, fact_div__1, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, fact_div__if, fact_transfer__nat__int__relations_I1_J, fact_zadd__left__mono, fact_sum__squares__le__zero__iff, arity_Int__Oint__Rings_Olinordered__semiring__1__strict, fact_mult__right_Ozero, fact_mult__le__cancel__left__neg, fact_minus__real__def, fact_add__le__imp__le__left, fact_nat__mult__distrib__neg, fact_sum__squares__ge__zero, fact_add__increasing2, fact_split__div_H, fact_natceiling__mono, fact_linorder__antisym__conv1, arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, fact_add__nonneg__eq__0__iff, fact_lessE, fact_zdiv__zero, fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, fact_mult_Ozero__left, fact_real__mult__commute, fact_split__div__lemma, fact_gr0I, arity_Int__Oint__Rings_Olinordered__ring, fact_le__funD, fact_add__right__mono, fact_le__fun__def, fact_reals__Archimedean4, fact_power__minus, fact_of__nat__mult, fact_of__nat__aux_Osimps_I1_J, fact_real__of__nat__less__iff, fact_one__less__power, fact_power__strict__increasing, fact_one__le__power, fact_mult__eq__1__iff, fact_even__less__0__iff, fact_self__quotient__aux1, fact_power__commutes, fact_power__real__of__nat, fact_le__natfloor__eq__one, arity_Int__Oint__Groups_Ocomm__monoid__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_RealDef__Oreal__Groups_Omonoid__mult, fact_add__0__left, fact_add__mono, fact_nonneg1__imp__zdiv__pos__iff, fact_add__eq__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_add__0__iff, fact_int__int__eq, fact_zero__less__imp__eq__int, fact_nat__less__real__le, fact_funpow__code__def, fact_real__mult__assoc, fact_nat__0, arity_Nat__Onat__Rings_Osemiring__0, fact_diff__le__self, fact_nat__diff__distrib, arity_Nat__Onat__Rings_Oordered__comm__semiring, fact_power__eq__0__iff, fact_diff__Suc__eq__diff__pred, fact_nat__mult__1__right, fact_mult__left_Odiff, fact_zero__le__natceiling, arity_Int__Oint__Rings_Oidom, fact_ord__less__eq__trans, fact_zero__reorient, fact_mult__right_Odiff, fact_le__iff__add, fact_one__reorient, fact_diff__commute, fact_minus__less__iff, fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J, fact_xt1_I9_J, fact_less__add__eq__less, fact_minus__mult__commute, fact_linorder__less__linear, fact_natceiling__zero, fact_order__less__imp__not__less, fact_int__zle__neg, fact_add__lessD1, fact_div__mult__self1__is__id, fact_add__le__mono1, fact_LIMSEQ__inverse__realpow__zero__lemma, fact_less__eq__nat_Osimps_I1_J, fact_strict__monoI, fact_lessI, fact_zero__le__square, fact_transfer__int__nat__numerals_I1_J, fact_pos__imp__zdiv__neg__iff, arity_Int__Oint__Groups_Oordered__ab__group__add, arity_RealDef__Oreal__Rings_Olinordered__idom, fact_termination__basic__simps_I4_J, fact_minus__le__iff, fact_of__int__mult, arity_RealDef__Oreal__Groups_Ocancel__semigroup__add, fact_add__0__right, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_split__mult__pos__le, fact_div__nonneg__neg__le0, fact_nat_Oinject, fact_mult__left__le__one__le, arity_Int__Oint__Rings_Oring__no__zero__divisors, fact_nat__le__real__less, fact_not__add__less2, fact_decseq__def, fact_less__or__eq__imp__le, fact_Suc__less__SucD, fact_power__strict__mono, fact_int__div__less__self, fact_div__neg__neg__trivial, arity_Int__Oint__Rings_Oordered__cancel__semiring, fact_real__add__minus__iff, fact_zadd__strict__right__mono, fact_q__neg__lemma, fact_minus__apply, fact_zadd__zless__mono, fact_split__div, fact_mult__pos__neg, fact_power__gt1__lemma, fact_funpow__swap1, fact_nat__eq__add__iff2, fact_real__le__eq__diff, fact_mult__less__mono1, fact_Suc__leI, fact_add__neg__nonpos, fact_split__zdiv, fact_pos__imp__zdiv__pos__iff, fact_unique__quotient__lemma__neg, arity_RealDef__Oreal__Rings_Ozero__neq__one, fact_diff__less, fact_convex__bound__lt, fact_comp__cong, fact_mult__right__mono__neg, fact_zpower__zadd__distrib, fact_div__mult2__eq, fact_le__add2, fact_minus__nat_Odiff__0, fact_zadd__assoc, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J, arity_Nat__Onat__Orderings_Opreorder, fact_div__mult__self2, fact_mult__pos__neg2, fact_nat__0__le, arity_RealDef__Oreal__RealVector_Oreal__normed__algebra, fact_not__less__less__Suc__eq, fact_power__Suc2, fact_comp__funpow, fact_nat__mult__1, fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J, fact_diff__is__0__eq_H, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_pos__zmult__eq__1__iff, arity_Int__Oint__Groups_Ocancel__semigroup__add, fact_of__nat__less__iff, fact_zadd__int__left, fact_order__antisym, fact_xt1_I10_J, fact_less__irrefl__nat, fact_mult_Oprod__diff__prod, fact_zle__diff1__eq, arity_Nat__Onat__Nat_Osemiring__char__0, fact_order__less__imp__not__eq2, fact_Suc__lessD, fact_ln__le__cancel__iff, fact_natfloor__neg, fact_Suc__n__not__le__n, fact_of__nat__diff, fact_of__int__less__iff, fact_ln__gt__zero__imp__gt__one, fact_add__left__imp__eq, arity_Int__Oint__Rings_Osemiring__0, fact_trans__less__add2, fact_less__Suc__eq__le, fact_of__int__le__iff, fact_real__zero__not__eq__one, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_zpower__zpower, fact_add__leD2, fact_mult__mono_H, fact_real__add__mult__distrib, fact_real__of__nat__le__zero__cancel__iff, arity_Nat__Onat__Rings_Ocomm__semiring__1, fact_realpow__minus__mult, fact_less__natfloor, fact_order__refl, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_of__nat__power, fact_add__diff__assoc, arity_Nat__Onat__Power_Opower, fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_not__less0, fact_nat__aux__def, fact_zdiv__mono1__neg, arity_Int__Oint__Power_Opower, fact_gr0__implies__Suc, fact_ln__ge__zero, arity_Int__Oint__Nat_Osemiring__char__0, fact_nat__diff__split, fact_zadd__0, fact_negative__zless, fact_xt1_I5_J, arity_RealDef__Oreal__Rings_Omult__zero, fact_natceiling__one, fact_real__mult__right__cancel, fact_not__one__less__zero, fact_Cauchy__convergent, fact_ln__mult, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, arity_Int__Oint__Groups_Oab__semigroup__mult, fact_mult__left__less__imp__less, fact_diff__mult__distrib2, arity_Nat__Onat__Groups_Ominus, fact_neg__less__iff__less, arity_Int__Oint__Divides_Osemiring__div, fact_less__zeroE, fact_termination__basic__simps_I2_J, fact_int__power, fact_one__le__mult__iff, fact_natceiling__add__one, arity_RealDef__Oreal__Rings_Olinordered__semiring, fact_of__nat__0__less__iff, fact_not__less__eq, fact_nat_Osimps_I2_J, fact_nat__less__iff, fact_mult__le__cancel1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, fact_zero__le__double__add__iff__zero__le__single__add, fact_o__eq__dest, fact_nat__neq__iff, fact_nat__1__eq__mult__iff, fact_add__mult__distrib2, fact_eq__add__iff1, arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, fact_nat__diff__split__asm, fact_add__left__cancel, arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, fact_neg__less__nonneg, arity_Nat__Onat__Divides_Osemiring__div, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, arity_Int__Oint__Rings_Oordered__semiring, fact_nat__add__left__cancel__le, fact_not__int__zless__negative, fact_less__imp__neq, arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, fact_xt1_I8_J, fact_power__less__imp__less__base, fact_less__eq__real__def, fact_less__not__refl3, fact_nat__zminus__int, fact_add__right__cancel, fact_mult__strict__mono_H, fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J, fact_nat__one__le__power, fact_one__less__mult, fact_zle__antisym, fact_realpow__pos__nth2, fact_mult__nonneg__nonneg, fact_add__less__cancel__left, fact_zero__less__mult__pos2, fact_natceiling__real__of__