%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW181+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:09:35 AM UTC 2026
% Result : Theorem 166.04s 42.99s
% Output : Refutation 170.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 1269
% Syntax : Number of formulae : 3268 ( 845 unt; 0 typ; 2 def)
% Number of atoms : 9175 (2671 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 44164 (1839 ~;1330 |; 652 &;36910 @)
% ( 257 <=>;3176 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 115 ( 112 usr; 11 con; 0-5 aty)
% Number of variables : 6564 ( 1 ^;6471 !; 90 ?;6564 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(tc_RealDef_Oreal_decl,type,
tc_RealDef_Oreal: $i ).
thf(c_Groups_Ozero__class_Ozero_decl,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(c_RealVector_Onorm__class_Onorm_decl,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(tc_Complex_Ocomplex_decl,type,
tc_Complex_Ocomplex: $i ).
thf(v_r_decl,type,
v_r: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Polynomial_Opoly_decl,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(c_Polynomial_OpCons_decl,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(v_c_____decl,type,
v_c____: $i ).
thf(v_cs_____decl,type,
v_cs____: $i ).
thf(class_Rings_Olinordered__idom_decl,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_Groups_Oabs__class_Oabs_decl,type,
c_Groups_Oabs__class_Oabs: $i > $i > $i ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(c_Groups_Ouminus__class_Ouminus_decl,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(c_Rings_Odvd__class_Odvd_decl,type,
c_Rings_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i > $i ).
thf(c_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(c_RComplete_Onatfloor_decl,type,
c_RComplete_Onatfloor: $i > $i ).
thf(c_Groups_Oone__class_Oone_decl,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_RealDef_Oreal_decl,type,
c_RealDef_Oreal: $i > $i > $i ).
thf(class_Groups_Ogroup__add_decl,type,
class_Groups_Ogroup__add: $i > $o ).
thf(tc_Polynomial_Opoly_decl,type,
tc_Polynomial_Opoly: $i > $i ).
thf(c_Polynomial_Opos__poly_decl,type,
c_Polynomial_Opos__poly: $i > $i > $o ).
thf(c_Groups_Ominus__class_Ominus_decl,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Groups_Oordered__ab__group__add__abs_decl,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(c_Power_Opower_Opower_decl,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(c_Groups_Otimes__class_Otimes_decl,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(class_Rings_Oordered__cancel__semiring_decl,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_decl,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__comm__semiring__strict_decl,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(tc_Int_Oint_decl,type,
tc_Int_Oint: $i ).
thf(class_Groups_Ocomm__monoid__add_decl,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Groups_Omonoid__add_decl,type,
class_Groups_Omonoid__add: $i > $o ).
thf(class_Rings_Ocomm__semiring__1_decl,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_decl,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_fequal_decl,type,
c_fequal: $i > $i > $i ).
thf(class_Rings_Oidom_decl,type,
class_Rings_Oidom: $i > $o ).
thf(c_Polynomial_Oorder_decl,type,
c_Polynomial_Oorder: $i > $i > $i > $i ).
thf(class_Rings_Oring_decl,type,
class_Rings_Oring: $i > $o ).
thf(class_Rings_Ocomm__semiring__0_decl,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
thf(class_Rings_Osemiring_decl,type,
class_Rings_Osemiring: $i > $o ).
thf(c_Groups_Osgn__class_Osgn_decl,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(class_Groups_Ominus_decl,type,
class_Groups_Ominus: $i > $o ).
thf(class_Rings_Olinordered__semidom_decl,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_decl,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Groups_Oab__group__add_decl,type,
class_Groups_Oab__group__add: $i > $o ).
thf(class_Groups_Oordered__ab__group__add_decl,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(class_Rings_Odvd_decl,type,
class_Rings_Odvd: $i > $o ).
thf(class_Rings_Oordered__comm__semiring_decl,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(class_Rings_Oordered__semiring_decl,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(class_Rings_Ocomm__semiring_decl,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(class_Groups_Osgn__if_decl,type,
class_Groups_Osgn__if: $i > $o ).
thf(class_Groups_Ouminus_decl,type,
class_Groups_Ouminus: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Rings_Olinordered__ring_decl,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_Groups_Oab__semigroup__add_decl,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(c_RComplete_Onatceiling_decl,type,
c_RComplete_Onatceiling: $i > $i ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_decl,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_Rings_Oring__1__no__zero__divisors_decl,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Rings_Ocomm__ring_decl,type,
class_Rings_Ocomm__ring: $i > $o ).
thf(class_Rings_Olinordered__semiring__1_decl,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_Rings_Olinordered__semiring__1__strict_decl,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(class_Rings_Omult__zero_decl,type,
class_Rings_Omult__zero: $i > $o ).
thf(c_Polynomial_Osynthetic__div_decl,type,
c_Polynomial_Osynthetic__div: $i > $i > $i > $i ).
thf(class_Rings_Ocomm__ring__1_decl,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_decl,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(class_Groups_Oabs__if_decl,type,
class_Groups_Oabs__if: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_decl,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Groups_Ocancel__comm__monoid__add_decl,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_decl,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_decl,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(class_Rings_Oordered__ring_decl,type,
class_Rings_Oordered__ring: $i > $o ).
thf(class_Groups_Omonoid__mult_decl,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Groups_Olinordered__ab__group__add_decl,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(class_Rings_Oring__1_decl,type,
class_Rings_Oring__1: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_decl,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(class_RealVector_Oreal__normed__div__algebra_decl,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_decl,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Rings_Ozero__neq__one_decl,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Rings_Ono__zero__divisors_decl,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Rings_Osemiring__0_decl,type,
class_Rings_Osemiring__0: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_decl,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Groups_Ozero_decl,type,
class_Groups_Ozero: $i > $o ).
thf(class_Rings_Olinordered__semiring_decl,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Rings_Olinordered__ring__strict_decl,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(class_Rings_Oordered__ring__abs_decl,type,
class_Rings_Oordered__ring__abs: $i > $o ).
thf(class_Lattices_Oboolean__algebra_decl,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(class_Int_Oring__char__0_decl,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra__1_decl,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(class_Groups_Oone_decl,type,
class_Groups_Oone: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_decl,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(c_Polynomial_Opcompose_decl,type,
c_Polynomial_Opcompose: $i > $i > $i > $i ).
thf(c_SEQ_OBseq_decl,type,
c_SEQ_OBseq: $i > $i > $o ).
thf(v_m_____decl,type,
v_m____: $i ).
thf(class_Lattices_Oab__semigroup__idem__mult_decl,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(c_Nat__Transfer_Otsub_decl,type,
c_Nat__Transfer_Otsub: $i > $i > $i ).
thf(c_Polynomial_Opoly__rec_decl,type,
c_Polynomial_Opoly__rec: $i > $i > $i > $i > $i > $i ).
thf(c_If_decl,type,
c_If: $i > $i > $i > $i > $i ).
thf(c_SEQ_Oincseq_decl,type,
c_SEQ_Oincseq: $i > $i > $o ).
thf(c_SEQ_Odecseq_decl,type,
c_SEQ_Odecseq: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk53_decl,type,
sk53: $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ).
thf(sk53_def,definition,
( sk53
= ( @+[A: $i] :
( ! [B: $i] :
( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ).
thf(4,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
thf(1276,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1277,plain,
( ! [A: $i] :
( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ),
inference(miniscope,[status(thm)],[1276]) ).
thf(1278,plain,
! [B: $i,A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(cnf,[status(esa)],[1277]) ).
thf(1279,plain,
! [A: $i] :
( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(cnfConj,[status(thm)],[1278]) ).
thf(1281,plain,
! [A: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(lifteq,[status(thm)],[1279]) ).
thf(459,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(2802,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(2803,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(polarity_switch,[status(thm)],[2802]) ).
thf(2804,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[2803]) ).
thf(5593,plain,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,2804]) ).
thf(5594,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[5593:[bind(A,$thf( tc_Int_Oint @ c_Groups_Oone__class_Oone ))]]) ).
thf(13880,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,5594]) ).
thf(13881,plain,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[13880:[]]) ).
thf(13950,plain,
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[13881]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
thf(1404,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( C @ class_Groups_Oordered__ab__group__add ) )
& ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( C @ class_Groups_Oordered__ab__group__add ) ) ),
inference(cnf,[status(esa)],[1404]) ).
thf(1406,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( C @ class_Groups_Oordered__ab__group__add ) ),
inference(cnfConj,[status(thm)],[1405]) ).
thf(1,conjecture,
? [A: $i] :
( ! [B: $i] :
( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ! [B: $i] :
( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1269,plain,
~ ? [A: $i] :
( ! [B: $i] :
( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1270,plain,
! [A: $i] :
( ( ~ ( A @ ( A @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(cnf,[status(esa)],[1269]) ).
thf(1271,plain,
! [A: $i] :
( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(cnfConj,[status(thm)],[1270]) ).
thf(27117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
!= ( D @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( v_r @ ( D @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ~ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( C @ class_Groups_Oordered__ab__group__add ) ),
inference(paramod_ordered,[status(thm)],[1406,1271]) ).
thf(27118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
!= ( D @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( v_r @ ( D @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( C @ class_Groups_Oordered__ab__group__add ) ),
inference(simp,[status(thm)],[27117]) ).
thf(27119,plain,
! [A: $i] :
( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add ) ),
inference(pattern_uni,[status(thm)],[27118:[bind(A,$thf( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )),bind(B,$thf( G )),bind(C,$thf( tc_RealDef_Oreal )),bind(D,$thf( G @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ))]]) ).
thf(27317,plain,
! [A: $i] :
( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add ) ),
inference(simp,[status(thm)],[27119]) ).
thf(939,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
thf(4320,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(27535,plain,
! [A: $i] :
( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[27317,4320]) ).
thf(27536,plain,
! [A: $i] :
( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[27535]) ).
thf(20,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(1337,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
thf(3883,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(1220,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(5329,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(848,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(4022,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
thf(3434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(337,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ono__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
thf(2412,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(752,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
thf(3698,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__le) ).
thf(1982,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
thf(1286,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) )
& ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1287,plain,
( ! [A: $i,B: $i] :
( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1286]) ).
thf(1288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( D @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( D = C )
| ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( D = C )
| ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( B != A )
| ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(cnf,[status(esa)],[1287]) ).
thf(1292,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( B = A )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(cnfConj,[status(thm)],[1288]) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[1292]) ).
thf(1298,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( B = A ) ),
inference(simp,[status(thm)],[1297]) ).
thf(6343,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_RealDef_Oreal )
| ( v_r @ ( C @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1298,1271]) ).
thf(6344,plain,
! [B: $i,A: $i] :
( ( v_r @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[6343:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).
thf(6690,plain,
! [B: $i,A: $i] :
( ( v_r @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[6344]) ).
thf(160,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(1818,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ! [E: $i,F: $i] :
( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
thf(1956,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ! [E: $i,F: $i] :
( ( ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1239,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(5385,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1272,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(cnfConj,[status(thm)],[1270]) ).
thf(5483,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[1271,1272]) ).
thf(5484,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5483]) ).
thf(5485,plain,
! [B: $i,A: $i] :
( ( v_r != B )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ) )
| ( tc_RealDef_Oreal != tc_RealDef_Oreal )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5484]) ).
thf(5486,plain,
! [A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5485]) ).
thf(5488,plain,
! [A: $i] :
( ~ $true
| ( ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[5486]) ).
thf(5489,plain,
( ( ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[5488:[bind(A,$thf( v_r ))]]) ).
thf(5491,plain,
( ( ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ( tc_Complex_Ocomplex != tc_Complex_Ocomplex )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5489]) ).
thf(5492,plain,
( ( ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5491]) ).
thf(5658,plain,
! [A: $i] :
( ( A
!= ( v_r @ sk1 ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,5492]) ).
thf(5659,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[5658:[bind(A,$thf( v_r @ sk1 ))]]) ).
thf(1254,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
thf(5437,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(1501,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(1385,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1386,plain,
( ! [A: $i,B: $i] :
( ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1385]) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ c_Nat_OSuc @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( D
!= ( C @ c_Nat_OSuc ) ) )
& ( ( C @ c_Nat_OSuc @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(cnf,[status(esa)],[1386]) ).
thf(1390,plain,
! [B: $i,A: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B
!= ( A @ c_Nat_OSuc ) ) ),
inference(cnfConj,[status(thm)],[1387]) ).
thf(1393,plain,
! [B: $i,A: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B
!= ( A @ c_Nat_OSuc ) ) ),
inference(lifteq,[status(thm)],[1390]) ).
thf(1394,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(simp,[status(thm)],[1393]) ).
thf(1389,plain,
! [B: $i,A: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(cnfConj,[status(thm)],[1387]) ).
thf(1392,plain,
! [B: $i,A: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[1389]) ).
thf(546,axiom,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(3062,plain,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(3063,plain,
~ ? [A: $i] : ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(miniscope,[status(thm)],[3062]) ).
thf(3064,plain,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(cnf,[status(esa)],[3063]) ).
thf(20242,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(paramod_ordered,[status(thm)],[1392,3064]) ).
thf(20243,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[20242]) ).
thf(20244,plain,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(pattern_uni,[status(thm)],[20243:[bind(A,$thf( E )),bind(B,$thf( E @ c_Nat_OSuc @ c_Nat_OSuc )),bind(C,$thf( E @ c_Nat_OSuc ))]]) ).
thf(20328,plain,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(simp,[status(thm)],[20244]) ).
thf(20442,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(paramod_ordered,[status(thm)],[1392,20328]) ).
thf(20443,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[20442]) ).
thf(20444,plain,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(pattern_uni,[status(thm)],[20443:[bind(A,$thf( F )),bind(B,$thf( F @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )),bind(C,$thf( F @ c_Nat_OSuc ))]]) ).
thf(20525,plain,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(simp,[status(thm)],[20444]) ).
thf(29815,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1394,20525]) ).
thf(29816,plain,
! [B: $i,A: $i] :
( ( A @ c_Nat_OSuc @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[29815]) ).
thf(29912,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc )
!= B )
| ( ( A @ c_Nat_OSuc )
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[29816]) ).
thf(29956,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( A @ c_Nat_OSuc ) ),
inference(simp,[status(thm)],[29912]) ).
thf(29982,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
!= A ),
inference(simp,[status(thm)],[29956]) ).
thf(30301,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= B )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,29982]) ).
thf(30302,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= A )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[30301:[bind(A,$thf( E @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )),bind(B,$thf( E ))]]) ).
thf(30353,plain,
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(simp,[status(thm)],[30302]) ).
thf(895,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(4201,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1265,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(5469,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(825,axiom,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(3944,plain,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(1410,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1411,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(cnf,[status(esa)],[1410]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(2744,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
thf(1368,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1369,plain,
! [A: $i] :
( ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring )
| ~ ( A @ class_Rings_Ocomm__semiring__0 ) ),
inference(cnf,[status(esa)],[1368]) ).
thf(1086,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).
thf(4835,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(2295,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(642,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(3345,plain,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(266,axiom,
tc_Int_Oint @ class_Groups_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
thf(2172,plain,
tc_Int_Oint @ class_Groups_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
thf(1408,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1409,plain,
! [A: $i] :
( ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ ( A @ class_Groups_Oab__group__add ) ),
inference(cnf,[status(esa)],[1408]) ).
thf(28741,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2172,1409]) ).
thf(28742,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[28741]) ).
thf(28743,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[28742:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(33024,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28743,1409]) ).
thf(33025,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[33024]) ).
thf(33026,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[33025:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly ))]]) ).
thf(34080,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33026,1409]) ).
thf(34081,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[34080]) ).
thf(34082,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[34081:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(36009,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34082,1409]) ).
thf(36010,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[36009]) ).
thf(36011,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[36010:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(39157,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36011,1409]) ).
thf(39158,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[39157]) ).
thf(39159,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[39158:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
thf(1402,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1403,plain,
! [A: $i] :
( ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ ( A @ class_Groups_Oab__group__add ) ),
inference(cnf,[status(esa)],[1402]) ).
thf(40786,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39159,1403]) ).
thf(40787,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[40786]) ).
thf(40788,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[40787:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(2131,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(1453,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1454,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(cnf,[status(esa)],[1453]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
thf(3399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
thf(4169,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(657,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ~ ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_Opos__poly ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
thf(3397,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ~ ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_Opos__poly ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1249,axiom,
? [A: $i] :
( ! [B: $i] :
( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons) ).
thf(5426,plain,
? [A: $i] :
( ! [B: $i] :
( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(5427,plain,
! [A: $i] :
( ( ( sk53 @ ( A @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( v_r @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(cnf,[status(esa)],[5426]) ).
thf(5428,plain,
sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
inference(cnfConj,[status(thm)],[5427]) ).
thf(20253,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[1271,1392]) ).
thf(20254,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20253]) ).
thf(20304,plain,
! [C: $i,B: $i,A: $i] :
( ( v_r != B )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= C )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[20254]) ).
thf(20324,plain,
! [A: $i] :
( ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( v_r @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[20304]) ).
thf(35398,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ $true
| ( v_r @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(paramod_ordered,[status(thm)],[5428,20324]) ).
thf(35399,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( v_r @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[35398]) ).
thf(35400,plain,
( ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( v_r @ c_Nat_OSuc @ ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(pattern_uni,[status(thm)],[35399:[bind(A,$thf( sk53 ))]]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).
thf(1899,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(607,axiom,
tc_Int_Oint @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(3245,plain,
tc_Int_Oint @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ class_Power_Opower )
=> ( ( A @ c_Power_Opower__class_Opower )
= ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
thf(1326,plain,
! [A: $i] :
( ( A @ class_Power_Opower )
=> ( ( A @ c_Power_Opower__class_Opower )
= ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1327,plain,
! [A: $i] :
( ( ( A @ c_Power_Opower__class_Opower )
= ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) ) )
| ~ ( A @ class_Power_Opower ) ),
inference(cnf,[status(esa)],[1326]) ).
thf(1328,plain,
! [A: $i] :
( ~ ( A @ class_Power_Opower )
| ( ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) )
= ( A @ c_Power_Opower__class_Opower ) ) ),
inference(lifteq,[status(thm)],[1327]) ).
