%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG372-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 05:25:06 PM UTC 2025
% Result : Unsatisfiable 172.93s 143.11s
% Output : CNFRefutation 172.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 52
% Syntax : Number of formulae : 191 ( 85 unt; 0 typ; 0 def)
% Number of atoms : 330 ( 141 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 279 ( 140 ~; 139 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 78 ( 76 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 5 con; 0-3 aty)
% Number of variables : 207 ( 207 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring__1__no__zero__divisors > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring__abs > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Olordered__ring > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odivision__ring > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring__0 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Ocomm__ring__1 > class_Ring__and__Field_Ocomm__ring > class_Ring__and__Field_Oabs__if > class_RealVector_Oreal__vector > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__field > class_RealVector_Oreal__algebra__1 > class_RealVector_Oreal__algebra > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add__meet > class_OrderedGroup_Olordered__ab__group__add__join > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__comm__monoid__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Nat_Osemiring__char__0 > class_Lattices_Oupper__semilattice > class_Lattices_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Odistrib__lattice > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > c_RealVector_OscaleR__class_OscaleR > c_Power_Opower__class_Opower > c_Polynomial_Opoly > c_Lattices_Oupper__semilattice__class_Osup > c_Lattices_Olower__semilattice__class_Oinf > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_HOL_Oinverse__class_Odivide > v_sko__unknown__thm__rV2__1 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 > c_RealVector_Oof__real > c_RealVector_Onorm__class_Onorm > c_Nat_Osemiring__1__class_Oof__nat > c_HOL_Ouminus__class_Ouminus > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > #nlpp > tc_Polynomial_Opoly > c_HOL_Ozero__class_Ozero > c_Complex_ORe > v_r > v_p > tc_nat > tc_RealDef_Oreal > tc_Complex_Ocomplex
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(class_OrderedGroup_Ocancel__comm__monoid__add,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__0,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(class_OrderedGroup_Oordered__ab__group__add,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring__abs,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(class_RealVector_Oreal__vector,type,
class_RealVector_Oreal__vector: $i > $o ).
tff(class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(c_RealVector_OscaleR__class_OscaleR,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(class_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add__abs,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(tc_Polynomial_Opoly,type,
tc_Polynomial_Opoly: $i > $i ).
tff(class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
tff(c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add__meet,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
tff(class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add__join,type,
class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).
tff(tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(c_HOL_Oinverse__class_Odivide,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Odivision__by__zero,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(v_sko__unknown__thm__rV2__1,type,
v_sko__unknown__thm__rV2__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_nat,type,
tc_nat: $i ).
tff(class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(class_RealVector_Oreal__normed__div__algebra,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__mult,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_Ring__and__Field_Oabs__if,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(class_Ring__and__Field_Ocomm__ring,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(class_RealVector_Oreal__algebra,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(class_RealVector_Oreal__algebra__1,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(v_r,type,
v_r: $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
tff(class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Polynomial_Opoly,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(class_Ring__and__Field_Omult__mono1,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_RealVector_Onorm__class_Onorm,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Olordered__ab__group__add__abs,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(class_Ring__and__Field_Olordered__ring,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(class_Ring__and__Field_Omult__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_RealVector_Oof__real,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_Ring__and__Field_Odivision__ring,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(v_p,type,
v_p: $i ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(class_RealVector_Oreal__field,type,
class_RealVector_Oreal__field: $i > $o ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_Complex_ORe,type,
c_Complex_ORe: $i > $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(f_6452,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6435,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_959,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_6422,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_4831,axiom,
! [T_a,V_x,V_y] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ),
file(unknown,unknown) ).
tff(f_6442,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_5834,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_3941,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a),T_a) = V_b ) ),
file(unknown,unknown) ).
tff(f_6248,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) )
| ( V_a = V_b ) ),
file(unknown,unknown) ).