nat, fact_natfloor__one, fact_zmult__assoc, fact_of__int__0, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_xt1_I3_J, fact_double__zero__sym, fact_div__by__1, fact_le__diff__conv, fact_zmult__1, arity_Nat__Onat__Rings_Osemiring__1, fact_mult__left__mono, fact_less__Suc__eq__0__disj, fact_le__Suc__eq, fact_natceiling__le__eq, fact_ln__add__one__self__le__self, fact_negative__zle, fact_zminus__zadd__distrib, fact_mult__left_Ozero, fact_one__neq__zero, fact_div__less, fact_diff__cancel, fact_power__decreasing, fact_nat__eq__iff2, fact_le__add__iff1, fact_ln__ge__zero__imp__ge__one, fact_mult__left_Oadd, fact_of__nat__aux_Osimps_I2_J, fact_real__minus__mult__self__le, fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, arity_RealDef__Oreal__Orderings_Opreorder, fact_less__add__iff2, fact_add__strict__mono, fact_of__nat__0__le__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, arity_RealDef__Oreal__Orderings_Olinorder, fact_z3div__def, fact_mult__neg__pos, fact_nat__mult__le__cancel1, fact_order__neq__le__trans, fact_not__one__le__zero, fact_Suc__le__eq, fact_mult__cancel2, fact_zdiv__int, arity_RealDef__Oreal__Nat_Osemiring__char__0, fact_le__funE, fact_of__int__of__nat, fact_diff__int__def__symmetric, arity_Nat__Onat__Groups_Ocomm__monoid__add, fact_zero__less__nat__eq, arity_RealDef__Oreal__SEQ_Ocomplete__space, fact_le__add__diff__inverse2, arity_RealDef__Oreal__Orderings_Oorder, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_Divides_Otransfer__nat__int__functions_I1_J, fact_zdiff__int, fact_Suc__mult__less__cancel1, fact_less__antisym, fact_not__real__square__gt__zero, fact_div__0, fact_one__less__nat__eq, arity_RealDef__Oreal__Rings_Ocomm__semiring, fact_int__Suc, fact_of__int__0__le__iff, arity_Nat__Onat__Rings_Ocomm__semiring, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, arity_Int__Oint__Rings_Olinordered__semidom, fact_int__power__div__base, fact_mult__less__le__imp__less, fact_nat__mult__assoc, fact_nat__diff__add__eq2, fact_natceiling__add, fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J, arity_Nat__Onat__Groups_Omonoid__add, fact_ln__less__self, fact_less__add__Suc2, fact_mult_Ominus__left, fact_nat__mult__eq__cancel1, fact_int__1, fact_ord__le__eq__trans, fact_zdiv__mono2__neg, arity_Nat__Onat__Orderings_Oord, fact_equal__neg__zero, fact_diff__int__def, fact_divmod__int__rel__div__eq, fact_power__Suc__less__one, arity_fun__Orderings_Opreorder, fact_not__sum__squares__lt__zero, fact_real__mult__1, fact_less__eq__Suc__le, fact_mult__nonneg__nonpos2, fact_div__le__mono2, fact_natfloor__subtract, fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096, fact_zle__int, fact_div__mult__self1__is__m, fact_less__imp__diff__less, arity_RealDef__Oreal__Rings_Oordered__cancel__semiring, fact_div__add__self1, fact_power__add, arity_Int__Oint__Rings_Oring__1__no__zero__divisors, fact_Suc__pred_H, fact_zmult__commute, fact_int__nat__eq, arity_RealDef__Oreal__Rings_Oring, fact_comm__mult__strict__left__mono, fact_linorder__neq__iff, fact_zero__le__imp__of__nat, fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J, fact_real__of__nat__Suc, fact_neg__imp__zdiv__neg__iff, fact_natfloor__zero, fact_convergent__Cauchy, arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, fact_tsub__def, fact_real__mult__le__cancel__iff1, fact_reals__Archimedean6, fact_real__of__nat__def, fact_add__is__1, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, fact_less__minus__iff, fact_zero__less__power__nat__eq, fact_power_Opower_Opower__0, fact_power__Suc__less, fact_nat__mono__iff, fact_linorder__neqE__nat, fact_mult__less__mono2, arity_RealDef__Oreal__Rings_Osemiring, fact_nat__mult__div__cancel__disj, fact_not__less__iff__gr__or__eq, fact_diffs0__imp__equal, fact_diff__diff__left