thf(14356,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Power_Opower )
!= ( A @ class_Power_Opower ) )
| ~ $true
| ( ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) )
= ( A @ c_Power_Opower__class_Opower ) ) ),
inference(paramod_ordered,[status(thm)],[3245,1328]) ).
thf(14357,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Power_Opower )
!= ( A @ class_Power_Opower ) )
| ( ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) )
= ( A @ c_Power_Opower__class_Opower ) ) ),
inference(simp,[status(thm)],[14356]) ).
thf(14358,plain,
( ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Power_Opower_Opower ) ) )
= ( tc_Int_Oint @ c_Power_Opower__class_Opower ) ),
inference(pattern_uni,[status(thm)],[14357:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(1061,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oabs__if )
=> ( ( ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= A ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).
thf(4728,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oabs__if )
=> ( ( ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= A ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ c_RComplete_Onatceiling )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
thf(1554,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ c_RComplete_Onatceiling )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(4904,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(583,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).
thf(3172,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
thf(1686,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1204,axiom,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(5278,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(687,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(3489,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(3490,plain,
! [A: $i] :
( ? [B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(miniscope,[status(thm)],[3489]) ).
thf(3491,plain,
! [B: $i,A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(cnf,[status(esa)],[3490]) ).
thf(3492,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[3491]) ).
thf(3493,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(simp,[status(thm)],[3492]) ).
thf(38065,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5278,3493]) ).
thf(38066,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[38065]) ).
thf(38214,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= A )
| ( tc_Int_Oint != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[38066]) ).
thf(38266,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Int_Oint != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[38214]) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
thf(2250,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(139,axiom,
tc_Int_Oint @ class_Groups_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
thf(1750,plain,
tc_Int_Oint @ class_Groups_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1280,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(cnfConj,[status(thm)],[1278]) ).
thf(1282,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(lifteq,[status(thm)],[1280]) ).
thf(1283,plain,
tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ),
inference(simp,[status(thm)],[1282]) ).
thf(5660,plain,
! [A: $i] :
( ( A
!= ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,5492]) ).
thf(5661,plain,
( ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[5660:[bind(A,$thf( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) ))]]) ).
thf(7843,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,5661]) ).
thf(7844,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7843]) ).
thf(7873,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7844]) ).
thf(7875,plain,
( ( ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7873]) ).
thf(8127,plain,
! [A: $i] :
( ( A
!= ( v_r @ sk1 ) )
| ( ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,7875]) ).
thf(8128,plain,
! [A: $i] :
( ( A
!= ( v_r @ sk1 ) )
| ( ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[8127]) ).
thf(8129,plain,
( ( ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[8128:[bind(A,$thf( v_r @ sk1 ))]]) ).
thf(946,axiom,
tc_RealDef_Oreal @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
thf(4339,plain,
tc_RealDef_Oreal @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1882,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
thf(2527,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(37,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
thf(1401,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(676,axiom,
! [A: $i,B: $i] : ( B @ c_Nat_OSuc @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(3460,plain,
! [A: $i,B: $i] : ( B @ c_Nat_OSuc @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(3098,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(2014,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(558,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).
thf(3108,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(4326,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(741,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(3680,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1210,axiom,
tc_RealDef_Oreal @ class_Groups_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
thf(5294,plain,
tc_RealDef_Oreal @ class_Groups_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(29768,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5294,1403]) ).
thf(29769,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[29768]) ).
thf(29770,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[29769:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).
thf(854,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
thf(4043,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__pCons) ).
thf(1596,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(1188,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(5225,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(3317,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(904,axiom,
tc_Complex_Ocomplex @ class_Groups_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
thf(4226,plain,
tc_Complex_Ocomplex @ class_Groups_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(279,axiom,
tc_Int_Oint @ class_Groups_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
thf(2231,plain,
tc_Int_Oint @ class_Groups_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(799,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
thf(3858,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(461,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(2808,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).
thf(1522,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
thf(3762,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).
thf(2644,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__minus) ).
thf(2062,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(704,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
thf(3549,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(1430,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1431,plain,
( ! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1430]) ).
thf(1432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
| ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
| ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(cnf,[status(esa)],[1431]) ).
thf(1434,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(cnfConj,[status(thm)],[1432]) ).
thf(1443,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(lifteq,[status(thm)],[1434]) ).
thf(450,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(2776,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(691,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(3509,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(5242,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(1136,axiom,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(5017,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(37450,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5017,3064]) ).
thf(37451,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[37450]) ).
thf(37509,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= A )
| ( ( A @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Int_Oint != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[37451]) ).
thf(37517,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Int_Oint != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[37509]) ).
thf(204,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__one) ).
thf(1954,plain,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1955,plain,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
inference(lifteq,[status(thm)],[1954]) ).
thf(290,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(2275,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(2276,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(lifteq,[status(thm)],[2275]) ).
thf(34729,plain,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(rewrite,[status(thm)],[1955,2276]) ).
thf(293,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
thf(2282,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ c_RComplete_Onatfloor )
= ( B @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__subtract) ).
thf(2837,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ c_RComplete_Onatfloor )
= ( B @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(209,axiom,
tc_Int_Oint @ class_Rings_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(1971,plain,
tc_Int_Oint @ class_Rings_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(659,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
thf(3402,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1190,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(5237,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1027,axiom,
! [A: $i] :
~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
thf(4621,plain,
! [A: $i] :
~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(4622,plain,
~ ? [A: $i] : ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(miniscope,[status(thm)],[4621]) ).
thf(4623,plain,
! [A: $i] :
~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(cnf,[status(esa)],[4622]) ).
thf(1124,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(4973,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring )
=> ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(3017,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring )
=> ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(5604,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,1271]) ).
thf(5605,plain,
! [A: $i] :
( ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[5604:[bind(A,$thf( E @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )),bind(B,$thf( E ))]]) ).
thf(5624,plain,
! [A: $i] :
( ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[5605]) ).
thf(5741,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,5624]) ).
thf(5742,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5741]) ).
thf(5758,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[5742]) ).
thf(5762,plain,
! [A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[5758]) ).
thf(16340,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[5762,3064]) ).
thf(16341,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16340]) ).
thf(16371,plain,
! [B: $i,A: $i] :
( ( B != v_r )
| ( ( B @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16341]) ).
thf(16393,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( v_r @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16371]) ).
thf(20038,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16393]) ).
thf(35215,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,20038]) ).
thf(35216,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(simp,[status(thm)],[35215]) ).
thf(35217,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(pattern_uni,[status(thm)],[35216:[bind(A,$thf( sk53 ))]]) ).
thf(439,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2740,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(967,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
thf(4398,plain,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
thf(1333,plain,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1334,plain,
! [A: $i] :
( ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add )
| ~ ( A @ class_Groups_Ocomm__monoid__add ) ),
inference(cnf,[status(esa)],[1333]) ).
thf(20967,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add )
!= ( A @ class_Groups_Ocomm__monoid__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4398,1334]) ).
thf(20968,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add )
!= ( A @ class_Groups_Ocomm__monoid__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
inference(simp,[status(thm)],[20967]) ).
thf(20969,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add,
inference(pattern_uni,[status(thm)],[20968:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).
thf(979,axiom,
tc_RealDef_Oreal @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
thf(4440,plain,
tc_RealDef_Oreal @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(3693,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(3414,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__vector )
=> ( ( C @ ( D @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__add__less) ).
thf(3562,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__vector )
=> ( ( C @ ( D @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
thf(2901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(1507,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1163,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( ( ( B @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( D @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( D = C ) )
& ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth__unique) ).
thf(5120,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( ( ( B @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( D @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( D = C ) )
& ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odvd )
=> ( ( C
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).
thf(1426,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Odvd )
=> ( ( C
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(696,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
thf(3530,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(770,axiom,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).
thf(3745,plain,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(973,axiom,
! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
thf(4418,plain,
! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(1064,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
thf(4739,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(28727,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4226,1409]) ).
thf(28728,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[28727]) ).
thf(28729,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[28728:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).
thf(32986,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28729,1409]) ).
thf(32987,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[32986]) ).
thf(32988,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[32987:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).
thf(33976,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32988,1409]) ).
thf(33977,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[33976]) ).
thf(33978,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[33977:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(35600,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33978,1409]) ).
thf(35601,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[35600]) ).
thf(35602,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[35601:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(398,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
thf(2607,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(142,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1756,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1017,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
thf(4575,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B = A )
=> ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(868,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(4097,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(3942,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
thf(3649,plain,
! [A: $i,B: $i] :
( ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(542,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(3044,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
thf(1735,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(900,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
thf(4220,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1006,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
thf(4528,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(3175,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(349,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
thf(2448,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
thf(2933,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus) ).
thf(1273,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) )
| ~ ( C @ class_Rings_Olinordered__idom ) ),
inference(cnf,[status(esa)],[1273]) ).
thf(1275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ class_Rings_Olinordered__idom )
| ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ),
inference(lifteq,[status(thm)],[1274]) ).
thf(258,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(2141,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1216,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
thf(5316,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(1037,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(4650,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(2476,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(29760,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5294,1409]) ).
thf(29761,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[29760]) ).
thf(29762,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[29761:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).
thf(33064,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29762,1409]) ).
thf(33065,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[33064]) ).
thf(33066,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[33065:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).
thf(34580,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33066,1409]) ).
thf(34581,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[34580]) ).
thf(34582,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[34581:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(36147,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34582,1409]) ).
thf(36148,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[36147]) ).
thf(36149,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[36148:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(39329,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36149,1409]) ).
thf(39330,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[39329]) ).
thf(39331,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[39330:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(40954,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39331,1409]) ).
thf(40955,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[40954]) ).
thf(40956,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[40955:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(190,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__one) ).
thf(1919,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
thf(5178,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( B = A )
<=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
thf(2844,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sum__triangle__ineq) ).
thf(1458,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(993,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
thf(4485,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(23209,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0 )
!= ( A @ class_Rings_Ocomm__semiring__0 ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4485,1369]) ).
thf(23210,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0 )
!= ( A @ class_Rings_Ocomm__semiring__0 ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
inference(simp,[status(thm)],[23209]) ).
thf(23211,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Rings_Osemiring,
inference(pattern_uni,[status(thm)],[23210:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).
thf(1247,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(5412,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(3276,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(387,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2575,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(856,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
thf(4047,plain,
! [A: $i,B: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(3545,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1198,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(5252,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(776,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_SEQ_OBseq ) )
<=> ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__iff) ).
thf(3766,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_SEQ_OBseq ) ) )
& ( ( A @ ( B @ c_SEQ_OBseq ) )
=> ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sgn) ).
thf(1935,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(191,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(1921,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
thf(4198,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(2825,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(155,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
thf(1803,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(3688,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(1000,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
thf(4511,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).
thf(2957,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(793,axiom,
tc_RealDef_Oreal @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(3836,plain,
tc_RealDef_Oreal @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(949,axiom,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__algebra )
=> ? [B: $i] :
( ! [C: $i,D: $i] : ( B @ ( D @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ononneg__bounded) ).
thf(4343,plain,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__algebra )
=> ? [B: $i] :
( ! [C: $i,D: $i] : ( B @ ( D @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
thf(3629,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
thf(2491,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1242,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).
thf(5393,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(447,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(2763,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2548,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(2985,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
thf(2227,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1388,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(cnfConj,[status(thm)],[1387]) ).
thf(1391,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B
= ( A @ c_Nat_OSuc ) ) ),
inference(lifteq,[status(thm)],[1388]) ).
thf(1433,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(cnfConj,[status(thm)],[1432]) ).
thf(1441,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(lifteq,[status(thm)],[1433]) ).
thf(919,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatfloor )
= ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add) ).
thf(4266,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatfloor )
= ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(552,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(3088,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
thf(3777,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(5470,plain,
( ! [A: $i] :
( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(miniscope,[status(thm)],[5469]) ).
thf(5471,plain,
! [B: $i,A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(cnf,[status(esa)],[5470]) ).
thf(5473,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[5471]) ).
thf(5475,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[5473]) ).
thf(5476,plain,
tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ),
inference(simp,[status(thm)],[5475]) ).
thf(915,axiom,
tc_Complex_Ocomplex @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
thf(4260,plain,
tc_Complex_Ocomplex @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(19797,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Power_Opower )
!= ( A @ class_Power_Opower ) )
| ~ $true
| ( ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) )
= ( A @ c_Power_Opower__class_Opower ) ) ),
inference(paramod_ordered,[status(thm)],[4260,1328]) ).
thf(19798,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Power_Opower )
!= ( A @ class_Power_Opower ) )
| ( ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) )
= ( A @ c_Power_Opower__class_Opower ) ) ),
inference(simp,[status(thm)],[19797]) ).
thf(19799,plain,
( ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Power_Opower_Opower ) ) )
= ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower ) ),
inference(pattern_uni,[status(thm)],[19798:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).
thf(620,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
thf(3281,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(679,axiom,
tc_Int_Oint @ class_Groups_Oabs__if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
thf(3466,plain,
tc_Int_Oint @ class_Groups_Oabs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1213,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(5301,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(851,axiom,
tc_RealDef_Oreal @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
thf(4030,plain,
tc_RealDef_Oreal @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
thf(1475,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(267,axiom,
tc_Int_Oint @ class_Rings_Olinordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(2173,plain,
tc_Int_Oint @ class_Rings_Olinordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1025,axiom,
! [A: $i] :
( ( ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__def) ).
thf(4607,plain,
! [A: $i] :
( ( ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(1115,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(4948,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
thf(2405,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
thf(3938,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(437,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(2735,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(227,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Omult__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
thf(2039,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(443,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
thf(2755,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(4224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(289,axiom,
tc_Int_Oint @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(2274,plain,
tc_Int_Oint @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(425,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
thf(2682,plain,
! [A: $i] :
( ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
thf(1460,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1461,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
| ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(cnf,[status(esa)],[1460]) ).
thf(1462,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(lifteq,[status(thm)],[1461]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(2571,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(809,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
thf(3891,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).
thf(4637,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(609,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).
thf(3248,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(4238,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(613,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
thf(3263,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(600,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
thf(3221,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__comm__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(4546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__comm__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(834,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
thf(3976,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(4524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
thf(1760,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1660,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(860,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
thf(4070,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(561,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
thf(3116,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(418,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Olinordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
thf(2667,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Olinordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).
thf(2339,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(34600,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33066,1403]) ).
thf(34601,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[34600]) ).
thf(34602,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[34601:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(2708,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(791,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
thf(3821,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(1144,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
thf(5064,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
thf(2501,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1038,axiom,
tc_RealDef_Oreal @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
thf(4654,plain,
tc_RealDef_Oreal @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatceiling )
= ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add) ).
thf(3617,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatceiling )
= ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(15,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(1330,plain,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).
thf(2217,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
thf(3612,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(574,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
thf(3148,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(4130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).
thf(1312,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1313,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ class_Groups_Oordered__ab__group__add__abs ) ),
inference(cnf,[status(esa)],[1312]) ).
thf(922,axiom,
tc_RealDef_Oreal @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
thf(4275,plain,
tc_RealDef_Oreal @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
thf(1577,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( A @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1455,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( A @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1176,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
<=> ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def2) ).
thf(5182,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) )
& ( ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(796,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(3845,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(769,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
thf(3744,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(2683,plain,
( ! [A: $i] :
( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(miniscope,[status(thm)],[2682]) ).
thf(2684,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(cnf,[status(esa)],[2683]) ).
thf(2686,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[2684]) ).
thf(2688,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[2686]) ).
thf(2689,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
inference(simp,[status(thm)],[2688]) ).
thf(882,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
thf(4150,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(4151,plain,
( ! [A: $i,B: $i] :
( ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(miniscope,[status(thm)],[4150]) ).
thf(4152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( D = C )
| ~ ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B != A )
| ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(cnf,[status(esa)],[4151]) ).
thf(4154,plain,
! [B: $i,A: $i] :
( ( B != A )
| ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(cnfConj,[status(thm)],[4152]) ).
thf(4156,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[4154]) ).
thf(4157,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(simp,[status(thm)],[4156]) ).
thf(42777,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2689,4157]) ).
thf(42778,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[42777]) ).
thf(42870,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= A )
| ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
!= A )
| ( tc_Int_Oint != tc_Int_Oint ) ),
inference(simp,[status(thm)],[42778]) ).
thf(42947,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(simp,[status(thm)],[42870]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
thf(2466,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(33038,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28743,1403]) ).
thf(33039,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[33038]) ).
thf(33040,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[33039:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly ))]]) ).
thf(1205,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
thf(5279,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).
thf(2703,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).
thf(2691,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(16342,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[1271,3064]) ).
thf(16343,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16342]) ).
thf(16369,plain,
! [B: $i,A: $i] :
( ( v_r != B )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16343]) ).
thf(16391,plain,
! [A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16369]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(4119,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(952,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(4353,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).
thf(1704,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(3258,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(171,axiom,
! [A: $i] :
( ( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zsgn__def) ).
thf(1847,plain,
! [A: $i] :
( ( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1020,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(4595,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(1800,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1223,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__neg) ).
thf(5338,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(1892,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(1377,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(cnf,[status(esa)],[1377]) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(lifteq,[status(thm)],[1378]) ).
thf(653,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opos__poly ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__total) ).
thf(3385,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opos__poly ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(891,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
thf(4194,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).
thf(2049,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(997,axiom,
tc_RealDef_Oreal @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
thf(4492,plain,
tc_RealDef_Oreal @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
thf(2373,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(406,axiom,
tc_Int_Oint @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(2635,plain,
tc_Int_Oint @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(681,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
thf(3470,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(3312,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(1568,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(766,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(3734,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(3014,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(4141,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).
thf(1641,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(756,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
thf(3708,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1815,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(985,axiom,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(4460,plain,
tc_Complex_Ocomplex @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(1077,axiom,
tc_RealDef_Oreal @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
thf(4793,plain,
tc_RealDef_Oreal @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(3557,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(1072,axiom,
! [A: $i,B: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
thf(4771,plain,
! [A: $i,B: $i] :
( ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(3231,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1149,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(5077,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(4514,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(328,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(2388,plain,
tc_Nat_Onat @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(23667,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,20038]) ).