tff(f_3544,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_6457,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6463,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_949,axiom,
! [T_a,V_x] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_6411,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6404,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6460,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_2927,axiom,
! [T_a,V_y,V_x] :
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_6338,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6232,axiom,
! [V_z,V_w] :
( ( V_z = V_w )
| ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal)
| ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_128,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ),
file(unknown,unknown) ).
tff(f_5979,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ),
file(unknown,unknown) ).
tff(f_2715,axiom,
! [T_a,V_y,V_x_H,V_x,V_y_H] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) )
| c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_y_H,V_x_H,T_a) ),
file(unknown,unknown) ).
tff(f_6191,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ),
file(unknown,unknown) ).
tff(f_6477,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_6462,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6060,axiom,
! [T_a,V_x] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ),
file(unknown,unknown) ).
tff(f_4050,axiom,
! [V_x,V_r] :
( c_lessequals(V_x,V_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_283,axiom,
c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_5884,axiom,
! [T_a] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file(unknown,unknown) ).
tff(f_4067,axiom,
! [V_x] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(V_x),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6413,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6151,axiom,
! [V_x] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6101,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ),
file(unknown,unknown) ).
tff(f_4629,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ),
file(unknown,unknown) ).
tff(f_6494,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_6305,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_5793,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) ) ),
file(unknown,unknown) ).
tff(f_6486,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_819,axiom,
! [T_a,V_x] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_6085,axiom,
! [T_a,V_x] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ),
file(unknown,unknown) ).
tff(f_6343,axiom,
( ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_1284,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_563,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_6047,axiom,
! [V_w] : c_lessequals(V_w,V_w,tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_6470,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_6080,axiom,
! [T_a] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_3885,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ),
file(unknown,unknown) ).
tff(f_6485,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_1666,axiom,
! [T_a] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_4778,axiom,
! [T_a,V_r] :
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(V_r,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) ) ),
file(unknown,unknown) ).
tff(f_6473,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_5765,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) ) ),
file(unknown,unknown) ).
tff(c_1710,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6452]) ).
tff(c_1676,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6435]) ).
tff(c_262,plain,
! [T_a_390,V_a_391] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a_390),V_a_391,T_a_390) = V_a_391 )
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a_390) ),
inference(cnfTransformation,[status(thm)],[f_959]) ).
tff(c_1650,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6422]) ).
tff(c_6439,plain,
! [V_y_2748,V_x_2749,T_a_2750] :
( ( c_HOL_Oplus__class_Oplus(V_y_2748,V_x_2749,T_a_2750) = c_HOL_Oplus__class_Oplus(V_x_2749,V_y_2748,T_a_2750) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a_2750) ),
inference(cnfTransformation,[status(thm)],[f_4831]) ).
tff(c_6786,plain,
! [V_y_2775,V_x_2776] : ( c_HOL_Oplus__class_Oplus(V_y_2775,V_x_2776,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_x_2776,V_y_2775,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1650,c_6439]) ).
tff(c_6954,plain,
! [V_a_391] :
( ( c_HOL_Oplus__class_Oplus(V_a_391,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = V_a_391 )
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_262,c_6786]) ).
tff(c_7034,plain,
! [V_a_391] : ( c_HOL_Oplus__class_Oplus(V_a_391,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = V_a_391 ),
inference(demodulation,[status(thm),theory(equality)],[c_1676,c_6954]) ).
tff(c_1690,plain,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6442]) ).
tff(c_1354,plain,
! [V_a_2218,T_a_2217] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a_2218,T_a_2217),V_a_2218,T_a_2217) = c_HOL_Ozero__class_Ozero(T_a_2217) )
| ~ class_OrderedGroup_Oab__group__add(T_a_2217) ),
inference(cnfTransformation,[status(thm)],[f_5834]) ).
tff(c_6806,plain,
! [V_x_2776] :
( ( c_HOL_Oplus__class_Oplus(V_x_2776,c_HOL_Ouminus__class_Ouminus(V_x_2776,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_6786,c_1354]) ).