, fact_power__inject__exp, arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add, arity_Nat__Onat__Groups_Ozero, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_less__imp__of__nat__less, fact_nat__mult__less__cancel1, fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J, fact_unique__quotient__lemma, fact_diff__Suc__diff__eq2, fact_diff__add__assoc2, fact_mult_Ozero__right, fact_zdiv__zmult2__eq, fact_div__mult__self1, fact_xt1_I12_J, fact_power__increasing__iff, fact_zless__le, fact_mult__right_Oadd, fact_zadd__left__commute, fact_le__natfloor, fact_real__natceiling__ge, fact_order__less__le, fact_nat__le__0, fact_diff__diff__right, fact_of__int__of__nat__eq, fact_nat__div__distrib, fact_power__le__imp__le__exp, fact_power__one__right, fact_add__nonneg__pos, fact_mult__less__cancel__right__disj, arity_RealDef__Oreal__Groups_Oab__semigroup__add, fact_add__less__cancel__right, fact_Suc__mult__cancel1, fact_mult__strict__right__mono, arity_Nat__Onat__Groups_Ocomm__monoid__mult, fact_real__of__nat__ge__zero, fact_add__nonpos__nonpos, arity_Int__Oint__Groups_Omonoid__mult, arity_RealDef__Oreal__Rings_Olinordered__semiring__strict, fact_Suc__le__lessD, arity_RealDef__Oreal__Rings_Oordered__ring, fact_add__increasing, fact_not__add__less1, fact_int__Suc0__eq__1, fact_mult__idem, fact_div__pos__pos__trivial, fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J, arity_fun__Orderings_Oord, fact_less__diff__conv, fact_le__imp__neg__le, fact_zless__imp__add1__zle, fact_mult__le__cancel__left__pos, fact_eq__diff__iff, fact_zero__less__double__add__iff__zero__less__single__add, fact_div__mult__mult2, fact_zero__le__power, fact_transfer__nat__int__relations_I3_J, fact_real__mult__less__iff1, fact_nat__le__add__iff2, arity_RealDef__Oreal__Rings_Olinordered__ring__strict, fact_negD, fact_Suc__inject, fact_of__nat__le__iff, fact_ext, fact_order__less__not__sym, fact_crossproduct__noteq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, arity_Nat__Onat__Rings_Olinordered__semiring, fact_zle__trans, arity_RealDef__Oreal__Groups_Oordered__ab__group__add, fact_natceiling__neg, fact_less__add__iff1, fact_div__mult__mult1__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_mult_Oadd__left, fact_of__nat__nat, fact_nat__power__less__imp__less, fact_linorder__le__less__linear, fact_nat__lt__two__imp__zero__or__one, fact_Suc__neq__Zero, fact_zdiv__mono1, fact_g_I1_J, fact_power__strict__increasing__iff, fact_diff__less__Suc, fact_add__eq__self__zero, fact_funpow__mult, fact_mult__le__cancel2, arity_Int__Oint__Rings_Omult__zero, fact_real__le__antisym, fact_div__less__dividend, fact_mult__le__mono, arity_Nat__Onat__Orderings_Olinorder, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, arity_Int__Oint__Rings_Oring, fact_mult__le__0__iff, fact_le__iff__diff__le__0, fact_mult__is__0, fact_nat__add__left__cancel, fact_Suc__diff__1, fact_of__nat__less__0__iff, fact_less__le__not__le, fact_n__not__Suc__n, fact_nat__le__linear, fact_natceiling__eq, fact_transfer__int__nat__quantifiers_I1_J, fact_linorder__le__cases, fact_mult__zero__right, fact_nat__less__add__iff1, arity_RealDef__Oreal__RealVector_Ometric__space, fact_real__natfloor__add__one__gt, fact_div__by__0, fact_zminus__0, fact_order__less__le__trans, fact_power__less__imp__less__exp, arity_Nat__Onat__Rings_Omult__zero, arity_RealDef__Oreal__Groups_Ocomm__monoid__add, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, fact_of__nat__0, fact_less__minus__self__iff, fact_le__add__diff, fact_not__leE, arity_Int__Oint__Groups_Oordered__comm__monoid__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_times_Oidem, fact_nat__0__less__mult__iff, fact_diff__less__mono2, arity_RealDef__Oreal__Rings_Ocomm__semiring__1, fact_diff__eq__diff__less, fact_add__mult