thf(23668,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[23667]) ).
thf(23669,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[23668:[bind(A,$thf( E @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )),bind(B,$thf( E ))]]) ).
thf(23768,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[23669]) ).
thf(1200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( E
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B != A )
& ( D = C ) )
=> ( ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(5264,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( E
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B != A )
& ( D = C ) )
=> ( ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
thf(3524,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__le) ).
thf(2794,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
thf(3966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(1632,plain,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(285,axiom,
tc_Int_Oint @ class_Rings_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
thf(2259,plain,
tc_Int_Oint @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(413,axiom,
tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
thf(2650,plain,
tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(485,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(2880,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
thf(2073,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(35212,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,16391]) ).
thf(35213,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35212]) ).
thf(35214,plain,
( ( ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(pattern_uni,[status(thm)],[35213:[bind(A,$thf( sk53 ))]]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
thf(2950,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B = A )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1131,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_RComplete_Onatfloor @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).
thf(4988,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_RComplete_Onatfloor @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(1415,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(1946,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(4396,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(1463,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1464,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
inference(cnf,[status(esa)],[1463]) ).
thf(1465,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
inference(lifteq,[status(thm)],[1464]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(2105,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
thf(1811,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(26379,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4226,1403]) ).
thf(26380,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[26379]) ).
thf(26381,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[26380:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
thf(1450,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(981,axiom,
tc_Complex_Ocomplex @ class_Groups_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
thf(4443,plain,
tc_Complex_Ocomplex @ class_Groups_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(1153,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
thf(5084,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
thf(1373,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(761,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
thf(3724,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1022,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__zero) ).
thf(4600,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(628,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(3295,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(2782,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(1416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le ) )
& ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ) ),
inference(cnf,[status(esa)],[1415]) ).
thf(1418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
inference(cnfConj,[status(thm)],[1416]) ).
thf(672,axiom,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3453,plain,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(2451,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
thf(3473,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(3702,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(668,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
thf(3438,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(880,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
thf(4147,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(1828,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(40992,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39331,1403]) ).
thf(40993,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[40992]) ).
thf(40994,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[40993:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(711,axiom,
tc_RealDef_Oreal @ class_Groups_Oabs__if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).
thf(3569,plain,
tc_RealDef_Oreal @ class_Groups_Oabs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
thf(2540,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(3300,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(380,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
thf(2555,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(625,axiom,
tc_Int_Oint @ class_Rings_Ocomm__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
thf(3290,plain,
tc_Int_Oint @ class_Rings_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(90,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1581,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1049,axiom,
tc_Complex_Ocomplex @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
thf(4686,plain,
tc_Complex_Ocomplex @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(2335,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(1259,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(5457,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(1229,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(5360,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).
thf(3771,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(1081,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(4810,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(4718,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(193,axiom,
tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
thf(1928,plain,
tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
thf(2833,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(2190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(743,axiom,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
thf(3685,plain,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(3036,plain,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).
thf(2103,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(897,axiom,
tc_RealDef_Oreal @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
thf(4211,plain,
tc_RealDef_Oreal @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(652,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(3378,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(838,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
thf(3986,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
thf(2058,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1227,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).
thf(5353,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(4842,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
thf(5220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(1182,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__comm__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(5210,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__comm__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(35626,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33978,1403]) ).
thf(35627,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[35626]) ).
thf(35628,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[35627:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(1284,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(cnf,[status(esa)],[1284]) ).
thf(20738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[20324,1285]) ).
thf(20739,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20738]) ).
thf(20740,plain,
! [B: $i,A: $i] :
( ( A @ ( v_r @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[20739:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( v_r @ c_Nat_OSuc )),bind(D,$thf( G @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ))]]) ).
thf(20794,plain,
! [B: $i,A: $i] :
( ( A @ ( v_r @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20740]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
thf(1447,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).
thf(2483,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(865,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
thf(4087,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(342,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
thf(2424,plain,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).
thf(2979,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(40488,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Int_Oint != tc_Nat_Onat ) ),
inference(paramod_ordered,[status(thm)],[2276,37517]) ).
thf(40512,plain,
( ( tc_Int_Oint != tc_Nat_Onat )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Int_Oint != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[40488]) ).
thf(40513,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Int_Oint != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[40512]) ).
thf(1195,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
thf(5246,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__div__algebra )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power) ).
thf(4307,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__div__algebra )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(739,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(3676,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(33996,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32988,1403]) ).
thf(33997,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[33996]) ).
thf(33998,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[33997:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ~ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oabs__class_Oabs ) )
= A ) )
& ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__poly__def) ).
thf(2002,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ~ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oabs__class_Oabs ) )
= A ) )
& ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(606,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(3243,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( A @ ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__1) ).
thf(1344,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( A @ ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1345,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( C @ class_Rings_Oidom ) ),
inference(cnf,[status(esa)],[1344]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ! [E: $i,F: $i] :
( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
thf(2286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ class_Rings_Odvd )
& ( D @ class_Rings_Ocomm__ring ) )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ! [E: $i,F: $i] :
( ( ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(5664,plain,
! [A: $i] :
( ( A
!= ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) ) )
| ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,5492]) ).
thf(5665,plain,
( ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[5664:[bind(A,$thf( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) ))]]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__no__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(3588,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__no__zero__divisors )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
thf(4379,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1019,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
thf(4588,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(34744,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[2276,2804]) ).
thf(34790,plain,
( ( tc_Int_Oint != tc_Nat_Onat )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[34744]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(3184,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(2586,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(2982,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
thf(2884,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(99,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
thf(1604,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).
thf(4604,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1245,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
thf(5399,plain,
! [A: $i] :
( ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(5400,plain,
( ! [A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ! [A: $i] :
( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(miniscope,[status(thm)],[5399]) ).
thf(5401,plain,
! [B: $i,A: $i] :
( ( ~ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( B
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(cnf,[status(esa)],[5400]) ).
thf(5403,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[5401]) ).
thf(5405,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[5403]) ).
thf(5406,plain,
~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(simp,[status(thm)],[5405]) ).
thf(941,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).
thf(4323,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(5775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[1271,1285]) ).
thf(5776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5775]) ).
thf(5778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_r != C )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= D )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[5776]) ).
thf(5781,plain,
! [B: $i,A: $i] :
( ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[5778]) ).
thf(20278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( C @ c_Nat_OSuc @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[5781,1392]) ).
thf(20279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( C @ c_Nat_OSuc @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20278]) ).
thf(20280,plain,
! [B: $i,A: $i] :
( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[20279:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( J @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )),bind(D,$thf( G @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ))]]) ).
thf(20348,plain,
! [B: $i,A: $i] :
( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20280]) ).
thf(697,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(3531,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__dvd) ).
thf(2118,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1162,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
thf(5117,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(1470,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
thf(4925,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( B @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__if__abs__eq) ).
thf(1730,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( B @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1212,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Opcompose ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opcompose ) ) @ ( A @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
thf(5298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Opcompose ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opcompose ) ) @ ( A @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(174,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
thf(1863,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(575,axiom,
! [A: $i] :
~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
thf(3151,plain,
! [A: $i] :
~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(2011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(631,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
thf(3303,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1120,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(4962,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(38985,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35602,1409]) ).
thf(38986,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[38985]) ).
thf(38987,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[38986:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
thf(2473,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(710,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).
thf(3567,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(1691,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(837,axiom,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
thf(3984,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(991,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(4480,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(20726,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[20324,1392]) ).
thf(20727,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20726]) ).
thf(20728,plain,
! [A: $i] :
( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[20727:[bind(A,$thf( F )),bind(B,$thf( v_r @ c_Nat_OSuc )),bind(C,$thf( F @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ))]]) ).
thf(20848,plain,
! [A: $i] :
( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20728]) ).
thf(35236,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,20848]) ).
thf(35237,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35236]) ).
thf(35238,plain,
( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(pattern_uni,[status(thm)],[35237:[bind(A,$thf( sk53 ))]]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(1338,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1168,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
thf(5142,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(39361,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36149,1403]) ).
thf(39362,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[39361]) ).
thf(39363,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[39362:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( F @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( F @ ( E @ c_Polynomial_Opoly__rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( F @ ( E @ c_Polynomial_Opoly__rec ) ) ) ) @ ( D @ ( F @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_fequal ) @ ( E @ c_If ) ) ) @ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec_Osimps) ).
thf(4370,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ozero )
=> ( ( A @ ( B @ ( F @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( F @ ( E @ c_Polynomial_Opoly__rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( F @ ( E @ c_Polynomial_Opoly__rec ) ) ) ) @ ( D @ ( F @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_fequal ) @ ( E @ c_If ) ) ) @ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Polynomial_Opos__poly ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__poly__def) ).
thf(1304,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Polynomial_Opos__poly ) )
| ( B = A ) )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Polynomial_Opos__poly ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1305,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Polynomial_Opos__poly ) )
| ~ ( C @ class_Rings_Olinordered__idom ) )
& ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B != A )
| ~ ( C @ class_Rings_Olinordered__idom ) )
& ( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Polynomial_Opos__poly ) )
| ( B = A )
| ~ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ class_Rings_Olinordered__idom ) ) ),
inference(cnf,[status(esa)],[1304]) ).
thf(1307,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B != A )
| ~ ( C @ class_Rings_Olinordered__idom ) ),
inference(cnfConj,[status(thm)],[1305]) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ class_Rings_Olinordered__idom )
| ( B != A ) ),
inference(lifteq,[status(thm)],[1307]) ).
thf(1311,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ class_Rings_Olinordered__idom ) ),
inference(simp,[status(thm)],[1310]) ).
thf(280,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
thf(2232,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(2307,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(4031,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
thf(2621,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1222,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(5334,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(176,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
thf(1868,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
thf(2382,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(449,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(2773,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(5281,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym_H) ).
thf(3261,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(2428,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
thf(1519,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1099,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(4878,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).
thf(1570,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(768,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
thf(3742,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(3371,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1181,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(5206,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(421,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
thf(2673,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(1142,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(5049,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(395,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(2589,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(1105,axiom,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).
thf(4915,plain,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(2409,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(758,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(3711,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_fequal ) @ hBOOL )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1340,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_fequal ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_fequal ) @ hBOOL )
| ( B != A ) ),
inference(cnf,[status(esa)],[1340]) ).
thf(1342,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_fequal ) @ hBOOL )
| ( B != A ) ),
inference(lifteq,[status(thm)],[1341]) ).
thf(1343,plain,
! [A: $i] : ( A @ ( A @ c_fequal ) @ hBOOL ),
inference(simp,[status(thm)],[1342]) ).
thf(845,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
thf(4016,plain,
tc_Complex_Ocomplex @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(460,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
thf(2805,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
thf(3972,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
thf(4920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(291,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
thf(2277,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
thf(4375,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Opcompose ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pcompose) ).
thf(4434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_Opcompose ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(534,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
thf(3022,plain,
tc_Nat_Onat @ class_Groups_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(1258,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(5455,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
thf(1751,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
thf(1487,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(772,axiom,
tc_RealDef_Oreal @ class_Rings_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).
thf(3752,plain,
tc_RealDef_Oreal @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(839,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oidom )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
| ( B
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
thf(3989,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oidom )
=> ( ( ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
| ( B
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
| ( B
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(4128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(576,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(3154,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(567,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__2) ).
thf(3134,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(4493,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(104,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
thf(1619,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
thf(2150,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).
thf(1370,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(787,axiom,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
thf(3814,plain,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1243,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
thf(5396,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(6355,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_Complex_Ocomplex )
| ( v_r @ ( C @ sk1 @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1298,1271]) ).
thf(6356,plain,
! [B: $i,A: $i] :
( ( v_r @ ( B @ sk1 @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Complex_Ocomplex @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_Complex_Ocomplex @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[6355:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).
thf(6696,plain,
! [B: $i,A: $i] :
( ( v_r @ ( B @ sk1 @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Complex_Ocomplex @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_Complex_Ocomplex @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[6356]) ).
thf(489,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(2890,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(2414,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(883,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
thf(4160,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(737,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
thf(3664,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).
thf(3207,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(332,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(2396,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(7532,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,5659]) ).
thf(7533,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7532]) ).
thf(7564,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7533]) ).
thf(7565,plain,
( ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7564]) ).
thf(3681,plain,
~ ? [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(miniscope,[status(thm)],[3680]) ).
thf(3682,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(cnf,[status(esa)],[3681]) ).
thf(855,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
thf(4044,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(3286,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).
thf(1560,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(1419,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
| ( B != A )
| ~ ( D @ class_Groups_Ocancel__semigroup__add ) )
& ( ( B = A )
| ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
!= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
| ~ ( D @ class_Groups_Ocancel__semigroup__add ) ) ),
inference(cnf,[status(esa)],[1419]) ).
thf(1421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = A )
| ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
!= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
| ~ ( D @ class_Groups_Ocancel__semigroup__add ) ),
inference(cnfConj,[status(thm)],[1420]) ).
thf(1423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ class_Groups_Ocancel__semigroup__add )
| ( B = A )
| ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
!= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(lifteq,[status(thm)],[1421]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).
thf(3877,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
thf(2068,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ouminus )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).
thf(1656,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ouminus )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(3028,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1407,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( C @ class_Groups_Oordered__ab__group__add ) ),
inference(cnfConj,[status(thm)],[1405]) ).
thf(539,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(3033,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
thf(1301,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1302,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
| ~ ( B @ class_Groups_Ogroup__add ) ),
inference(cnf,[status(esa)],[1301]) ).
thf(1303,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Groups_Ogroup__add )
| ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[1302]) ).
thf(7602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
!= ( D @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ c_Groups_Ozero__class_Ozero @ ( C @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ class_Groups_Ogroup__add ) ),
inference(paramod_ordered,[status(thm)],[1303,5781]) ).
thf(7604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
!= v_r )
| ( B != tc_Nat_Onat )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( B @ class_Groups_Ogroup__add )
| ( B @ c_Groups_Ozero__class_Ozero @ ( C @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[7602]) ).
thf(7608,plain,
! [B: $i,A: $i] :
( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ouminus__class_Ouminus ) )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ class_Groups_Ogroup__add )
| ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[7604]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__eq) ).
thf(2445,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(930,axiom,
tc_RealDef_Oreal @ class_Groups_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
thf(4295,plain,
tc_RealDef_Oreal @ class_Groups_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(2464,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(1938,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(925,axiom,
tc_RealDef_Oreal @ class_Groups_Ouminus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).
thf(4280,plain,
tc_RealDef_Oreal @ class_Groups_Ouminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(2758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(482,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
thf(2873,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(835,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(3980,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(166,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
thf(1837,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__lemma) ).
thf(1602,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
thf(4192,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(420,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(2670,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(857,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
thf(4053,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(27537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( D @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( v_r @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ~ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( C @ class_Groups_Oordered__ab__group__add ) ),
inference(paramod_ordered,[status(thm)],[1406,27536]) ).
thf(27538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( D @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( v_r @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( C @ class_Groups_Oordered__ab__group__add ) ),
inference(simp,[status(thm)],[27537]) ).
thf(27539,plain,
! [A: $i] :
( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add ) ),
inference(pattern_uni,[status(thm)],[27538:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )),bind(C,$thf( tc_RealDef_Oreal )),bind(D,$thf( A ))]]) ).
thf(28438,plain,
! [A: $i] :
( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[27539,4320]) ).
thf(28439,plain,
! [A: $i] :
( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[28438]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(1968,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
thf(3198,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(40748,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39159,1409]) ).
thf(40749,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[40748]) ).
thf(40750,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[40749:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(311,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(2332,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
thf(2820,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(629,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(3297,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(568,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
thf(3137,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(547,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3065,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
thf(1951,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1260,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra__1 )
=> ( A @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
thf(5460,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra__1 )
=> ( A @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(1137,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(5018,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(5019,plain,
( ! [A: $i] :
( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(miniscope,[status(thm)],[5018]) ).
thf(5020,plain,
! [B: $i,A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(cnf,[status(esa)],[5019]) ).
thf(5022,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[5020]) ).
thf(5024,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[5022]) ).
thf(5025,plain,
tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ),
inference(simp,[status(thm)],[5024]) ).
thf(37831,plain,
! [B: $i,A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5025,1392]) ).
thf(37832,plain,
! [B: $i,A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[37831]) ).
thf(37833,plain,
tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ),
inference(pattern_uni,[status(thm)],[37832:[bind(A,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )),bind(B,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ))]]) ).
thf(40365,plain,
! [A: $i] :
( ( ( A @ ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37833,20525]) ).
thf(40366,plain,
! [A: $i] :
( ( A @ ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[40365]) ).
thf(40418,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Nat_Onat != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[40366]) ).
thf(40444,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[40418]) ).
thf(1224,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__div__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).
thf(5341,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__div__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
= ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(572,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(3144,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(1065,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).
thf(4746,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
thf(4402,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(699,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(3535,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(1160,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
thf(5113,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(304,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).
thf(2313,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(377,axiom,
tc_Int_Oint @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
thf(2547,plain,
tc_Int_Oint @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
thf(2344,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(986,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(4461,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
thf(1573,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1221,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(5330,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(783,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(3799,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(4316,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(1145,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(5066,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(1202,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Oidom )
& ( B @ class_Int_Oring__char__0 ) )
=> ( ( ( A @ ( B @ c_Polynomial_Opoly ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) ) )
<=> ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).
thf(5270,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Oidom )
& ( B @ class_Int_Oring__char__0 ) )
=> ( ( ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Polynomial_Opoly ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) ) ) )
& ( ( ( A @ ( B @ c_Polynomial_Opoly ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) ) )
=> ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(1248,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
thf(5423,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(1011,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(4544,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
thf(1587,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1230,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(5362,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
<=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(2726,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( A
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ c_Groups_Oone__class_Oone )
= A ) )
& ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1088,axiom,
tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
thf(4840,plain,
tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
thf(2638,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(3001,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(3731,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(832,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
thf(3968,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(871,axiom,
! [A: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
thf(4123,plain,
! [A: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
thf(1349,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1350,plain,
( ! [A: $i,B: $i] :
( ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B = A )
| ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1349]) ).