tff(c_6962,plain,
! [V_x_2776] : ( c_HOL_Oplus__class_Oplus(V_x_2776,c_HOL_Ouminus__class_Ouminus(V_x_2776,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1690,c_6806]) ).
tff(c_16624,plain,
! [V_a_2941,T_a_2942,V_b_2943] :
( ( c_HOL_Oplus__class_Oplus(V_a_2941,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a_2941,T_a_2942),V_b_2943,T_a_2942),T_a_2942) = V_b_2943 )
| ~ class_OrderedGroup_Ogroup__add(T_a_2942) ),
inference(cnfTransformation,[status(thm)],[f_3941]) ).
tff(c_16707,plain,
! [V_a_2941] :
( ( c_HOL_Oplus__class_Oplus(V_a_2941,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a_2941,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_6962,c_16624]) ).
tff(c_17024,plain,
! [V_a_2945] : ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a_2945,tc_RealDef_Oreal),tc_RealDef_Oreal) = V_a_2945 ),
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_7034,c_16707]) ).
tff(c_1478,plain,
! [V_b_2352,V_a_2351,T_a_2350] :
( ( V_b_2352 = V_a_2351 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_2352,T_a_2350) != c_HOL_Ouminus__class_Ouminus(V_a_2351,T_a_2350) )
| ~ class_OrderedGroup_Ogroup__add(T_a_2350) ),
inference(cnfTransformation,[status(thm)],[f_6248]) ).
tff(c_17076,plain,
! [V_a_2945,V_b_2352] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_2945,tc_RealDef_Oreal) = V_b_2352 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_2352,tc_RealDef_Oreal) != V_a_2945 )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_17024,c_1478]) ).
tff(c_34303,plain,
! [V_b_2352] : ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b_2352,tc_RealDef_Oreal),tc_RealDef_Oreal) = V_b_2352 ),
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_17076]) ).
tff(c_12050,plain,
! [V_a_2874,V_b_2875,T_a_2876] :
( ( c_HOL_Oplus__class_Oplus(V_a_2874,c_HOL_Ouminus__class_Ouminus(V_b_2875,T_a_2876),T_a_2876) = c_HOL_Ominus__class_Ominus(V_a_2874,V_b_2875,T_a_2876) )
| ~ class_OrderedGroup_Oab__group__add(T_a_2876) ),
inference(cnfTransformation,[status(thm)],[f_3544]) ).
tff(c_1720,plain,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6457]) ).
tff(c_1732,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6463]) ).
tff(c_258,plain,
! [V_x_387,T_a_386] :
( ( c_HOL_Oplus__class_Oplus(V_x_387,c_HOL_Ozero__class_Ozero(T_a_386),T_a_386) = V_x_387 )
| ~ class_Int_Onumber__ring(T_a_386)
| ~ class_Ring__and__Field_Oidom(T_a_386) ),
inference(cnfTransformation,[status(thm)],[f_949]) ).
tff(c_6810,plain,
! [V_x_2776] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2776,tc_RealDef_Oreal) = V_x_2776 )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_6786,c_258]) ).
tff(c_6964,plain,
! [V_x_2776] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2776,tc_RealDef_Oreal) = V_x_2776 ),
inference(demodulation,[status(thm),theory(equality)],[c_1720,c_1732,c_6810]) ).
tff(c_12079,plain,
! [V_b_2875] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b_2875,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(V_b_2875,tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_12050,c_6964]) ).
tff(c_12195,plain,
! [V_b_2875] : ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b_2875,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(V_b_2875,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1690,c_12079]) ).
tff(c_1628,plain,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6411]) ).
tff(c_1614,plain,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6404]) ).
tff(c_1726,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6460]) ).
tff(c_688,plain,
! [V_x_1148,V_y_1147,T_a_1146] :
( c_lessequals(V_x_1148,V_y_1147,T_a_1146)
| c_HOL_Oord__class_Oless(V_y_1147,V_x_1148,T_a_1146)
| ~ class_Orderings_Olinorder(T_a_1146) ),
inference(cnfTransformation,[status(thm)],[f_2927]) ).