__distrib, fact_nat__mult__distrib, fact_leD, fact_add__strict__left__mono, fact_add__Suc, fact_diff__add__assoc, fact_strict__mono__less, fact_sum__squares__gt__zero__iff, fact_funpow_Osimps_I2_J, fact_nat__le__add__iff1, fact_mult__less__cancel1, fact_order__less__asym, fact_real__of__nat__mult, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, arity_RealDef__Oreal__Rings_Ono__zero__divisors, fact_add__gr__0, arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict, fact_zdiff__zmult__distrib2, fact_add__diff__assoc2, fact_power__Suc, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, fact_tsub__eq, fact_Suc__eq__plus1__left, fact_Zero__not__Suc, arity_RealDef__Oreal__Rings_Olinordered__semiring__1, fact_div__geq, fact_zero__less__one, fact_power__0__left, fact_real__diff__def, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_div__add__self2, arity_Nat__Onat__Rings_Oordered__cancel__semiring, fact_decr__mult__lemma, fact_diff__mult__distrib, fact_int__0__neq__1, fact_le__natfloor__eq, fact_add__less__imp__less__right, fact_le__Suc__ex__iff, arity_RealDef__Oreal__Rings_Oring__no__zero__divisors, fact_zdiff__zmult__distrib, fact_subseq__def, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le, fact_zless__nat__eq__int__zless, fact_mult__strict__mono, fact_diff__less__mono, fact_Suc__leD, fact_not__real__of__nat__less__zero, fact_power__0, fact_neg__equal__zero, fact_power__mult, fact_real__of__nat__1, fact_add_Ocomm__neutral, fact_strict__monoD, fact_realpow__pos__nth, fact_mult__Suc, fact_less__trans__Suc, fact_xt1_I6_J, fact_le__minus__self__iff, fact_less__not__refl2, fact_incseq__def, fact_trans__le__add2, fact_power__eq__if, fact_mult__right__le__one__le, arity_Nat__Onat__Rings_Oordered__semiring, fact_linorder__linear, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_natfloor__eq, fact_mult__zero__left, fact_of__int__less__0__iff, arity_Int__Oint__Groups_Oordered__ab__semigroup__add, fact_left__add__mult__distrib, fact_add__scale__eq__noteq, fact_Nat_Odiff__diff__eq, fact_le__refl, fact_nat__add__assoc, fact_eq__add__iff2, fact_zadd__zmult__distrib2, fact_le__add1, fact_mult__cancel1, arity_RealDef__Oreal__Groups_Oone, arity_Int__Oint__Rings_Olinordered__semiring, fact_linorder__not__less, fact_less__add__Suc1, fact_add__neg__neg, fact_add__is__0, fact_mult__diff__mult, fact_realpow__num__eq__if, fact_add__less__imp__less__left, fact_power_Opower_Opower__Suc, fact_le__imp__less__Suc, fact_mult__right__mono, fact_xt1_I2_J, fact_strict__mono__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_strict__mono__less__eq, fact_Suc__mult__le__cancel1, fact_ln__less__zero, fact_less__fun__def, fact_One__nat__def, fact_update__accessor__noopE, fact_comm__semiring__class_Odistrib, fact_update__accessor__noop__compE, fact_div__mult__self__is__m, fact_square__eq__iff, fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096, fact_neg__imp__zdiv__nonneg__iff, fact_nat__diff__add__eq1, fact_termination__basic__simps_I3_J, fact_swap__nilpotent, arity_Int__Oint__Rings_Oordered__ring, fact_o__eq__dest__lhs, fact_nat__eq__iff, fact_add__0, fact_nat__less__add__iff2, fact_Cauchy__convergent__iff, fact_power__mono, fact_diff__self__eq__0, fact_Divides_Otransfer__nat__int__function__closures_I1_J, fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J, fact_diff__add__0, fact_mult__nonpos__nonneg, fact_Zero__neq__Suc, fact_add__pos__pos, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_diff__cancel2, fact_add__nonneg__nonneg, fact_nat__eq__add__iff1, arity_RealDef__Oreal__Power_Opower, fact_Suc__eq__plus1, fact_real__of__nat__power, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, fact_mult__le__mono1, fact_Divides_Otransfer__int__nat__functions_I1_J, arity_Int__Oint__Rings_Olinordered