thf(1351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( D != C ) )
& ( ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( D @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( B = A )
| ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(cnf,[status(esa)],[1350]) ).
thf(1355,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( B != A ) ),
inference(cnfConj,[status(thm)],[1351]) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[1355]) ).
thf(1360,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(simp,[status(thm)],[1359]) ).
thf(1177,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
thf(5189,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
thf(2300,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(680,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(3467,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1364,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1365,plain,
~ ? [A: $i] :
( ( A @ c_Nat_OSuc )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(miniscope,[status(thm)],[1364]) ).
thf(1366,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(cnf,[status(esa)],[1365]) ).
thf(1367,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[1366]) ).
thf(5610,plain,
! [B: $i,A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( B @ c_Nat_OSuc ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,1367]) ).
thf(5611,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[5610:[bind(A,$thf( A )),bind(B,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ))]]) ).
thf(5626,plain,
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(simp,[status(thm)],[5611]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(3782,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(3615,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(13864,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,5594]) ).
thf(13865,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[13864]) ).
thf(13921,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[13865]) ).
thf(13946,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[13921]) ).
thf(792,axiom,
! [A: $i] :
( ( ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__real__def) ).
thf(3824,plain,
! [A: $i] :
( ( ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(3825,plain,
( ! [A: $i] :
( ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) )
& ! [A: $i] :
( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(miniscope,[status(thm)],[3824]) ).
thf(3826,plain,
! [B: $i,A: $i] :
( ( ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(cnf,[status(esa)],[3825]) ).
thf(3827,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[3826]) ).
thf(3830,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[3827]) ).
thf(3831,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[3830]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).
thf(2157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(474,axiom,
tc_Int_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(2840,plain,
tc_Int_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(685,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
thf(3482,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(247,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oabs__class_Oabs ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).
thf(2100,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oabs__class_Oabs ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(147,axiom,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero) ).
thf(1772,plain,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(509,axiom,
! [A: $i] :
( ( A @ class_Groups_Ogroup__add )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
thf(2946,plain,
! [A: $i] :
( ( A @ class_Groups_Ogroup__add )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(6345,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_RealDef_Oreal )
| ( v_r @ ( C @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ ( A @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1298,1271]) ).
thf(6346,plain,
! [B: $i,A: $i] :
( ( v_r @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( A @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[6345:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).
thf(6691,plain,
! [B: $i,A: $i] :
( ( v_r @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( A @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[6346]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(4248,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
thf(2841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(20886,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1394,3064]) ).
thf(20887,plain,
! [B: $i,A: $i] :
( ( A @ c_Nat_OSuc @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[20886]) ).
thf(20921,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc )
!= B )
| ( ( A @ c_Nat_OSuc )
!= ( B @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[20887]) ).
thf(20944,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( A @ c_Nat_OSuc ) ),
inference(simp,[status(thm)],[20921]) ).
thf(994,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__algebra )
=> ( ( C @ ( D @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).
thf(4486,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__algebra )
=> ( ( C @ ( D @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).
thf(2359,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_Power_Opower ) ),
inference(cnf,[status(esa)],[1373]) ).
thf(1375,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ class_Power_Opower )
| ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[1374]) ).
thf(1053,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(4693,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(1091,axiom,
tc_Complex_Ocomplex @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
thf(4845,plain,
tc_Complex_Ocomplex @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(11,axiom,
! [A: $i] :
( A
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1314,plain,
! [A: $i] :
( A
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1315,plain,
~ ? [A: $i] :
( A
= ( A @ c_Nat_OSuc ) ),
inference(miniscope,[status(thm)],[1314]) ).
thf(1316,plain,
! [A: $i] :
( A
!= ( A @ c_Nat_OSuc ) ),
inference(cnf,[status(esa)],[1315]) ).
thf(1317,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= A ),
inference(lifteq,[status(thm)],[1316]) ).
thf(7646,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= B )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,1317]) ).
thf(7647,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= A )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[7646:[bind(A,$thf( C @ c_Nat_OSuc )),bind(B,$thf( C ))]]) ).
thf(7653,plain,
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(simp,[status(thm)],[7647]) ).
thf(7993,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,7653]) ).
thf(7994,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[7993]) ).
thf(8013,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[7994]) ).
thf(8016,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(simp,[status(thm)],[8013]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
thf(1672,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ( B = A )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
thf(1719,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ( B = A )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(905,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(4227,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(813,axiom,
tc_RealDef_Oreal @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
thf(3916,plain,
tc_RealDef_Oreal @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(604,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(3237,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B != A )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
thf(2268,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B != A )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(669,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd1__eq) ).
thf(3440,plain,
! [A: $i] :
( ( ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(3060,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(917,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
thf(4263,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(15758,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ class_Rings_Ocomm__semiring__0 )
!= ( A @ class_Rings_Ocomm__semiring__0 ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2873,1369]) ).
thf(15759,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ class_Rings_Ocomm__semiring__0 )
!= ( A @ class_Rings_Ocomm__semiring__0 ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
inference(simp,[status(thm)],[15758]) ).
thf(15760,plain,
tc_Nat_Onat @ tc_Polynomial_Opoly @ class_Rings_Osemiring,
inference(pattern_uni,[status(thm)],[15759:[bind(A,$thf( tc_Nat_Onat ))]]) ).
thf(571,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(3143,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1018,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
thf(4582,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
thf(5080,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(1123,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
thf(4970,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(4971,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(polarity_switch,[status(thm)],[4970]) ).
thf(4972,plain,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[4971]) ).
thf(5570,plain,
! [A: $i] :
( ( A
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,4972]) ).
thf(5571,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[5570:[bind(A,$thf( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ))]]) ).
thf(13414,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,5571]) ).
thf(13415,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[13414]) ).
thf(13471,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[13415]) ).
thf(13495,plain,
( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[13471]) ).
thf(763,axiom,
tc_Complex_Ocomplex @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
thf(3728,plain,
tc_Complex_Ocomplex @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(965,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Oidom )
& ( C @ class_Int_Oring__char__0 ) )
=> ( ( ( B @ ( C @ c_Polynomial_Opoly ) )
= ( A @ ( C @ c_Polynomial_Opoly ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
thf(4389,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Oidom )
& ( C @ class_Int_Oring__char__0 ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Polynomial_Opoly ) )
= ( A @ ( C @ c_Polynomial_Opoly ) ) ) )
& ( ( ( B @ ( C @ c_Polynomial_Opoly ) )
= ( A @ ( C @ c_Polynomial_Opoly ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(971,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(4406,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
thf(2613,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).
thf(2551,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(1644,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(1493,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
thf(1683,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).
thf(2798,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(828,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(3954,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(14,axiom,
tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(1329,plain,
tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(2877,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(827,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
thf(3952,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(1117,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(4951,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
thf(1361,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1094,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
thf(4860,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring )
=> ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(923,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(4276,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(114,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(1659,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(3922,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( B @ c_Groups_Osgn__class_Osgn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).
thf(2561,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( B @ c_Groups_Osgn__class_Osgn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
thf(3210,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(555,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
thf(3094,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(4167,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(5464,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(1067,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(4750,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(1113,axiom,
tc_Complex_Ocomplex @ class_Groups_Ouminus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
thf(4938,plain,
tc_Complex_Ocomplex @ class_Groups_Ouminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1199,axiom,
tc_RealDef_Oreal @ class_Rings_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
thf(5263,plain,
tc_RealDef_Oreal @ class_Rings_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(1412,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1413,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(cnf,[status(esa)],[1412]) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(lifteq,[status(thm)],[1413]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
thf(2240,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(1842,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A
!= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__poly__def) ).
thf(1791,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A
!= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1036,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(4648,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Ozero__neq__one )
& ( C @ class_Rings_Ono__zero__divisors )
& ( C @ class_Rings_Omult__zero )
& ( C @ class_Power_Opower ) )
=> ( ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
thf(2108,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Ozero__neq__one )
& ( C @ class_Rings_Ono__zero__divisors )
& ( C @ class_Rings_Omult__zero )
& ( C @ class_Power_Opower ) )
=> ( ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1436,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(cnfConj,[status(thm)],[1432]) ).
thf(1446,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(lifteq,[status(thm)],[1436]) ).
thf(1097,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
thf(4867,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__interval__iff) ).
thf(4444,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(417,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(2666,plain,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(412,axiom,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(2649,plain,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(40578,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38987,1403]) ).
thf(40579,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[40578]) ).
thf(40580,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[40579:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(2317,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(1240,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
thf(5387,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__neg) ).
thf(1744,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(819,axiom,
tc_RealDef_Oreal @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
thf(3935,plain,
tc_RealDef_Oreal @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(20888,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1394,20328]) ).
thf(20889,plain,
! [B: $i,A: $i] :
( ( A @ c_Nat_OSuc @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[20888]) ).
thf(20920,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Nat_OSuc )
!= B )
| ( ( A @ c_Nat_OSuc )
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[20889]) ).
thf(20943,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( A @ c_Nat_OSuc ) ),
inference(simp,[status(thm)],[20920]) ).
thf(21059,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc @ c_Nat_OSuc )
!= A ),
inference(simp,[status(thm)],[20943]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ c_fequal ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(1831,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ c_fequal ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(2851,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(390,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(2581,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(1984,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(950,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(4347,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A )
<=> ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
thf(1874,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ) )
& ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A )
=> ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(640,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(3333,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(815,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
thf(3920,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(1825,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(515,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(2968,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(1217,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(5317,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).
thf(4846,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(721,axiom,
tc_Complex_Ocomplex @ class_Rings_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
thf(3611,plain,
tc_Complex_Ocomplex @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(350,axiom,
tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(2450,plain,
tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(3486,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Osgn__if )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).
thf(1478,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Osgn__if )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) )
& ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).
thf(4384,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(74,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
thf(1530,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1531,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(lifteq,[status(thm)],[1530]) ).
thf(36731,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(rewrite,[status(thm)],[1531,2276]) ).
thf(36732,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
!= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[36731,4623]) ).
thf(36733,plain,
~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(pattern_uni,[status(thm)],[36732:[bind(A,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ))]]) ).
thf(1235,axiom,
! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
thf(5374,plain,
! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(301,axiom,
tc_Int_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(2304,plain,
tc_Int_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).
thf(1382,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1166,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__pos) ).
thf(5134,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
thf(2355,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(4482,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(1932,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(4244,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(1083,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).
thf(4829,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(3819,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(906,axiom,
tc_RealDef_Oreal @ class_Groups_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
thf(4237,plain,
tc_RealDef_Oreal @ class_Groups_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(1112,axiom,
~ ! [A: $i] :
~ ! [B: $i] :
( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(4934,plain,
~ ! [A: $i] :
~ ! [B: $i] :
( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(4540,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(1143,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
thf(5058,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(821,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(3937,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
| ( C
!= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( D @ class_Rings_Odvd ) ),
inference(cnf,[status(esa)],[1426]) ).
thf(1428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( D @ class_Rings_Odvd )
| ( C
!= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[1427]) ).
thf(1429,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( C @ class_Rings_Odvd ) ),
inference(simp,[status(thm)],[1428]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).
thf(3409,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(748,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(3692,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oring )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
thf(2052,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oring )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1599,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(914,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
thf(4259,plain,
tc_Complex_Ocomplex @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(1051,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
thf(4689,plain,
tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(1138,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(5026,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(3005,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(579,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(3162,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(591,axiom,
tc_Nat_Onat @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(3201,plain,
tc_Nat_Onat @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(902,axiom,
tc_RealDef_Oreal @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
thf(4223,plain,
tc_RealDef_Oreal @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(144,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1759,plain,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__iff) ).
thf(3215,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(1267,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).
thf(5479,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
thf(1525,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1194,axiom,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(5245,plain,
tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(956,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_Opos__poly ) )
<=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
| ( A @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
thf(4361,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
| ( A @ ( C @ c_Polynomial_Opos__poly ) ) )
=> ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_Opos__poly ) ) )
& ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_Opos__poly ) )
=> ( ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
& ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
| ( A @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(35273,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ $true
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(paramod_ordered,[status(thm)],[5428,5762]) ).
thf(35274,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[35273]) ).
thf(35275,plain,
( ( ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(pattern_uni,[status(thm)],[35274:[bind(A,$thf( sk53 ))]]) ).
thf(673,axiom,
! [A: $i] : ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
thf(3454,plain,
! [A: $i] : ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( B
= ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_RComplete_Onatfloor )
= ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__power) ).
thf(2203,plain,
! [A: $i,B: $i] :
( ( B
= ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_RComplete_Onatfloor )
= ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1035,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(4644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(4081,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(1121,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( D @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) @ hAPP ) )
= B )
=> ( ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( B @ ( D @ ( A @ c_Polynomial_Opoly__rec ) ) ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__0) ).
thf(4966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ozero )
=> ( ( ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( D @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) @ hAPP ) )
= B )
=> ( ( D @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ ( B @ ( D @ ( A @ c_Polynomial_Opoly__rec ) ) ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(11274,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Groups_Ogroup__add )
!= ( tc_Nat_Onat @ class_Groups_Ogroup__add ) )
| ( ( B @ ( tc_Nat_Onat @ c_Groups_Ouminus__class_Ouminus ) )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ $true
| ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(paramod_ordered,[status(thm)],[2231,7608]) ).
thf(11275,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Groups_Ogroup__add )
!= ( tc_Nat_Onat @ class_Groups_Ogroup__add ) )
| ( ( B @ ( tc_Nat_Onat @ c_Groups_Ouminus__class_Ouminus ) )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[11274]) ).
thf(11407,plain,
! [B: $i,A: $i] :
( ( tc_Int_Oint != tc_Nat_Onat )
| ( ( B @ ( tc_Nat_Onat @ c_Groups_Ouminus__class_Ouminus ) )
!= v_r )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[11275]) ).
thf(1253,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
thf(5434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
thf(1466,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(731,axiom,
! [A: $i] :
( ( v_r @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( v_m____ @ ( A @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m) ).
thf(3639,plain,
! [A: $i] :
( ( v_r @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( v_m____ @ ( A @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(2995,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(313,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(2338,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(2909,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(881,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(4148,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(2788,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
thf(1318,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1172,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(5153,plain,
! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(500,axiom,
tc_Nat_Onat @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(2926,plain,
tc_Nat_Onat @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
thf(2043,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(619,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(3279,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
thf(4212,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(1100,axiom,
! [A: $i] :
( ( ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= A ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__abs__def) ).
thf(4889,plain,
! [A: $i] :
( ( ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= A ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(82,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
thf(1563,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1564,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(cnf,[status(esa)],[1563]) ).
thf(41909,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(rewrite,[status(thm)],[1564,2276]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).
thf(3306,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( C @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(239,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ouminus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
thf(2076,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ouminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(7734,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,7565]) ).
thf(7735,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[7734]) ).
thf(7736,plain,
( ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[7735:[bind(A,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) ))]]) ).
thf(14959,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,7736]) ).
thf(14960,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[14959]) ).
thf(15077,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[14960]) ).
thf(15136,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( v_r @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[15077]) ).
thf(841,axiom,
tc_RealDef_Oreal @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
thf(3999,plain,
tc_RealDef_Oreal @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(335,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(2408,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(454,axiom,
tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2793,plain,
tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
thf(1663,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(2089,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1211,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(5295,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(2617,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(1196,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
thf(5249,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(5818,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[5781,1285]) ).
thf(5819,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5818]) ).
thf(5820,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[5819:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( K @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )),bind(E,$thf( H @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ))]]) ).
thf(5840,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5820]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(2529,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
thf(2144,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(21345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[20848,1392]) ).
thf(21346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[21345]) ).
thf(21347,plain,
! [A: $i] :
( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[21346:[bind(A,$thf( F )),bind(B,$thf( v_r @ c_Nat_OSuc @ c_Nat_OSuc )),bind(C,$thf( F @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ))]]) ).
thf(21473,plain,
! [A: $i] :
( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[21347]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(2936,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(216,axiom,
tc_Nat_Onat @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(2001,plain,
tc_Nat_Onat @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1256,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
thf(5451,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(6351,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_RealDef_Oreal )
| ( v_r @ ( C @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1298,1271]) ).
thf(6352,plain,
! [B: $i,A: $i] :
( ( v_r @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[6351:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).
thf(6694,plain,
! [B: $i,A: $i] :
( ( v_r @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[6352]) ).
thf(16347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[6694,3064]) ).
thf(16348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[16347]) ).
thf(16368,plain,
! [C: $i,B: $i,A: $i] :
( ( v_r != C )
| ( ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( C @ c_Nat_OSuc ) )
| ( A != tc_Nat_Onat )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[16348]) ).
thf(16390,plain,
! [A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( tc_Nat_Onat @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[16368]) ).
thf(1015,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
thf(4562,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(999,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(4503,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
thf(1727,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1219,axiom,
! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
thf(5327,plain,
! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(13981,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,13946]) ).
thf(13982,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[13981:[]]) ).
thf(14020,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[13982]) ).
thf(423,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
thf(2677,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1057,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
thf(4708,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).
thf(1754,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__int) ).
thf(2292,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(330,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
thf(2391,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(2904,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(121,axiom,
tc_Int_Oint @ class_Rings_Olinordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1680,plain,
tc_Int_Oint @ class_Rings_Olinordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
thf(3358,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
thf(2033,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order) ).
thf(2253,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( B
!= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
thf(3871,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(223,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
thf(2028,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(947,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(4340,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(95,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(1595,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(436,axiom,
tc_Int_Oint @ class_Rings_Oring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(2734,plain,
tc_Int_Oint @ class_Rings_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(955,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(4359,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(559,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
thf(3111,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(920,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).
thf(4269,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(3686,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(846,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(4017,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(370,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ c_RComplete_Onatceiling )
= ( B @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__subtract) ).
thf(2524,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ c_RComplete_Onatceiling )
= ( B @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
thf(2376,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(984,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(4453,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(3343,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
thf(2260,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(853,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
thf(4041,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1042,axiom,
tc_RealDef_Oreal @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
thf(4662,plain,
tc_RealDef_Oreal @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(549,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(3070,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(693,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
thf(3519,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(1448,plain,
! [A: $i] :
( ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring )
| ~ ( A @ class_Rings_Olinordered__idom ) ),
inference(cnf,[status(esa)],[1447]) ).