tff(c_1506,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6338]) ).
tff(c_4983,plain,
! [V_z_2682,V_w_2683] :
( ~ c_lessequals(V_z_2682,V_w_2683,tc_RealDef_Oreal)
| ~ c_lessequals(V_w_2683,V_z_2682,tc_RealDef_Oreal)
| ( V_z_2682 = V_w_2683 ) ),
inference(cnfTransformation,[status(thm)],[f_6232]) ).
tff(c_5158,plain,
( ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r ) ),
inference(resolution,[status(thm)],[c_1506,c_4983]) ).
tff(c_5215,plain,
~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(splitLeft,[status(thm)],[c_5158]) ).
tff(c_5223,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_688,c_5215]) ).
tff(c_5231,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1726,c_5223]) ).
tff(c_9699,plain,
! [T_a_2837,V_a_2838] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a_2837),V_a_2838,T_a_2837)
| ( c_HOL_Oabs__class_Oabs(V_a_2838,T_a_2837) = V_a_2838 )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_2837) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_9702,plain,
( ( c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_5231,c_9699]) ).
tff(c_9705,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r,
inference(demodulation,[status(thm),theory(equality)],[c_1614,c_9702]) ).
tff(c_1404,plain,
! [V_a_2273,T_a_2272] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a_2273,T_a_2272),T_a_2272),c_HOL_Ozero__class_Ozero(T_a_2272),T_a_2272)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_2272) ),
inference(cnfTransformation,[status(thm)],[f_5979]) ).
tff(c_9712,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_9705,c_1404]) ).
tff(c_9752,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1614,c_9712]) ).
tff(c_122967,plain,
! [V_x_4011,V_y_4010,V_x_H_4008,T_a_4012,V_y_H_4009] :
( ~ c_lessequals(V_y_H_4009,V_x_H_4008,T_a_4012)
| c_lessequals(V_y_4010,V_x_4011,T_a_4012)
| ( c_HOL_Ominus__class_Ominus(V_x_H_4008,V_y_H_4009,T_a_4012) != c_HOL_Ominus__class_Ominus(V_x_4011,V_y_4010,T_a_4012) )
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_4012) ),
inference(cnfTransformation,[status(thm)],[f_2715]) ).
tff(c_123155,plain,
! [V_y_4010,V_x_4011] :
( c_lessequals(V_y_4010,V_x_4011,tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(V_x_4011,V_y_4010,tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_9752,c_122967]) ).
tff(c_123543,plain,
! [V_y_4013,V_x_4014] :
( c_lessequals(V_y_4013,V_x_4014,tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(V_x_4014,V_y_4013,tc_RealDef_Oreal) != v_r ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1628,c_34303,c_12195,c_123155]) ).
tff(c_1466,plain,
! [V_a_2335,T_a_2334] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a_2335,T_a_2334),c_HOL_Ozero__class_Ozero(T_a_2334),T_a_2334)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a_2334),V_a_2335,T_a_2334)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_2334) ),
inference(cnfTransformation,[status(thm)],[f_6191]) ).
tff(c_123635,plain,
! [V_a_2335] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a_2335,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(V_a_2335,tc_RealDef_Oreal),tc_RealDef_Oreal) != v_r ) ),
inference(resolution,[status(thm)],[c_123543,c_1466]) ).
tff(c_124671,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_34303,c_12195,c_1628,c_123635]) ).
tff(c_1760,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_6477]) ).
tff(c_1730,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6462]) ).
tff(c_1428,plain,
! [V_x_2301,T_a_2300] :
( c_lessequals(V_x_2301,V_x_2301,T_a_2300)
| ~ class_Orderings_Oorder(T_a_2300) ),
inference(cnfTransformation,[status(thm)],[f_6060]) ).