__idom, arity_Int__Oint__Rings_Ocomm__semiring__1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_self__quotient__aux2, arity_RealDef__Oreal__Rings_Olinordered__semidom, fact_realpow__two__disj, fact_div__neg__pos__less0, arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, fact_nat__mult__div__cancel1, fact_Suc__diff__le, fact_of__int__diff, fact_order__eq__iff, arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, fact_int__less__0__conv, arity_Nat__Onat__Groups_Oab__semigroup__add, arity_Int__Oint__Groups_Ocomm__monoid__mult, fact_power__mult__distrib, fact_ord__eq__less__trans, fact_less__1__mult, arity_Int__Oint__Rings_Oordered__comm__semiring, fact_square__eq__1__iff, fact_le__trans, fact_Suc__pred, fact_ge__natfloor__plus__one__imp__gt, arity_fun__Groups_Ominus, fact_of__int__le__0__iff, arity_Int__Oint__Groups_Oone, arity_Nat__Onat__Rings_Olinordered__semidom, fact_add__le__cancel__right, fact_add__left__mono, fact_real__add__eq__0__iff, fact_power__Suc__0, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_n__less__n__mult__m, fact_mult__right_Ominus, fact_less__not__refl, fact_double__add__le__zero__iff__single__add__le__zero, fact_mult__less__cancel__left__neg, fact_le0, fact_power__one, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, arity_Int__Oint__Orderings_Oorder, fact_int__eq__0__conv, fact_le__diff__conv2, fact_mult__pos__pos, fact_minus__mult__minus, fact_ex__least__nat__less, fact_crossproduct__eq, fact_zmult__zless__mono2, fact_zdiff__int__split, fact_diff__Suc__diff__eq1, fact_comm__mult__left__mono, arity_Int__Oint__Groups_Oab__semigroup__add, fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J, fact_gr__implies__not0, fact_mult__strict__right__mono__neg, fact_zdiv__zminus__zminus, fact_le__mult__natfloor, fact_less__add__one, fact_mult__less__imp__less__right, fact_zero__neq__one, fact_add__leE, fact_natceiling__subtract, arity_Int__Oint__Rings_Oring__1, arity_RealDef__Oreal__Rings_Osemiring__1, fact_diff__Suc__1, fact_add__less__le__mono, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_real__of__nat__Suc__gt__zero, fact_real__two__squares__add__zero__iff, fact_power__less__power__Suc, fact_int__one__le__iff__zero__less, fact_Cauchy__subseq__Cauchy, fact_zdiv__mono2, arity_Nat__Onat__Rings_Olinordered__semiring__strict, fact_nat__less__eq__zless, fact_natfloor__add__one, fact_power__eq__imp__eq__base, fact_less__Suc__eq, fact_nat__add__commute, arity_Int__Oint__Rings_Ono__zero__divisors, fact_diff__eq__diff__less__eq, fact_swap__self, fact_of__nat__eq__iff, fact_Suc__less__eq, fact_mult__neg__neg, arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, fact_neg__0__le__iff__le, fact_mult_Odiff__left, fact_ln__realpow, fact_zdiv__mono2__lemma, fact_zmult__zminus, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, arity_RealDef__Oreal__Rings_Oring__1, fact_zdiv__zminus2, fact_zle__iff__zadd, fact_zero__less__Suc, fact_add1__zle__eq, fact_eq__imp__le, fact_nat__le__eq__zle, fact_ln__less__zero__iff, fact_div__self, fact_mult_Ocomm__neutral, fact_real__add__left__mono, fact_add__strict__increasing, fact_real__mult__order, arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_zmult__zless__mono2__lemma, fact_zdiv__self, arity_RealDef__Oreal__Rings_Oordered__semiring, fact_le__SucE, fact_le__less__Suc__eq, fact_pos__imp__zdiv__nonneg__iff, fact_nat__power__eq__Suc__0__iff, fact_nat__1, fact_nat__mult__commute, fact_diff__add__inverse2, arity_Int__Oint__Rings_Olinordered__semiring__1, fact_plus__nat_Oadd__0, fact_subseq__Suc__iff, fact_order__le__imp__less__or__eq, fact_of__nat__Suc, fact_minus__le__self__iff, fact_eq__nat__nat__iff, fact_add__nonpos__neg, fact_mult__left__idem, fact_div__le__mono, fact_Suc__n__not__n, fact_comp__swap, fact_mult__left