thf(37714,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Rings_Olinordered__idom )
!= ( A @ class_Rings_Olinordered__idom ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3744,1448]) ).
thf(37715,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Rings_Olinordered__idom )
!= ( A @ class_Rings_Olinordered__idom ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring ) ),
inference(simp,[status(thm)],[37714]) ).
thf(37716,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring,
inference(pattern_uni,[status(thm)],[37715:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( B = A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
thf(1620,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
thf(2393,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(810,axiom,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
thf(3893,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(3894,plain,
( ! [A: $i] :
( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(miniscope,[status(thm)],[3893]) ).
thf(3895,plain,
! [B: $i,A: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(cnf,[status(esa)],[3894]) ).
thf(3897,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[3895]) ).
thf(3899,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[3897]) ).
thf(3900,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[3899]) ).
thf(943,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__def) ).
thf(4328,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(34754,plain,
( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(paramod_ordered,[status(thm)],[2276,13495]) ).
thf(34755,plain,
( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[34754]) ).
thf(34788,plain,
( ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
inference(simp,[status(thm)],[34755]) ).
thf(513,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(2959,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(842,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
thf(4000,plain,
! [A: $i,B: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(588,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(3187,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( ( C = A )
| ( D = B ) )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(3636,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(603,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
thf(3234,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
thf(2859,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(4283,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(3255,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ominus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(2791,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ominus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(605,axiom,
! [A: $i] :
( ( A @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oabs__class_Oabs ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).
thf(3240,plain,
! [A: $i] :
( ( A @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oabs__class_Oabs ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(720,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(3609,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
thf(2657,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oboolean__algebra )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(767,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
thf(3736,plain,
! [A: $i,B: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(3081,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( C = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
thf(1929,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(621,axiom,
tc_Int_Oint @ class_Rings_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(3283,plain,
tc_Int_Oint @ class_Rings_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
thf(4677,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(615,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(3266,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(2016,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) ) )
& ( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(2514,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).
thf(2568,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
thf(3272,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(1080,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(4801,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(37452,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( A @ ( A @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5017,20328]) ).
thf(37453,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( A @ ( A @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[37452]) ).
thf(37511,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
!= A )
| ( ( A @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Int_Oint != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[37453]) ).
thf(37519,plain,
( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Int_Oint != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[37511]) ).
thf(13531,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,13495]) ).
thf(13532,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[13531:[]]) ).
thf(13569,plain,
( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[13532]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
thf(1535,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(16276,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add )
!= ( A @ class_Groups_Ocomm__monoid__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3814,1334]) ).
thf(16277,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add )
!= ( A @ class_Groups_Ocomm__monoid__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
inference(simp,[status(thm)],[16276]) ).
thf(16278,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add,
inference(pattern_uni,[status(thm)],[16277:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).
thf(1476,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( B @ class_Rings_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[1475]) ).
thf(46865,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__1 )
!= ( B @ class_Rings_Ocomm__semiring__1 ) )
| ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2880,1476]) ).
thf(46866,plain,
! [B: $i,A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__1 )
!= ( B @ class_Rings_Ocomm__semiring__1 ) )
| ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[46865]) ).
thf(46867,plain,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ),
inference(pattern_uni,[status(thm)],[46866:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).
thf(523,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
thf(2991,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(2716,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(718,axiom,
tc_Complex_Ocomplex @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(3604,plain,
tc_Complex_Ocomplex @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1__strict )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(4381,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1__strict )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1191,axiom,
tc_Complex_Ocomplex @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
thf(5239,plain,
tc_Complex_Ocomplex @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
thf(1965,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1125,axiom,
tc_Complex_Ocomplex @ class_Rings_Oring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
thf(4975,plain,
tc_Complex_Ocomplex @ class_Rings_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(465,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(2817,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le) ).
thf(4769,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1008,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(4537,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(597,axiom,
tc_Nat_Onat @ class_Power_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(3214,plain,
tc_Nat_Onat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(14329,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ class_Power_Opower )
!= ( A @ class_Power_Opower ) )
| ~ $true
| ( ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) )
= ( A @ c_Power_Opower__class_Opower ) ) ),
inference(paramod_ordered,[status(thm)],[3214,1328]) ).
thf(14330,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ class_Power_Opower )
!= ( A @ class_Power_Opower ) )
| ( ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) )
= ( A @ c_Power_Opower__class_Opower ) ) ),
inference(simp,[status(thm)],[14329]) ).
thf(14331,plain,
( ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Power_Opower_Opower ) ) )
= ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ),
inference(pattern_uni,[status(thm)],[14330:[bind(A,$thf( tc_Nat_Onat ))]]) ).
thf(44216,plain,
( ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower_Opower ) ) )
= ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ),
inference(rewrite,[status(thm)],[14331,2276]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(3118,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).
thf(2326,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(33000,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28729,1403]) ).
thf(33001,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[33000]) ).
thf(33002,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[33001:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).
thf(1154,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
thf(5086,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
thf(3416,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(553,axiom,
tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(3091,plain,
tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
thf(3223,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(912,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
thf(4251,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(535,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opcompose ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__0) ).
thf(3023,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opcompose ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(1669,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1079,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_SEQ_OBseq ) )
<=> ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__iff1a) ).
thf(4796,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_SEQ_OBseq ) ) )
& ( ( A @ ( B @ c_SEQ_OBseq ) )
=> ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(762,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(3726,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(750,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(3695,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(639,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(3330,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(438,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__one) ).
thf(2738,plain,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(4149,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(cnf,[status(esa)],[4148]) ).
thf(886,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(4171,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(736,axiom,
tc_RealDef_Oreal @ class_Groups_Osgn__if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).
thf(3663,plain,
tc_RealDef_Oreal @ class_Groups_Osgn__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
thf(1865,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1044,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(4672,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__leI) ).
thf(1733,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1170,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(5148,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(17,axiom,
tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
thf(1332,plain,
tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
thf(2442,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1178,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(5190,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A = B )
=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(442,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
thf(2753,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(1215,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(5314,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
thf(2055,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(753,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(3700,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) )
& ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__sgn) ).
thf(4060,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) )
& ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(5681,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,5626]) ).
thf(5682,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[5681]) ).
thf(5701,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Nat_Onat != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[5682]) ).
thf(5703,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[5701]) ).
thf(381,axiom,
tc_Int_Oint @ class_Rings_Oordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(2557,plain,
tc_Int_Oint @ class_Rings_Oordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(732,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(3641,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ c_Nat_OSuc )
!= A )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(1638,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ c_Nat_OSuc )
!= A )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1252,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(5432,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__not__sym) ).
thf(2148,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(759,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1 )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(3719,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1 )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(36173,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34582,1403]) ).
thf(36174,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[36173]) ).
thf(36175,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[36174:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(582,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD) ).
thf(3170,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
thf(1675,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(23273,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= B )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,21059]) ).
thf(23274,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= A )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[23273:[bind(A,$thf( D @ c_Nat_OSuc @ c_Nat_OSuc )),bind(B,$thf( D ))]]) ).
thf(23299,plain,
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(simp,[status(thm)],[23274]) ).
thf(740,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
thf(3678,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1147,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
thf(5071,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(424,axiom,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__algebra__1 )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Osgn__class_Osgn ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__one) ).
thf(2679,plain,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__algebra__1 )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Osgn__class_Osgn ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1183,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ononneg__bounded) ).
thf(5212,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(403,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
thf(2624,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(27626,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[27536,20328]) ).
thf(27627,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[27626]) ).
thf(27737,plain,
! [B: $i,A: $i] :
( ( v_r != B )
| ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[27627]) ).
thf(27809,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[27737]) ).
thf(294,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Osgn__if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).
thf(2284,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Osgn__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(37707,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Olinordered__idom )
!= ( A @ class_Rings_Olinordered__idom ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2173,1448]) ).
thf(37708,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Olinordered__idom )
!= ( A @ class_Rings_Olinordered__idom ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring ) ),
inference(simp,[status(thm)],[37707]) ).
thf(37709,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring,
inference(pattern_uni,[status(thm)],[37708:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(4601,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[4600]) ).
thf(27622,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[27536,1392]) ).
thf(27623,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[27622]) ).
thf(27729,plain,
! [C: $i,B: $i,A: $i] :
( ( v_r != B )
| ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= C )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[27623]) ).
thf(27799,plain,
! [A: $i] :
( ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( v_r @ c_Nat_OSuc @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[27729]) ).
thf(1238,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(5381,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(31,axiom,
tc_Nat_Onat @ class_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(1376,plain,
tc_Nat_Onat @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(2065,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(369,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff__def) ).
thf(2521,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(1076,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(4790,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(2538,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
thf(3155,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(788,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(3815,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(829,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(3957,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(742,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(3683,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
thf(3515,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(780,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(3779,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(664,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
thf(3419,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A ) )
& ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(23391,plain,
! [A: $i] :
( ( ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1360,23299]) ).
thf(23392,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[23391]) ).
thf(23443,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[23392]) ).
thf(23453,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(simp,[status(thm)],[23443]) ).
thf(419,axiom,
tc_Int_Oint @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
thf(2669,plain,
tc_Int_Oint @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1187,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
thf(5222,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(4958,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(1246,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( B @ c_SEQ_Odecseq ) )
<=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decseq__def) ).
thf(5407,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ c_SEQ_Odecseq ) ) )
& ( ( A @ ( B @ c_SEQ_Odecseq ) )
=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(21350,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[20848,20328]) ).
thf(21351,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[21350]) ).
thf(21411,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc )
!= B )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[21351]) ).
thf(21442,plain,
! [A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[21411]) ).
thf(35306,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,21442]) ).
thf(35307,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35306]) ).
thf(35308,plain,
( ( ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(pattern_uni,[status(thm)],[35307:[bind(A,$thf( sk53 ))]]) ).
thf(589,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
thf(3197,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(4073,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
thf(2856,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(28532,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[28439,20328]) ).
thf(28533,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[28532]) ).
thf(28644,plain,
! [B: $i,A: $i] :
( ( v_r != B )
| ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[28533]) ).
thf(28720,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[28644]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
thf(3500,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(674,axiom,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3456,plain,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(1232,axiom,
tc_RealDef_Oreal @ class_Rings_Ocomm__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
thf(5367,plain,
tc_RealDef_Oreal @ class_Rings_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(969,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
thf(4401,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1139,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(5035,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(1082,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(4818,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(918,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__natfloor) ).
thf(4264,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(444,axiom,
tc_Int_Oint @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(2757,plain,
tc_Int_Oint @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(2923,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(1135,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(5007,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(353,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(2461,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(462,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(2812,plain,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(13430,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,5571]) ).
thf(13431,plain,
! [A: $i] :
( ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[13430:[]]) ).
thf(13499,plain,
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[13431]) ).
thf(405,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(2632,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
thf(2610,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
inference(cnf,[status(esa)],[1338]) ).
thf(974,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(4420,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(79,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1557,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(844,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
thf(4009,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1151,axiom,
tc_RealDef_Oreal @ class_Rings_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
thf(5082,plain,
tc_RealDef_Oreal @ class_Rings_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(4569,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1103,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
thf(4911,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(550,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= A )
<=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
thf(3073,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= B )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= A ) )
& ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= A )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(30458,plain,
! [A: $i] :
( ( ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1360,30353]) ).
thf(30459,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[30458]) ).
thf(30528,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[30459]) ).
thf(30564,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(simp,[status(thm)],[30528]) ).
thf(31282,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[30564]) ).
thf(850,axiom,
! [A: $i] : ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
thf(4028,plain,
! [A: $i] : ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(3572,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(4897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(1129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(4985,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(580,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(3165,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(173,axiom,
tc_Nat_Onat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(1862,plain,
tc_Nat_Onat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(4208,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(20997,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Power_Opower )
!= ( A @ class_Power_Opower ) )
| ~ $true
| ( ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) )
= ( A @ c_Power_Opower__class_Opower ) ) ),
inference(paramod_ordered,[status(thm)],[4440,1328]) ).
thf(20998,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Power_Opower )
!= ( A @ class_Power_Opower ) )
| ( ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) )
= ( A @ c_Power_Opower__class_Opower ) ) ),
inference(simp,[status(thm)],[20997]) ).
thf(20999,plain,
( ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Power_Opower_Opower ) ) )
= ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower ) ),
inference(pattern_uni,[status(thm)],[20998:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).
thf(26063,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[21473,1392]) ).
thf(26064,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[26063]) ).
thf(26065,plain,
! [A: $i] :
( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[26064:[bind(A,$thf( F )),bind(B,$thf( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )),bind(C,$thf( F @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ))]]) ).
thf(26232,plain,
! [A: $i] :
( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[26065]) ).
thf(26835,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[26232,20328]) ).
thf(26836,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[26835]) ).
thf(26939,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
!= B )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[26836]) ).
thf(26999,plain,
! [A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[26939]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
thf(2593,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(3451,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(5655,plain,
! [A: $i] :
( ( A
!= ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) ) )
| ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,5492]) ).
thf(5656,plain,
( ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[5655:[bind(A,$thf( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) ))]]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(2874,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(931,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
<=> ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def) ).
thf(4296,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) )
& ( ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ? [C: $i] :
! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1263,axiom,
tc_Complex_Ocomplex @ class_Rings_Ocomm__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
thf(5466,plain,
tc_Complex_Ocomplex @ class_Rings_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(3583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(411,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
thf(2647,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1060,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).
thf(4726,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(416,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
thf(2664,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(801,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
thf(3861,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(2928,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
thf(1380,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( D @ class_Rings_Olinordered__semidom ) ),
inference(cnf,[status(esa)],[1380]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(4684,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(310,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
thf(2329,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(432,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(2710,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(495,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ c_RComplete_Onatfloor )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
thf(2911,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ c_RComplete_Onatfloor )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(1132,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(4990,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(389,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(2578,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(27624,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[27536,3064]) ).
thf(27625,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[27624]) ).
thf(27731,plain,
! [B: $i,A: $i] :
( ( v_r != B )
| ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[27625]) ).
thf(27802,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[27731]) ).
thf(321,axiom,
tc_Int_Oint @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(2365,plain,
tc_Int_Oint @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(1435,plain,
! [B: $i,A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[1432]) ).
thf(1444,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[1435]) ).
thf(1445,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(simp,[status(thm)],[1444]) ).
thf(1268,axiom,
tc_Complex_Ocomplex @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
thf(5482,plain,
tc_Complex_Ocomplex @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(814,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
thf(3917,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(257,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(2139,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__less) ).
thf(2931,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(148,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
thf(1775,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__0 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1106,axiom,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(4918,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_RComplete_Onatfloor )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__eq) ).
thf(2535,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_RComplete_Onatfloor )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(4196,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(864,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(4084,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(3539,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(2770,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(2418,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1085,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(4832,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(168,axiom,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
thf(1841,plain,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(2439,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(57,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
thf(1473,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1474,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[1473]) ).
thf(316,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(2350,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1184,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
thf(5216,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
thf(3759,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1236,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).
thf(5376,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(5377,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(lifteq,[status(thm)],[5376]) ).
thf(1179,axiom,
! [A: $i] :
( ( A @ class_Groups_Osgn__if )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).
thf(5197,plain,
! [A: $i] :
( ( A @ class_Groups_Osgn__if )
=> ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1155,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
thf(5094,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(5218,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(958,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(4373,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(109,axiom,
tc_Int_Oint @ class_Rings_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1643,plain,
tc_Int_Oint @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
thf(3159,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(738,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
thf(3674,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(59,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1477,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(570,axiom,
tc_Int_Oint @ class_Groups_Osgn__if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
thf(3142,plain,
tc_Int_Oint @ class_Groups_Osgn__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1118,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(4954,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(3178,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
thf(4626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(526,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(2999,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(643,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__nat) ).
thf(3348,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__vector )
=> ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
thf(4067,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__vector )
=> ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(2207,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(804,axiom,
tc_RealDef_Oreal @ class_Int_Oring__char__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
thf(3876,plain,
tc_RealDef_Oreal @ class_Int_Oring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
thf(1694,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
thf(2693,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) )
=> ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(46887,plain,
! [B: $i,A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1 )
!= ( B @ class_Rings_Ocomm__semiring__1 ) )
| ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5189,1476]) ).
thf(46888,plain,
! [B: $i,A: $i] :
( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1 )
!= ( B @ class_Rings_Ocomm__semiring__1 ) )
| ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[46887]) ).
thf(46889,plain,
! [A: $i] : ( A @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Rings_Odvd__class_Odvd ) ) ),
inference(pattern_uni,[status(thm)],[46888:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__abs__iff) ).
thf(1805,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(694,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
thf(3522,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(820,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
thf(3936,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(32198,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( v_r @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[20794,3064]) ).
thf(32199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( v_r @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[32198]) ).
thf(32311,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( v_r @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
!= C )
| ( ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( C @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[32199]) ).
thf(32364,plain,
! [B: $i,A: $i] :
( ( ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( A @ ( v_r @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[32311]) ).
thf(1098,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(4868,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(593,axiom,
tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(3206,plain,
tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(1905,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1007,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(4529,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(3146,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(4292,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(501,axiom,
tc_Nat_Onat @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(2927,plain,
tc_Nat_Onat @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(1990,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(2564,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(627,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Oabs__class_Oabs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).
thf(3292,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Oabs__class_Oabs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(944,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
thf(4336,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(391,axiom,
tc_Int_Oint @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(2582,plain,
tc_Int_Oint @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(464,axiom,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
thf(2816,plain,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1052,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(4690,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
thf(2914,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(538,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).
thf(3031,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ouminus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ouminus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
thf(1809,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ouminus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ouminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(26068,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[21473,20328]) ).
thf(26069,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[26068]) ).
thf(26167,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
!= B )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[26069]) ).
thf(26221,plain,
! [A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[26167]) ).
thf(35374,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,26221]) ).
thf(35375,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35374]) ).
thf(35376,plain,
( ( ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(pattern_uni,[status(thm)],[35375:[bind(A,$thf( sk53 ))]]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(4441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(876,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_RComplete_Onatfloor @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor) ).