tff(c_4163,plain,
! [V_x_2641,V_r_2642] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x_2641,tc_RealDef_Oreal),V_r_2642,tc_RealDef_Oreal)
| c_lessequals(V_x_2641,V_r_2642,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_4050]) ).
tff(c_4225,plain,
! [V_x_2641] :
( c_lessequals(V_x_2641,c_HOL_Oabs__class_Oabs(V_x_2641,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1428,c_4163]) ).
tff(c_4273,plain,
! [V_x_2641] : c_lessequals(V_x_2641,c_HOL_Oabs__class_Oabs(V_x_2641,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1730,c_4225]) ).
tff(c_84,plain,
c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_283]) ).
tff(c_1368,plain,
! [T_a_2234] :
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a_2234),T_a_2234) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__normed__vector(T_a_2234) ),
inference(cnfTransformation,[status(thm)],[f_5884]) ).
tff(c_2488,plain,
! [V_x_2547] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(V_x_2547),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_2547,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4067]) ).
tff(c_2492,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1368,c_2488]) ).
tff(c_2497,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1760,c_84,c_2492]) ).
tff(c_5052,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(resolution,[status(thm)],[c_2497,c_4983]) ).
tff(c_5138,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_4273,c_5052]) ).
tff(c_1632,plain,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6413]) ).
tff(c_1456,plain,
! [V_x_2325] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(V_x_2325,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_2325,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6151]) ).
tff(c_26123,plain,
! [V_a_3094,T_a_3095] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a_3094,T_a_3095),V_a_3094,T_a_3095)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a_3095),V_a_3094,T_a_3095)
| ~ class_OrderedGroup_Oordered__ab__group__add(T_a_3095) ),
inference(cnfTransformation,[status(thm)],[f_6101]) ).
tff(c_26168,plain,
! [V_x_2325] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_2325,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1456,c_26123]) ).
tff(c_26237,plain,
! [V_x_3096] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_3096,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1632,c_26168]) ).
tff(c_1086,plain,
! [T_a_1785,V_a_1786] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a_1785),V_a_1786,T_a_1785)
| ( c_HOL_Oabs__class_Oabs(V_a_1786,T_a_1785) = V_a_1786 )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_1785) ),
inference(cnfTransformation,[status(thm)],[f_4629]) ).
tff(c_26259,plain,
! [V_x_3096] :
( ( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_x_3096,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_x_3096,tc_Complex_Ocomplex) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_26237,c_1086]) ).
tff(c_27111,plain,
! [V_x_3113] : ( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_x_3113,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_x_3113,tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1614,c_26259]) ).
tff(c_27213,plain,
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1368,c_27111]) ).
tff(c_27260,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_1760,c_5138,c_27213]) ).
tff(c_1794,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_6494]) ).
tff(c_1496,plain,
! [V_a_2372,T_a_2371] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a_2372,T_a_2371),T_a_2371) = V_a_2372 )
| ~ class_OrderedGroup_Ogroup__add(T_a_2371) ),
inference(cnfTransformation,[status(thm)],[f_6305]) ).
tff(c_3590,plain,
! [T_a_2617,V_a_2618] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a_2617),V_a_2618,T_a_2617) = c_HOL_Ouminus__class_Ouminus(V_a_2618,T_a_2617) )
| ~ class_OrderedGroup_Ogroup__add(T_a_2617) ),
inference(cnfTransformation,[status(thm)],[f_5793]) ).
tff(c_1778,plain,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_6486]) ).
tff(c_2331,plain,
! [V_x_2532,T_a_2533] :
( ( c_HOL_Ominus__class_Ominus(V_x_2532,V_x_2532,T_a_2533) = c_HOL_Ozero__class_Ozero(T_a_2533) )
| ~ class_OrderedGroup_Oab__group__add(T_a_2533) ),
inference(cnfTransformation,[status(thm)],[f_819]) ).