__mono__neg, fact_le__antisym, fact_zadd__0__right, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, fact_diff__le__mono, fact_zero__less__mult__pos, fact_order__antisym__conv, fact_neq0__conv, fact_real__of__nat__gt__zero__cancel__iff, fact_mult__0__right, fact_real__add__less__0__iff, fact_zless__linear, fact_mult__less__cancel__left__pos, fact_real__mult__le__cancel__iff2, fact_trans__le__add1, fact_zless__iff__Suc__zadd, arity_Int__Oint__Groups_Ominus, fact_zmult__1__right, fact_double__eq__0__iff, fact_le__0__eq, fact_mult__Suc__right, fact_realpow__pos__nth__unique, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_mult__less__cancel2, fact_zle__add1__eq__le, fact_mult__1__right, fact_add__le__imp__le__right, fact_order__less__irrefl, fact_less__Suc0, fact_order__le__less, fact_zero__zle__int, fact_less__iff__Suc__add, fact_order__less__imp__le, fact_termination__basic__simps_I1_J, fact_real__0__le__add__iff, fact_order__less__trans, fact_negative__eq__positive, fact_zero__less__two, fact_nat__int, fact_diff__is__0__eq, fact_real__of__nat__one, fact_rp, fact_real__of__nat__le__iff, fact_real__mult__less__mono2, fact_sum__squares__eq__zero__iff, fact_le__add__diff__inverse, fact_nat__zero__less__power__iff, fact_of__nat__1, fact_of__int__0__less__iff, arity_Int__Oint__Rings_Ocomm__ring__1, fact_add__le__mono, fact_add__diff__inverse, fact_convex__bound__le, arity_Nat__Onat__Rings_Osemiring, fact_int__le__0__conv, arity_Int__Oint__Groups_Olinordered__ab__group__add, fact_nat__mult__eq__cancel__disj, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_mult__less__imp__less__left, fact_le__diff__iff, arity_Nat__Onat__Groups_Oone, fact_diff__Suc__Suc, fact_add__imp__eq, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_no__zero__divisors, fact_le__square, fact_divisors__zero, fact_reals__Archimedean6a, fact_div__mult__self2__is__id, fact_realpow__Suc__le__self, arity_RealDef__Oreal__Groups_Olinordered__ab__group__add, fact_ab__semigroup__add__class_Oadd__ac_I1_J, arity_RealDef__Oreal__Groups_Oab__semigroup__mult, arity_Int__Oint__Rings_Ozero__neq__one, fact_ln__gt__zero, arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, fact_transfer__nat__int__relations_I2_J, fact_power__gt1, fact_power__0__Suc, fact_nat__less__le, fact_less__iff__diff__less__0, fact_mult__eq__if, fact_split__nat, fact_zadd__zmult__distrib, fact_less__SucE, fact_le__cube, fact_zless__add1__eq, fact_linorder__cases, fact_real__natfloor__le, fact_xt1_I11_J, fact_add__less__mono1, fact_add__le__cancel__left, fact_real__le__linear, fact_ord__eq__le__trans, fact_f_I1_J, fact_zadd__zminus__inverse2, fact_o__assoc, fact_double__add__less__zero__iff__single__add__less__zero, fact_less__diff__iff, fact_real__natfloor__gt__diff__one, fact_odd__less__0, arity_Int__Oint__Groups_Omonoid__add, fact_order__trans, fact_power__le__imp__le__base, fact_mult__1, fact_real__eq__of__nat, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, arity_Int__Oint__Orderings_Opreorder, fact_real__of__nat__inject, fact_reals__Archimedean3, fact_negative__zless__0, fact_add__Suc__shift, fact_less__SucI, fact_Suc__not__Zero, fact_real__of__nat__add, fact_ln__gt__zero__iff, fact_xt1_I7_J, fact_not__square__less__zero, fact_Suc__lessI, fact_negative__zle__0, fact_add__Suc__right, fact_less__bin__lemma, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_mult_Odiff__right, fact_zdiv__mono2__neg__lemma, fact_ln__one, fact_nat__0__iff, fact_natfloor__mono, fact_ln__ge__zero__iff
% 25.36/6.85 % No. of inferences in proof: 2214
% 25.36/6.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6378 ms resp. 5784 ms w/o parsing
% 26.49/7.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.49/7.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------