thf(4136,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_RComplete_Onatfloor @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
thf(2096,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(524,axiom,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(2994,plain,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
thf(2124,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(15755,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__0 )
!= ( A @ class_Rings_Ocomm__semiring__0 ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1604,1369]) ).
thf(15756,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__0 )
!= ( A @ class_Rings_Ocomm__semiring__0 ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
inference(simp,[status(thm)],[15755]) ).
thf(15757,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ class_Rings_Osemiring,
inference(pattern_uni,[status(thm)],[15756:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(938,axiom,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
thf(4319,plain,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(3455,plain,
! [A: $i] : ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
inference(cnf,[status(esa)],[3454]) ).
thf(1471,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(cnf,[status(esa)],[1470]) ).
thf(1472,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(lifteq,[status(thm)],[1471]) ).
thf(953,axiom,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(4355,plain,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(6559,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
| ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1298,4972]) ).
thf(6560,plain,
! [A: $i] :
( ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[6559:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ))]]) ).
thf(6875,plain,
( ~ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[6560]) ).
thf(863,axiom,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
thf(4083,plain,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(17210,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__0 )
!= ( A @ class_Rings_Ocomm__semiring__0 ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4083,1369]) ).
thf(17211,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__0 )
!= ( A @ class_Rings_Ocomm__semiring__0 ) )
| ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
inference(simp,[status(thm)],[17210]) ).
thf(17212,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Rings_Osemiring,
inference(pattern_uni,[status(thm)],[17211:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).
thf(1255,axiom,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(5446,plain,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
thf(3376,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(3315,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
thf(2192,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(735,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
thf(3659,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(565,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(3129,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(4377,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ class_Orderings_Oord )
& ( D @ class_RealVector_Oreal__normed__vector ) )
=> ( ! [E: $i] :
( ( E @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( E @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ! [E: $i] :
( ( E @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ hAPP ) @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( A @ hAPP ) @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemmaCauchy) ).
thf(4630,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ class_Orderings_Oord )
& ( D @ class_RealVector_Oreal__normed__vector ) )
=> ( ! [E: $i] :
( ( E @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( E @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ! [E: $i] :
( ( E @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ hAPP ) @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( A @ hAPP ) @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(26830,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[26232,1392]) ).
thf(26831,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[26830]) ).
thf(26832,plain,
! [A: $i] :
( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(pattern_uni,[status(thm)],[26831:[bind(A,$thf( F )),bind(B,$thf( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )),bind(C,$thf( F @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ))]]) ).
thf(27008,plain,
! [A: $i] :
( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[26832]) ).
thf(1040,axiom,
tc_RealDef_Oreal @ class_Rings_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
thf(4658,plain,
tc_RealDef_Oreal @ class_Rings_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(2942,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
thf(3391,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1197,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
thf(5250,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(39017,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35602,1403]) ).
thf(39018,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[39017]) ).
thf(39019,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[39018:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(996,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
thf(4490,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(518,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
thf(2977,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(102,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(1611,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(921,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
thf(4272,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(1114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ozero )
=> ( ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
= ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
thf(4939,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ozero )
=> ( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
= ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
= ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel1) ).
thf(1395,plain,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
| ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ~ ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(cnf,[status(esa)],[1395]) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
| ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[1396]) ).
thf(1400,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
| ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[1398]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(1605,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(394,axiom,
tc_Int_Oint @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(2588,plain,
tc_Int_Oint @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1116,axiom,
tc_Complex_Ocomplex @ class_Rings_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
thf(4950,plain,
tc_Complex_Ocomplex @ class_Rings_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1108,axiom,
tc_RealDef_Oreal @ class_Rings_Oring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
thf(4922,plain,
tc_RealDef_Oreal @ class_Rings_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(35281,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,1271]) ).
thf(35282,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[35281]) ).
thf(35283,plain,
v_r @ ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
inference(pattern_uni,[status(thm)],[35282:[bind(A,$thf( sk53 ))]]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(1647,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(35329,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
!= ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,3493]) ).
thf(35330,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
!= ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[35329]) ).
thf(35427,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= sk53 )
| ( A
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35330]) ).
thf(35485,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= sk53 )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35427]) ).
thf(199,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(1941,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(677,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(3462,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(894,axiom,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
thf(4200,plain,
tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1003,axiom,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__algebra__1 )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).
thf(4517,plain,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__algebra__1 )
=> ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_RealVector_Onorm__class_Onorm ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(16349,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[5781,3064]) ).
thf(16350,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16349]) ).
thf(16374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
!= C )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( C @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16350]) ).
thf(16396,plain,
! [B: $i,A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16374]) ).
thf(1034,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(4641,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(987,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).
thf(4469,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(1780,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(470,axiom,
tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
thf(2831,plain,
tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1251,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
thf(5431,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(632,axiom,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(3305,plain,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(2920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(760,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(3722,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
thf(3202,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(734,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
thf(3655,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(20455,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[1271,20328]) ).
thf(20456,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20455]) ).
thf(20486,plain,
! [B: $i,A: $i] :
( ( v_r != B )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20456]) ).
thf(20506,plain,
! [A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20486]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(1579,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
thf(1335,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( C @ class_Rings_Ocomm__semiring__1 ) ),
inference(cnf,[status(esa)],[1335]) ).
thf(1203,axiom,
v_m____ @ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kp) ).
thf(5277,plain,
v_m____ @ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(867,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
thf(4089,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(4090,plain,
( ! [A: $i] :
( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(miniscope,[status(thm)],[4089]) ).
thf(4091,plain,
! [B: $i,A: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(cnf,[status(esa)],[4090]) ).
thf(4093,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[4091]) ).
thf(4095,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[4093]) ).
thf(4096,plain,
tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
inference(simp,[status(thm)],[4095]) ).
thf(43960,plain,
tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
inference(rewrite,[status(thm)],[4096,3900]) ).
thf(129,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oabs__if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).
thf(1711,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oabs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(2747,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(608,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(3246,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(978,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ozero )
=> ( ( ( D @ ( F @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( F @ c_Groups_Ozero__class_Ozero @ ( E @ hAPP ) @ hAPP ) @ hAPP ) )
= D )
=> ( ( A @ ( B @ ( F @ c_Polynomial_OpCons ) ) @ ( E @ ( D @ ( F @ ( C @ c_Polynomial_Opoly__rec ) ) ) ) )
= ( A @ ( E @ ( D @ ( F @ ( C @ c_Polynomial_Opoly__rec ) ) ) ) @ ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__pCons) ).
thf(4437,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Groups_Ozero )
=> ( ( ( D @ ( F @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( F @ c_Groups_Ozero__class_Ozero @ ( E @ hAPP ) @ hAPP ) @ hAPP ) )
= D )
=> ( ( A @ ( B @ ( F @ c_Polynomial_OpCons ) ) @ ( E @ ( D @ ( F @ ( C @ c_Polynomial_Opoly__rec ) ) ) ) )
= ( A @ ( E @ ( D @ ( F @ ( C @ c_Polynomial_Opoly__rec ) ) ) ) @ ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(670,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(3448,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(935,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(4314,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(908,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
thf(4240,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
thf(2092,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(1987,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
thf(1716,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
thf(3940,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1264,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(5467,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(1451,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) )
| ~ ( D @ class_Rings_Ocomm__semiring__0 ) ),
inference(cnf,[status(esa)],[1450]) ).
thf(1452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ class_Rings_Ocomm__semiring__0 )
| ( ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[1451]) ).
thf(747,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
thf(3691,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(3114,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(782,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
thf(3791,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(1785,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(683,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(3475,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__idom )
=> ( ( C @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).
thf(3026,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__idom )
=> ( ( C @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(784,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
thf(3801,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
thf(2219,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( ( B = A )
=> ( D = C ) )
& ( ( D = C )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(706,axiom,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
thf(3561,plain,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(46928,plain,
! [B: $i,A: $i] :
( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1 )
!= ( B @ class_Rings_Ocomm__semiring__1 ) )
| ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3561,1476]) ).
thf(46929,plain,
! [B: $i,A: $i] :
( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1 )
!= ( B @ class_Rings_Ocomm__semiring__1 ) )
| ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[46928]) ).
thf(46930,plain,
! [A: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Odvd__class_Odvd ) ) ),
inference(pattern_uni,[status(thm)],[46929:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( D @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
thf(3774,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( D @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(564,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Polynomial_Opos__poly ) )
=> ( ( A @ ( C @ c_Polynomial_Opos__poly ) )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
thf(3127,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Polynomial_Opos__poly ) )
=> ( ( A @ ( C @ c_Polynomial_Opos__poly ) )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(951,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(4351,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(185,axiom,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(1901,plain,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1171,axiom,
tc_Complex_Ocomplex @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
thf(5152,plain,
tc_Complex_Ocomplex @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(4132,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(2322,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__neq) ).
thf(2486,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(797,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(3847,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ! [D: $i] : ( B @ ( D @ ( A @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_SEQ_OBseq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_BseqI) ).
thf(3623,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ! [D: $i] : ( B @ ( D @ ( A @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_SEQ_OBseq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(708,axiom,
tc_Complex_Ocomplex @ class_Groups_Oone,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
thf(3564,plain,
tc_Complex_Ocomplex @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
thf(3041,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth) ).
thf(3853,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(365,axiom,
tc_Int_Oint @ class_Rings_Oordered__ring__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
thf(2500,plain,
tc_Int_Oint @ class_Rings_Oordered__ring__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(6193,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1298,2804]) ).
thf(6194,plain,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ~ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[6193:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint @ c_Groups_Oone__class_Oone ))]]) ).
thf(6633,plain,
( ~ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[6194]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2558,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(2379,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1054,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
thf(4695,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2939,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).
thf(3366,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(913,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(4257,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(3288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(422,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Odvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
thf(2675,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oidom )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
| ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
thf(5319,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oidom )
=> ( ( ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
| ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
| ( C
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(196,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(1934,plain,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(751,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
thf(3697,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
thf(1766,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(3099,plain,
( ! [A: $i,B: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(miniscope,[status(thm)],[3098]) ).
thf(3100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( D
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(cnf,[status(esa)],[3099]) ).
thf(3103,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[3100]) ).
thf(3106,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[3103]) ).
thf(3107,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[3106]) ).
thf(35317,plain,
! [B: $i,A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,16396]) ).
thf(35318,plain,
! [B: $i,A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35317]) ).
thf(35319,plain,
! [A: $i] :
( ( ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( A @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(pattern_uni,[status(thm)],[35318:[bind(A,$thf( sk53 ))]]) ).
thf(35502,plain,
! [A: $i] :
( ( ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( A @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35319]) ).
thf(183,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(1898,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(563,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
thf(3124,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(2426,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1226,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_SEQ_OBseq ) )
<=> ? [C: $i] :
( ? [D: $i] :
! [E: $i] : ( C @ ( D @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( E @ ( A @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__iff2) ).
thf(5347,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ? [C: $i] :
( ? [D: $i] :
! [E: $i] : ( C @ ( D @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( E @ ( A @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ c_SEQ_OBseq ) ) )
& ( ( A @ ( B @ c_SEQ_OBseq ) )
=> ? [C: $i] :
( ? [D: $i] :
! [E: $i] : ( C @ ( D @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( E @ ( A @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(1028,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(4624,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1126,axiom,
tc_RealDef_Oreal @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
thf(4976,plain,
tc_RealDef_Oreal @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(910,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
thf(4246,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1192,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(5240,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(995,axiom,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
thf(4488,plain,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(517,axiom,
! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
thf(2975,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
thf(2279,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(1066,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
thf(4748,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( B != A )
& ( D != C ) )
<=> ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(1972,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B != A )
& ( D != C ) ) )
& ( ( ( B != A )
& ( D != C ) )
=> ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(307,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
thf(2320,plain,
! [A: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1257,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
thf(5453,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(879,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(4143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(1111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(4932,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(976,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__pos) ).
thf(4431,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(654,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(3388,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le__int) ).
thf(1504,plain,
! [A: $i,B: $i] :
( ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
thf(1585,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
thf(4634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__0 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ ( B @ ( D @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(1231,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
thf(5364,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(510,axiom,
tc_Int_Oint @ class_Rings_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(2949,plain,
tc_Int_Oint @ class_Rings_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(2030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(35326,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,20506]) ).
thf(35327,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35326]) ).
thf(35328,plain,
( ( ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(pattern_uni,[status(thm)],[35327:[bind(A,$thf( sk53 ))]]) ).
thf(948,axiom,
tc_Complex_Ocomplex @ class_Rings_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
thf(4342,plain,
tc_Complex_Ocomplex @ class_Rings_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(1371,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A )
| ~ ( B @ class_Rings_Olinordered__idom ) ),
inference(cnf,[status(esa)],[1370]) ).
thf(1372,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Rings_Olinordered__idom )
| ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(lifteq,[status(thm)],[1371]) ).
thf(1087,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
thf(4838,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(1152,axiom,
tc_RealDef_Oreal @ class_Rings_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
thf(5083,plain,
tc_RealDef_Oreal @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(3914,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1156,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ononneg__bounded) ).
thf(5100,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(1002,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
thf(4516,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(26382,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2172,1403]) ).
thf(26383,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[26382]) ).
thf(26384,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[26383:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
thf(2479,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(709,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(3565,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(514,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
thf(2960,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) ) )
& ( ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(3533,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(1133,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(4997,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
thf(3625,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(12567,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ class_Groups_Ocomm__monoid__add )
!= ( A @ class_Groups_Ocomm__monoid__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2817,1334]) ).
thf(12568,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ class_Groups_Ocomm__monoid__add )
!= ( A @ class_Groups_Ocomm__monoid__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
inference(simp,[status(thm)],[12567]) ).
thf(12569,plain,
tc_Nat_Onat @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add,
inference(pattern_uni,[status(thm)],[12568:[bind(A,$thf( tc_Nat_Onat ))]]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(1998,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(481,axiom,
! [A: $i] :
( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= A ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).
thf(2865,plain,
! [A: $i] :
( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= A ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(581,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( A @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).
thf(3168,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( A @ ( A @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1033,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(4639,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(622,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(3284,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
= ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
thf(2760,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
= ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
thf(4548,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(924,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
thf(4278,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(167,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(1839,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(569,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).
thf(3139,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(3620,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(5487,plain,
! [A: $i] :
( ( ( A @ sk1 )
!= ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) ) )
| ( tc_Complex_Ocomplex != tc_Complex_Ocomplex )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5486]) ).
thf(5490,plain,
! [A: $i] :
( ( ( A @ sk1 )
!= ( v_r @ sk1 @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5487]) ).
thf(34100,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33026,1403]) ).
thf(34101,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[34100]) ).
thf(34102,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[34101:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(352,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(2458,plain,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(2626,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(675,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
thf(3457,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
thf(2352,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(4424,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(877,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).
thf(4138,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
= ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(1459,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(cnf,[status(esa)],[1458]) ).
thf(554,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
thf(3092,plain,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__lemma) ).
thf(2818,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(3067,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
thf(1949,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1069,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(4763,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(40540,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38987,1409]) ).
thf(40541,plain,
! [A: $i] :
( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
inference(simp,[status(thm)],[40540]) ).
thf(40542,plain,
tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
inference(pattern_uni,[status(thm)],[40541:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).
thf(2078,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(1834,plain,
! [A: $i,B: $i] :
( ( B
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
thf(1844,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(803,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(3874,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(1161,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
thf(5115,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(1063,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
thf(4738,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(1517,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(362,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(2490,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(4102,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(2187,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(843,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__neg) ).
thf(4006,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(637,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(3320,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(302,axiom,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
thf(2305,plain,
! [A: $i] :
( ( A @ class_Groups_Ozero )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
thf(1575,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(5389,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(817,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(3929,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(1146,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
thf(5068,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(934,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(4310,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(493,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(2907,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(3709,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(2853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(1233,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).
thf(5368,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).
thf(2971,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(2416,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(678,axiom,
tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
thf(3465,plain,
tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(764,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(3729,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(430,axiom,
tc_Nat_Onat @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(2707,plain,
tc_Nat_Onat @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(1104,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
thf(4913,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(4710,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(33078,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29762,1403]) ).
thf(33079,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[33078]) ).
thf(33080,plain,
tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[33079:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(2988,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__abs) ).
thf(2174,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(329,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
thf(2389,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(373,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(2532,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1047,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).
thf(4681,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(1165,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).
thf(5132,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(648,axiom,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
thf(3369,plain,
! [A: $i] :
( ( A @ class_Rings_Oidom )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).
thf(2823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(599,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(3220,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(1010,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
thf(4542,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(4696,plain,
( ! [A: $i,B: $i] :
( ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(miniscope,[status(thm)],[4695]) ).
thf(4697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( D = C )
| ~ ( C @ ( D @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B != A )
| ~ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(cnf,[status(esa)],[4696]) ).
thf(4699,plain,
! [B: $i,A: $i] :
( ( B != A )
| ~ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(cnfConj,[status(thm)],[4697]) ).
thf(4701,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[4699]) ).
thf(4702,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(simp,[status(thm)],[4701]) ).
thf(35403,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,4702]) ).
thf(35404,plain,
! [A: $i] :
( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[35403]) ).
thf(35418,plain,
! [A: $i] :
( ( sk53 != A )
| ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
!= A )
| ( tc_RealDef_Oreal != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35404]) ).
thf(35477,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
!= sk53 ),
inference(simp,[status(thm)],[35418]) ).
thf(20731,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[20324,20328]) ).
thf(20732,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20731]) ).
thf(20791,plain,
! [B: $i,A: $i] :
( ( ( v_r @ c_Nat_OSuc )
!= B )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20732]) ).
thf(20821,plain,
! [A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20791]) ).
thf(35380,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,20821]) ).
thf(35381,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35380]) ).
thf(35382,plain,
( ( ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(pattern_uni,[status(thm)],[35381:[bind(A,$thf( sk53 ))]]) ).
thf(771,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
thf(3748,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
thf(2026,plain,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1848,plain,
( ! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) )
& ! [A: $i] :
( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(miniscope,[status(thm)],[1847]) ).
thf(1849,plain,
! [B: $i,A: $i] :
( ( ( ( B @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(cnf,[status(esa)],[1848]) ).
thf(1850,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[1849]) ).
thf(1853,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
| ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[1850]) ).
thf(1854,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[1853]) ).
thf(945,axiom,
tc_Complex_Ocomplex @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
thf(4338,plain,
tc_Complex_Ocomplex @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Polynomial_Opos__poly ) )
=> ( ( A @ ( C @ c_Polynomial_Opos__poly ) )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__add) ).
thf(3003,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Polynomial_Opos__poly ) )
=> ( ( A @ ( C @ c_Polynomial_Opos__poly ) )
=> ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Polynomial_Opos__poly ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(1822,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(1055,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(4705,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(800,axiom,
! [A: $i] :
( ( v_r @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( v_m____ @ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bz_O_Acmod_Az_A_060_061_Ar_A_061_061_062_Acmod_A_Ipoly_A_IpCons_Ac_Acs_J_Az_J_A_060_061_A1_A_L_Acmod_Ac_A_L_Aabs_A_Ir_A_K_Am_J_096) ).
thf(3859,plain,
! [A: $i] :
( ( v_r @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( v_m____ @ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(1157,axiom,
tc_Complex_Ocomplex @ class_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
thf(5104,plain,
tc_Complex_Ocomplex @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(647,axiom,
tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
thf(3368,plain,
tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(1122,axiom,
tc_Complex_Ocomplex @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
thf(4969,plain,
tc_Complex_Ocomplex @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(80,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(1558,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).
thf(2262,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( C @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(4451,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(916,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(4261,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(2944,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(888,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
thf(4182,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
thf(1491,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
thf(2796,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(1437,plain,
! [B: $i,A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(cnfConj,[status(thm)],[1432]) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(lifteq,[status(thm)],[1437]) ).
thf(1440,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(simp,[status(thm)],[1439]) ).
thf(1308,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Polynomial_Opos__poly ) )
| ~ ( C @ class_Rings_Olinordered__idom ) ),
inference(cnfConj,[status(thm)],[1305]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).
thf(1607,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(644,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(3351,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= A )
=> ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2120,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(245,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(2095,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__antisym) ).
thf(2917,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(5601,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk1 ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1281,1271]) ).
thf(5602,plain,
! [A: $i] :
( ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[5601:[bind(A,$thf( C @ sk1 )),bind(B,$thf( C ))]]) ).
thf(5623,plain,
! [A: $i] :
( ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[5602]) ).
thf(5699,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,5623]) ).
thf(5700,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[5699]) ).
thf(5702,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( A @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[5700]) ).
thf(5704,plain,
! [A: $i] :
( ( ( A @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[5702]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
thf(4619,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
thf(1689,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1214,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring__abs )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
thf(5304,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring__abs )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(2081,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(3181,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1023,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(4602,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
thf(4321,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( ( A
= ( C @ c_Groups_Oone__class_Oone ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power) ).
thf(2399,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( ( A
= ( C @ c_Groups_Oone__class_Oone ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(2041,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(887,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(4175,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(689,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(3497,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(806,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
thf(3879,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(899,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
thf(4214,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(666,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__dvd__iff) ).
thf(3430,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(1777,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(717,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
thf(3598,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(1159,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(5109,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D2) ).
thf(2462,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(964,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(4387,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(388,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
thf(2576,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(990,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
thf(4478,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
thf(2362,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(264,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
thf(2162,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(1169,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(5144,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(39189,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36011,1403]) ).
thf(39190,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[39189]) ).
thf(39191,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[39190:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Oabs__class_Oabs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).
thf(2036,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( B @ c_Groups_Oabs__class_Oabs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1306,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Polynomial_Opos__poly ) )
| ( B = A )
| ~ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ class_Rings_Olinordered__idom ) ),
inference(cnfConj,[status(thm)],[1305]) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Polynomial_Opos__poly ) )
| ~ ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ class_Rings_Olinordered__idom )
| ( B = A ) ),
inference(lifteq,[status(thm)],[1306]) ).
thf(1164,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(5128,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(2315,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(364,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(2494,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(1438,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(cnfConj,[status(thm)],[1432]) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
inference(lifteq,[status(thm)],[1438]) ).
thf(1208,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_SEQ_OBseq ) )
<=> ? [C: $i] :
( ? [D: $i] :
! [E: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( E @ ( A @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__iff3) ).
thf(5287,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ? [C: $i] :
( ? [D: $i] :
! [E: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( E @ ( A @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ c_SEQ_OBseq ) ) )
& ( ( A @ ( B @ c_SEQ_OBseq ) )
=> ? [C: $i] :
( ? [D: $i] :
! [E: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( E @ ( A @ hAPP ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(36035,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34082,1403]) ).
thf(36036,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
!= ( A @ class_Groups_Oab__group__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
inference(simp,[status(thm)],[36035]) ).
thf(36037,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Ominus,
inference(pattern_uni,[status(thm)],[36036:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oabs__class_Oabs ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).
thf(1614,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__idom )
=> ( ( ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oabs__class_Oabs ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oabs__class_Oabs ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(2421,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__period) ).
thf(1908,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(1346,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_Rings_Oring ) ),
inference(cnf,[status(esa)],[1346]) ).
thf(1348,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ class_Rings_Oring )
| ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[1347]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
thf(3705,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__0 )
=> ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
thf(4596,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1250,axiom,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
thf(5430,plain,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(746,axiom,
tc_RealDef_Oreal @ class_Groups_Ozero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
thf(3690,plain,
tc_RealDef_Oreal @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(1244,axiom,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
thf(5398,plain,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(5041,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(253,axiom,
tc_Int_Oint @ class_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
thf(2123,plain,
tc_Int_Oint @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(872,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
thf(4125,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(300,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
thf(2302,plain,
! [A: $i] :
( ( A @ class_Groups_Ocancel__comm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(1078,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(4794,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(988,axiom,
! [A: $i,B: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
thf(4472,plain,
! [A: $i,B: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(968,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(4399,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1050,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(4687,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(327,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(2385,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1056,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_RComplete_Onatceiling @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__mono) ).
thf(4706,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_RComplete_Onatceiling @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(120,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
thf(1678,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(6349,plain,
! [C: $i,B: $i,A: $i] :
( ( B != v_r )
| ( A @ ( C @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(paramod_ordered,[status(thm)],[1298,1271]) ).
thf(6350,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( v_r @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( v_r @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(pattern_uni,[status(thm)],[6349:[bind(A,$thf( A )),bind(B,$thf( v_r ))]]) ).
thf(6693,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( v_r @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ~ ( A @ ( v_r @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(simp,[status(thm)],[6350]) ).
thf(626,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(3291,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(954,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(4356,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(840,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(3997,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1134,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(5004,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(7188,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,5656]) ).
thf(7189,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7188]) ).
thf(7220,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7189]) ).
thf(7231,plain,
( ( ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[7220]) ).
thf(1201,axiom,
! [A: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
thf(5268,plain,
! [A: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(2233,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(8242,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1283,5665]) ).
thf(8243,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
| ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[8242]) ).
thf(8274,plain,
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[8243]) ).
thf(8296,plain,
( ( ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( ( v_r @ sk1 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ hAPP ) )
!= ( v_r @ sk1 ) )
| ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[8274]) ).
thf(807,axiom,
tc_RealDef_Oreal @ class_Groups_Olinordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
thf(3882,plain,
tc_RealDef_Oreal @ class_Groups_Olinordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(3264,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(16361,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ( ( A @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[5704,3064]) ).
thf(16362,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( v_r @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( ( A @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16361]) ).
thf(16370,plain,
! [B: $i,A: $i] :
( ( B != v_r )
| ( ( B @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( ( A @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16362]) ).
thf(16392,plain,
! [A: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ( ( A @ sk1 )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[16370]) ).
thf(650,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(3373,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
thf(1593,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__ring )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(794,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(3837,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(25763,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[23453]) ).
thf(1228,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
thf(5356,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(463,axiom,
tc_Nat_Onat @ class_Rings_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
thf(2815,plain,
tc_Nat_Onat @ class_Rings_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1075,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
thf(4787,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(1089,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__ring__abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
thf(4841,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__ring__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__div__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__mult) ).
thf(2008,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__div__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Osgn__class_Osgn ) )
= ( A @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Nat_OSuc @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(1527,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Nat_OSuc @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1266,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(5477,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(566,axiom,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
thf(3132,plain,
! [A: $i] :
( ( A @ class_Groups_Oab__group__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(1234,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
thf(5371,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(143,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1757,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1043,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
thf(4663,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ozero )
=> ( ( ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(2800,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).
thf(1495,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__greater) ).
thf(4981,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(785,axiom,
! [A: $i] :
( ( ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= A ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__def) ).
thf(3804,plain,
! [A: $i] :
( ( ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= A ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(989,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).
thf(4474,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1158,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ c_RComplete_Onatfloor @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
thf(5105,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_RComplete_Onatfloor @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_RComplete_Onatfloor @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(1261,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
thf(5462,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).
thf(2366,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add__abs )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(638,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
thf(3323,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Osemiring__0 )
& ( C @ class_Rings_Odvd ) )
=> ( ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
<=> ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
thf(2651,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Osemiring__0 )
& ( C @ class_Rings_Odvd ) )
=> ( ( ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
& ( ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(937,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(4318,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(836,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(3982,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
thf(2636,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oboolean__algebra )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(42392,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4149,20328]) ).
thf(42393,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[42392]) ).
thf(42431,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( B @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( tc_Nat_Onat != tc_Nat_Onat ) ),
inference(simp,[status(thm)],[42393]) ).
thf(42457,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(simp,[status(thm)],[42431]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
thf(1859,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(932,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
thf(4303,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(1073,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(4777,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
| ~ ( C @ class_Groups_Ogroup__add ) ),
inference(cnf,[status(esa)],[1361]) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ class_Groups_Ogroup__add )
| ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(lifteq,[status(thm)],[1362]) ).
thf(926,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
thf(4281,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(928,axiom,
! [A: $i] :
( ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
thf(4286,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(2739,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatfloor ) ),
inference(lifteq,[status(thm)],[2738]) ).
thf(34953,plain,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(rewrite,[status(thm)],[2739,2276]) ).
thf(849,axiom,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__algebra )
=> ? [B: $i] :
( ! [C: $i,D: $i] : ( B @ ( D @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).
thf(4024,plain,
! [A: $i] :
( ( A @ class_RealVector_Oreal__normed__algebra )
=> ? [B: $i] :
( ! [C: $i,D: $i] : ( B @ ( D @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(2070,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(684,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
thf(3479,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).
thf(2714,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__ring__1 )
=> ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(3426,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(181,axiom,
tc_Int_Oint @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(1891,plain,
tc_Int_Oint @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1140,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( B @ c_SEQ_Oincseq ) )
<=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( D @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incseq__def) ).
thf(5036,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( D @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ c_SEQ_Oincseq ) ) )
& ( ( A @ ( B @ c_SEQ_Oincseq ) )
=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( D @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(1096,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
thf(4865,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1237,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(5378,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(729,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(3633,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(795,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(3843,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1180,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(5200,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(1207,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [B: $i] :
( ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6a) ).
thf(5283,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [B: $i] :
( ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(4923,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2159,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(702,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
thf(3543,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(1167,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).
thf(5140,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__vector )
=> ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1582,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(2583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1189,axiom,
tc_Complex_Ocomplex @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
thf(5236,plain,
tc_Complex_Ocomplex @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
thf(1713,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(28530,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[28439,3064]) ).
thf(28531,plain,
! [B: $i,A: $i] :
( ( ( v_r @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( B @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[28530]) ).
thf(28637,plain,
! [B: $i,A: $i] :
( ( v_r != B )
| ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[28531]) ).
thf(28712,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( v_r @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[28637]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(4221,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
thf(2127,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
=> ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1093,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
thf(4848,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
thf(3057,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(20464,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ~ $true
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(paramod_ordered,[status(thm)],[5781,20328]) ).
thf(20465,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
!= ( C @ ( C @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20464]) ).
thf(20493,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
!= C )
| ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( C @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_Nat_Onat )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20465]) ).
thf(20515,plain,
! [B: $i,A: $i] :
( ( ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
!= ( B @ ( v_r @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ c_Nat_OSuc ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(simp,[status(thm)],[20493]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1532,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
thf(2600,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(490,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
thf(2898,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(712,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(3570,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
thf(3411,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(1383,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
| ~ ( C @ class_Groups_Oordered__ab__group__add__abs ) ),
inference(cnf,[status(esa)],[1382]) ).
thf(1384,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ class_Groups_Oordered__ab__group__add__abs )
| ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
= ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(lifteq,[status(thm)],[1383]) ).
thf(719,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_SEQ_OBseq ) )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_BseqD) ).
thf(3605,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_SEQ_OBseq ) )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(1537,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1130,axiom,
tc_Complex_Ocomplex @ class_Groups_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
thf(4987,plain,
tc_Complex_Ocomplex @ class_Groups_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(3817,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(972,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(4410,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(533,axiom,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
thf(3020,plain,
! [A: $i] :
( ( A @ class_Groups_Ocomm__monoid__add )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1084,axiom,
tc_RealDef_Oreal @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
thf(4831,plain,
tc_RealDef_Oreal @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(2507,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B = A )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) )
& ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(700,axiom,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
thf(3538,plain,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
thf(1925,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Ogroup__add )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1041,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(4659,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(35270,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5428,21473]) ).
thf(35271,plain,
! [A: $i] :
( ( ( sk53 @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
!= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
| ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(simp,[status(thm)],[35270]) ).
thf(35272,plain,
( ( v_r @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc @ ( sk53 @ sk1 @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
inference(pattern_uni,[status(thm)],[35271:[bind(A,$thf( sk53 ))]]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(4019,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(12533,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Groups_Ocomm__monoid__add )
!= ( A @ class_Groups_Ocomm__monoid__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1756,1334]) ).
thf(12534,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ class_Groups_Ocomm__monoid__add )
!= ( A @ class_Groups_Ocomm__monoid__add ) )
| ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
inference(simp,[status(thm)],[12533]) ).
thf(12535,plain,
tc_Int_Oint @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add,
inference(pattern_uni,[status(thm)],[12534:[bind(A,$thf( tc_Int_Oint ))]]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
thf(1299,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(1902,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(656,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(3394,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).
thf(1885,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(786,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
thf(3812,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
thf(3494,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1397,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ~ ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(cnfConj,[status(thm)],[1396]) ).
thf(1399,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
| ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
| ( B
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
inference(lifteq,[status(thm)],[1397]) ).
thf(866,axiom,
tc_RealDef_Oreal @ class_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).
thf(4088,plain,
tc_RealDef_Oreal @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(1225,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(5344,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( A @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
thf(4674,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( A @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(16,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(1331,plain,
tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1174,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( A @ ( B @ c_SEQ_OBseq ) )
<=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__def) ).
thf(5172,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__vector )
=> ( ( ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ c_SEQ_OBseq ) ) )
& ( ( A @ ( B @ c_SEQ_OBseq ) )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(714,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(3580,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
thf(1962,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( B @ class_Power_Opower )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
thf(2881,plain,
! [A: $i,B: $i] :
( ( B @ class_Power_Opower )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(596,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
thf(3212,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(471,axiom,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(2832,plain,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(2436,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1127,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(4977,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(1095,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(4863,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(48,axiom,
tc_Int_Oint @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
thf(1449,plain,
tc_Int_Oint @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(543,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
<=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
thf(3047,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(773,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
thf(3753,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ c_Nat_OSuc ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(3901,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ c_Nat_OSuc ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ c_Nat_OSuc ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(530,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(3013,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
thf(3960,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
=> ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(4655,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(2640,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(5155,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
=> ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(826,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
thf(3950,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(1148,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).
thf(5073,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ? [C: $i] :
( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1004,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
thf(4520,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(112,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(1653,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(1944,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1074,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).
thf(4784,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
thf(1737,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ogroup__add )
=> ( ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(3096,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(274,axiom,
tc_Nat_Onat @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(2206,plain,
tc_Nat_Onat @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).
thf(1681,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(488,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(2887,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(1070,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_RComplete_Onatfloor @ ( A @ c_RComplete_Onatfloor @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
thf(4767,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_RComplete_Onatfloor @ ( A @ c_RComplete_Onatfloor @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(426,axiom,
tc_Int_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(2690,plain,
tc_Int_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(1565,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(62,axiom,
tc_Int_Oint @ class_Groups_Ouminus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
thf(1490,plain,
tc_Int_Oint @ class_Groups_Ouminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1068,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(4752,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
thf(2297,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(265,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
thf(2170,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__idom )
=> ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(889,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
thf(4189,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(242,axiom,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ozero__neq__one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
thf(2087,plain,
! [A: $i] :
( ( A @ class_Rings_Ocomm__semiring__1 )
=> ( A @ tc_Polynomial_Opoly @ class_Rings_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
thf(3933,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(1209,axiom,
tc_RealDef_Oreal @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
thf(5293,plain,
tc_RealDef_Oreal @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(1912,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
thf(4552,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(2177,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
inference(cnfConj,[status(thm)],[1416]) ).
thf(177,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(1870,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1062,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__less) ).
thf(4734,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(51490,plain,
$false,
inference(e,[status(thm)],[13950,27536,1337,3883,5329,4022,3434,2412,3698,1982,6690,1818,1956,5385,5659,5437,1501,30353,4201,5469,3944,1411,2744,1369,4835,2295,3345,40788,2131,1454,3399,4169,3397,35400,1899,14358,4728,1554,4904,3172,1686,38266,2250,1750,8129,4339,1882,2527,1401,3460,3098,2014,3108,4326,3680,29770,4043,1596,1406,5225,3317,4226,2231,3858,2808,1522,3762,2644,2062,3549,1443,2776,3509,5242,37517,34729,2282,2837,1269,1971,3402,5237,4623,4973,3017,35217,2740,20969,34082,4440,3693,3414,3562,2901,1507,5120,1426,3530,3745,4418,4739,35602,2607,1756,4575,4097,3942,3649,3044,1735,4220,4528,3175,2448,2933,1275,2141,5316,4650,2476,40956,1919,5178,1954,2844,1458,23211,5412,3276,2575,4047,3545,5252,3766,1935,1921,4198,2825,1803,3688,4511,2957,3836,4343,3629,2491,5393,2763,1782,2548,5486,2985,2227,1391,1441,4266,3088,3777,5476,19799,3281,3466,5301,4030,1475,2173,4607,4948,2405,3938,1430,2735,2039,2755,4224,2274,2682,1462,2571,3891,4637,3248,1409,4238,3263,3221,4546,3976,4524,1760,1660,1298,4070,3116,2667,2339,34602,2708,3821,5064,2501,4654,3617,1330,2217,3612,3148,4130,1313,4275,1577,1455,5182,3845,3744,42947,2466,33040,5279,2703,2691,16391,4119,4353,1704,20038,33026,3258,1847,4595,1800,5338,1892,1379,3385,4194,2049,4492,2373,2635,3470,3312,1568,3734,3014,4141,1641,3708,1815,4460,4793,3557,4771,3231,5077,4514,2388,23768,5264,3524,2794,3966,1632,2259,2650,2880,2073,35214,2950,4988,1415,1946,4396,1465,2105,1811,26381,1450,4443,5084,1373,3724,4600,3295,2782,1418,3453,2451,1334,3473,3702,3438,4147,1828,40994,3569,2540,3300,2555,3290,1581,4686,2335,5457,5360,3771,4810,4718,1928,2833,2190,3685,3036,5489,2103,4211,3378,3986,2058,1377,5353,4842,5220,5210,35628,20794,1447,2483,4087,2424,2979,40513,1394,5246,4307,3676,33998,2002,3243,1345,2286,2804,5665,3588,4379,4588,34790,3184,2586,2982,2884,1604,4604,5406,4323,20348,3531,2118,5117,1470,4925,1730,5298,1863,3151,2011,3303,4962,38987,2473,3567,1691,3984,4480,35238,5017,1338,5142,39363,4370,1311,2232,2307,4031,2621,5334,1868,2382,2773,5281,20848,3261,2428,1519,4878,1570,3742,3371,5206,2673,5049,2589,4915,2409,3711,1343,4016,2805,3972,4920,2277,4375,4434,3022,5455,1751,28743,1487,3752,3989,4128,3154,3134,4493,1619,2150,1370,3814,5396,6696,2890,2414,5594,4160,3664,3207,2396,7565,3682,4044,3286,1560,1423,3877,2068,1656,3028,1407,1281,3033,7608,2445,4295,2464,1938,4280,2758,2873,3980,5492,1837,3269,1602,4192,2670,4053,28439,1968,3198,40750,2332,2820,3297,3137,3065,1951,5460,40444,5341,3144,4746,4402,3535,5113,2313,2547,2344,4461,1392,1573,5330,3799,4316,5066,5270,5423,4544,1587,5362,2726,4840,2638,3001,1402,3731,3968,4123,1360,5189,2300,39331,3467,5626,3782,3615,13946,3831,2157,2840,3482,2100,1772,2946,6691,4248,2841,20944,1328,4486,2359,1375,4693,4845,8016,5428,1672,1719,4227,3916,3237,2268,3440,3060,4263,15760,3143,4582,5080,13495,3728,4389,4406,2613,2551,1644,1493,1683,4320,2798,3954,1329,2877,3952,4951,1361,4860,4276,1659,3922,2561,3210,3094,4167,5464,4750,4938,5263,1414,2240,1842,1791,2172,4648,2108,1446,4867,4444,2666,4621,2649,40580,2317,5387,1744,3935,1419,21059,1831,2851,2581,1984,4347,1874,3333,3920,1825,2968,5317,4846,3611,2450,3486,1478,4384,36733,29762,5374,2304,1530,1382,4970,5134,2355,4482,1932,4244,4829,3819,4237,4934,4540,5058,3937,1429,3409,3692,2052,1599,3064,4259,4689,5026,3005,3162,3201,4223,1759,3215,5479,1525,5245,4361,35275,3454,1333,2203,4644,4081,4966,11407,5434,1466,3639,2995,2338,2909,3824,4148,2788,1318,5153,2926,2043,3279,4212,4889,1563,41909,5571,3306,2076,15136,3999,1286,2408,2793,1663,2089,5295,2617,5249,5840,2529,20328,2144,21473,2936,2001,5451,5278,1273,16390,4562,4503,1727,5327,14020,2677,4708,1754,2292,2391,2904,1680,3358,2275,2033,5762,2253,3871,2028,1301,4340,1595,2734,4359,3111,4269,3686,4017,2524,2376,4453,3343,2260,4041,4662,3070,3519,37716,1620,2393,3900,1403,4328,34788,2959,4000,3187,3636,3234,2859,4283,3255,2791,3240,7736,3609,2657,3736,3081,1929,3283,4677,3266,2016,2514,2568,3272,4801,37519,13569,1535,16278,46867,2991,2716,3604,4381,5239,1965,4975,2817,4769,4537,4485,44216,3118,2326,33002,5086,3416,3091,3223,4251,3023,1669,4796,3726,1271,1312,33066,3695,3330,2738,4149,4171,3663,1865,7875,4672,1733,5148,1332,2442,5190,2753,5314,2055,3700,4060,5703,2557,3641,1638,5432,2148,3719,36175,3170,1675,23299,3678,5071,2679,5212,2624,27809,2284,37709,4601,27799,5381,20943,1376,2065,2521,4790,2538,1408,3155,3815,3957,3683,3515,3779,3419,1349,23453,2669,5222,4958,5407,35308,3197,4073,2856,2802,28720,3500,3456,5367,4401,5035,4818,4264,2757,2923,5007,2461,2812,13499,2632,2610,1339,4420,29982,1557,4009,29956,5082,4569,4911,3073,31282,4028,3572,4897,4985,3165,1862,4208,20999,26999,2593,3451,5656,2874,4296,5466,3583,1344,1460,2647,4726,2664,3861,2928,1381,4684,20525,2329,3893,2710,2911,4990,2578,27802,2365,1445,5482,3917,2139,2931,1775,4918,2535,4196,4084,3539,2770,2418,4832,1841,2439,1474,30564,2350,5216,3759,5377,5197,5094,5218,4373,1643,3159,3674,1477,3142,1364,4954,3178,4626,2999,3348,4067,2207,3876,1694,2693,46889,36149,1805,5661,3522,1304,3936,32364,4868,3206,1905,4529,3146,4292,2927,1990,1340,2564,3292,4336,2582,2816,4690,2914,3031,1809,35376,4441,4136,2096,4260,2994,2124,15757,4319,3455,1472,21442,4355,6875,17212,5446,3376,3315,5294,2192,3214,3659,3129,4377,4630,27008,5018,4658,2942,5624,3391,5250,39019,4490,2977,1611,4272,4939,1400,5399,1605,2588,4950,4922,35283,1647,35485,1941,3462,4200,1368,4517,16396,4641,4469,1780,2831,2689,34582,5431,3305,2920,3722,3202,3655,20506,1579,1336,5277,43960,1711,26232,2747,3246,4437,3448,4314,4398,4240,2092,1987,1716,3940,5467,1452,3691,3114,3791,39159,1785,3475,3026,2276,3801,2219,46930,3774,1317,3127,4351,1901,5152,4132,2322,2486,3847,3623,3564,1285,3041,3853,2500,6633,2558,3493,2379,4695,2939,3366,4257,3288,2675,1404,5319,1934,3697,1766,3107,35502,1898,36731,3124,2426,5347,4624,4976,4246,5240,4488,1284,2975,2279,4748,1972,2320,5453,4143,4932,4431,3388,1504,1585,4634,5364,2949,2030,35328,4342,1372,4838,5083,1272,3914,5100,4516,4150,26384,2479,3565,2960,3533,4997,1412,3625,1453,12569,1998,2865,3168,4639,3284,2760,4548,4278,1839,3139,3620,5490,34102,2458,2626,3457,2352,4424,4138,1459,32988,3092,2818,3067,1949,4763,40542,2078,1834,1844,3874,5115,4738,1517,1448,2490,4102,2187,4006,3320,2305,1575,5389,3929,5068,4310,2907,3709,2853,4089,5426,5368,2971,3561,2416,3465,1276,1326,3729,2707,4913,4710,33080,2988,1385,2174,2389,7653,1476,2532,4681,5132,3369,2823,3220,4542,35477,35382,3748,2026,1854,4338,3003,1822,4705,3859,5104,3368,6694,4969,1558,2262,4451,4261,2944,4182,1491,2796,1440,1308,1607,3351,2120,2095,2917,5704,4619,1689,5304,2081,3181,4602,4321,2399,2041,4175,3497,3879,4214,3430,1777,5781,3598,5109,2462,4387,2576,4478,2362,2162,5144,39191,2036,1309,5128,2315,2494,1442,5287,36037,1614,2421,1908,1348,16393,3705,4596,5430,3690,5398,3062,5041,2123,4125,2302,4794,4472,4399,4687,2385,4706,1678,6693,3291,4356,3997,5004,7231,5268,2233,8296,3882,1395,3264,16392,3373,1593,3837,25763,5356,1380,2815,4787,4841,2008,1303,1527,26221,5477,3132,5371,1757,4663,2800,1495,4981,33978,3804,4474,5105,5462,2366,3323,2651,4318,3982,2636,42457,1859,4303,20821,4777,1363,1314,4281,4286,34953,4157,1335,4083,4024,2070,3479,1410,2714,3426,1891,5036,4865,5378,1473,3633,3843,5200,5283,1346,4923,2159,3543,36011,5140,1582,2583,3489,5623,5236,1713,28712,4221,2127,4848,3057,20515,1532,2600,2898,3570,3411,1384,3605,1537,4972,28729,4987,3817,3245,4410,3020,4831,2507,3538,1925,4659,35272,4019,12535,1299,1902,5376,3394,1885,3812,3494,1399,4088,5344,4674,1331,5172,3580,1962,2881,3212,2832,2436,4977,4863,1449,3047,3753,3901,3013,3960,4655,2640,5155,3950,5073,4520,1653,1367,1944,4702,4784,1737,3096,2206,1681,2887,4767,2690,1463,1565,1490,4752,2297,2170,4189,2087,3933,5293,1912,20324,4552,2177,1417,1870,4734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW181+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n011.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 15:24:29 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.37/1.50 % [INFO] Parsing done (502ms).
% 2.83/1.51 % [INFO] Running in sequential loop mode.
% 3.67/1.89 % [INFO] eprover registered as external prover.
% 3.86/1.90 % [INFO] Scanning for conjecture ...
% 4.64/2.17 % [INFO] Found a conjecture (or negated_conjecture) and 1272 axioms. Running axiom selection ...
% 6.34/2.56 % [INFO] Axiom selection finished. Selected 1266 axioms (removed 6 axioms).
% 8.81/3.14 % [INFO] Problem is first-order (TPTP FOF).
% 9.09/3.20 % [INFO] Type checking passed.
% 9.09/3.21 % [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 ...
% 166.04/42.97 % External prover 'e' found a proof!
% 166.04/42.97 % [INFO] Killing All external provers ...
% 166.04/42.98 % Time passed: 42420ms (effective reasoning time: 41457ms)
% 166.04/42.98 % 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)>
% 166.04/42.99 % Axioms used in derivation (1266): fact_dvd_Oord__less__eq__trans, fact_xt1_I1_J, fact_le__SucI, arity_fun__Orderings_Oorder, fact_le__imp__diff__is__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_power__abs, fact_dvd_Oless__trans, fact_zle__refl, fact_minus__mult__left, fact_neg__le__0__iff__le, arity_Complex__Ocomplex__Rings_Odvd, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_one__dvd, fact_real__squared__diff__one__factored, arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, arity_Polynomial__Opoly__Rings_Osemiring__0, fact_abs__of__pos, fact_real__le__refl, fact_abs__le__D2, arity_Complex__Ocomplex__Rings_Oidom, fact_nat_Osimps_I3_J, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_mult__right__le__imp__le, fact_zdvd__antisym__abs, fact_real__less__def, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, fact_power__strict__decreasing, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_natfloor__real__of__nat, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, fact_mult__poly__0__right, arity_RealDef__Oreal__Orderings_Oord, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact_incr__mult__lemma, fact_natfloor__power, fact_complex__diff__def, fact_natfloor__add, fact_mult__1__left, fact_diff__0__eq__0, fact_dvd__mult__cancel__left, fact_zdvd__not__zless, fact_neg__equal__0__iff__equal, fact_inf__period_I4_J, fact_Bseq__iff3, fact_diff__add__inverse, fact_dvdI, fact_abs__minus__commute, fact_abs__if, fact_le__eq__less__or__eq, fact_xt1_I4_J, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_q__pos__lemma, fact_add__poly__code_I2_J, fact_abs__ge__self, arity_RealDef__Oreal__Rings_Oordered__comm__semiring, arity_Complex__Ocomplex__Groups_Oab__group__add, fact_order, fact_diff__0__right, fact_mult__less__cancel__left__disj, fact_nat__add__left__commute, fact_real__mult__left__cancel, fact_mult__nonpos__nonpos, fact_dvd_Oeq__iff, fact_order__le__less__trans, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_power__power__power, fact_real__of__nat__zero, fact_mult__left_Ominus, fact_zdvd__antisym__nonneg, fact_power__inject__base, fact_norm__power, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_one__is__add, fact_diff__le__mono2, arity_Int__Oint__Rings_Olinordered__semiring__strict, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_minus__mult__right, fact_real__of__nat__diff, fact_termination__basic__simps_I5_J, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, fact_norm__mult__less, fact_odd__nonzero, fact_mult_Opos__bounded, fact_dvd_Oorder__trans, fact_norm__diff__triangle__ineq, fact_zminus__zminus, fact_mult__nonneg__nonpos, fact_poly__eq__0__iff__dvd, fact_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_n__less__m__mult__n, fact_unity__coeff__ex, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_Suc__mono, fact_add__less__mono, fact_real__0__less__add__iff, fact_mult__eq__0__iff, fact_pow__divides__pow__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, arity_RealDef__Oreal__Groups_Ominus, arity_Nat__Onat__Orderings_Oorder, fact_mult__right__less__imp__less, fact_dvd__triv__right, fact_add__leD1, fact_abs__eq__mult, fact_split__mult__neg__le, fact_dvd_Oless__asym_H, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_zero__less__power, arity_Nat__Onat__Rings_Ocomm__semiring__0, 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_BseqD, fact_natceiling__le, arity_Nat__Onat__Groups_Omonoid__mult, fact_power__increasing, fact_diff__Suc__less, fact_real__add__le__0__iff, fact_mult__0, fact_abs__triangle__ineq2__sym, fact_order__less__asym_H, fact_mult__poly__0__left, arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, fact_linorder__antisym__conv2, fact_mult__mono, fact_linorder__neqE, 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_dvd_Oless__imp__not__less, fact_norm__add__less, arity_Nat__Onat__Rings_Ozero__neq__one, fact_poly__zero, fact_eq__neg__iff__add__eq__0, arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, fact_zero__le__zpower__abs, fact_add__right__imp__eq, fact_realpow__two__diff, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, arity_Polynomial__Opoly__Rings_Oidom, fact_zero__less__diff, fact_abs__poly__def, fact_BseqI, fact_diff__diff__cancel, fact_mult_Ononneg__bounded, fact_nat__add__right__cancel, fact_neg__le__iff__le, fact_gr0__conv__Suc, arity_Polynomial__Opoly__Groups_Ominus, arity_RealDef__Oreal__Groups_Omonoid__add, fact_neg__0__less__iff__less, fact_zdvd__mult__cancel, fact_abs__diff__triangle__ineq, fact_leI, fact_dvd_Oord__eq__less__trans, fact_mult__le__mono2, fact_Suc__diff__diff, fact_kp, fact_le__neq__implies__less, fact_mult__left__le__imp__le, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, fact_zle__linear, fact_zero__le__one, fact_poly__add, arity_RealDef__Oreal__Rings_Ocomm__ring__1, fact_nat__add__left__cancel__less, fact_le__minus__iff, fact_mult_Oadd__right, fact_mult_Ominus__right, fact_le__add__iff2, help_c__fequal__2, fact_mult__eq__self__implies__10, fact_minus__pCons, fact_minus__add__cancel, fact_add__pos__nonneg, fact_dvd__diffD, arity_Polynomial__Opoly__Rings_Ocomm__ring, fact_pow__divides__pow__nat, fact_lemma__NBseq__def2, arity_Int__Oint__Orderings_Oord, 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fact_abs__le__iff, fact_dvd__imp__le__int, fact_abs__triangle__ineq4, fact_xt1_I2_J, fact_abs__minus__cancel, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, fact_add__0, arity_Polynomial__Opoly__Rings_Oordered__ring, fact_diff__minus__eq__add, fact_power__mono, fact_add__nonneg__nonneg, fact_lemmaCauchy, fact_mult__le__mono1, fact_diff__self__eq__0, fact_add__eq__0__iff, fact_minus__poly__code_I2_J, fact_neg__equal__iff__equal, fact_compl__eq__compl__iff, arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, fact_diff__add__0, fact_uminus__dvd__conv_I1_J, fact_Zero__neq__Suc, fact_add__pos__pos, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_diff__cancel2, arity_RealDef__Oreal__Power_Opower, fact_Suc__eq__plus1, arity_RealDef__Oreal__Groups_Oab__group__add, fact_real__of__nat__power, fact_dvd__mult__cancel, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, arity_Int__Oint__Rings_Olinordered__idom, arity_Int__Oint__Rings_Ocomm__semiring__1, 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fact_not__square__less__zero, fact_Suc__lessI, fact_add__Suc__right, arity_Complex__Ocomplex__Groups_Ominus, fact_mult__1, fact_less__bin__lemma, arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_mult_Odiff__right, fact_zdiv__mono2__neg__lemma, fact_real__sgn__def, arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 166.04/42.99 % No. of inferences in proof: 3266
% 166.04/42.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 42420 ms resp. 41457 ms w/o parsing
% 170.93/43.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 170.93/43.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------