tff(c_2340,plain,
! [V_x_2532] : ( c_HOL_Ominus__class_Ominus(V_x_2532,V_x_2532,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1778,c_2331]) ).
tff(c_3601,plain,
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_3590,c_2340]) ).
tff(c_3623,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(demodulation,[status(thm),theory(equality)],[c_1794,c_3601]) ).
tff(c_4477,plain,
! [V_b_2656,V_a_2657,T_a_2658] :
( ( V_b_2656 = V_a_2657 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_2656,T_a_2658) != c_HOL_Ouminus__class_Ouminus(V_a_2657,T_a_2658) )
| ~ class_OrderedGroup_Ogroup__add(T_a_2658) ),
inference(cnfTransformation,[status(thm)],[f_6248]) ).
tff(c_4483,plain,
! [V_a_2657] :
( ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = V_a_2657 )
| ( c_HOL_Ouminus__class_Ouminus(V_a_2657,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_3623,c_4477]) ).
tff(c_4542,plain,
! [V_a_2660] :
( ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = V_a_2660 )
| ( c_HOL_Ouminus__class_Ouminus(V_a_2660,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1794,c_4483]) ).
tff(c_4553,plain,
! [V_a_2372] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_2372,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_a_2372 )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1496,c_4542]) ).
tff(c_4565,plain,
! [V_a_2372] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_2372,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_a_2372 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1794,c_4553]) ).
tff(c_26304,plain,
! [V_x_3096] : ( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_x_3096,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_x_3096,tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1614,c_26259]) ).
tff(c_1438,plain,
! [V_x_2308,T_a_2307] :
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x_2308,T_a_2307),T_a_2307) = c_RealVector_Onorm__class_Onorm(V_x_2308,T_a_2307) )
| ~ class_RealVector_Oreal__normed__vector(T_a_2307) ),
inference(cnfTransformation,[status(thm)],[f_6085]) ).
tff(c_27209,plain,
! [V_x_2308] :
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x_2308,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_x_2308,tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1438,c_27111]) ).
tff(c_27592,plain,
! [V_x_3117] : ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x_3117,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(V_x_3117,tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1760,c_26304,c_27209]) ).
tff(c_27650,plain,
! [V_a_2372] :
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(V_a_2372,tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_a_2372 ) ),
inference(superposition,[status(thm),theory(equality)],[c_4565,c_27592]) ).
tff(c_37172,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_27260,c_27650]) ).
tff(c_1508,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(cnfTransformation,[status(thm)],[f_6343]) ).
tff(c_264321,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34303,c_124671,c_37172,c_1508]) ).
tff(c_264322,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r,
inference(splitRight,[status(thm)],[c_5158]) ).
tff(c_1342,plain,
! [T_a_2204,V_a_2205] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a_2204),V_a_2205,T_a_2204) = c_HOL_Ouminus__class_Ouminus(V_a_2205,T_a_2204) )
| ~ class_OrderedGroup_Ogroup__add(T_a_2204) ),
inference(cnfTransformation,[status(thm)],[f_5793]) ).
tff(c_264359,plain,
! [V_a_2205] :
( ( c_HOL_Ominus__class_Ominus(v_r,V_a_2205,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(V_a_2205,tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_264322,c_1342]) ).
tff(c_264450,plain,
! [V_a_2205] : ( c_HOL_Ominus__class_Ominus(v_r,V_a_2205,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(V_a_2205,tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_264359]) ).
tff(c_266695,plain,
! [V_a_5092,V_b_5093,T_a_5094] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a_5092,V_b_5093,T_a_5094),V_b_5093,T_a_5094) = V_a_5092 )
| ~ class_OrderedGroup_Ogroup__add(T_a_5094) ),
inference(cnfTransformation,[status(thm)],[f_1284]) ).
tff(c_266724,plain,
! [V_a_2205] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a_2205,tc_RealDef_Oreal),V_a_2205,tc_RealDef_Oreal) = v_r )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_264450,c_266695]) ).
tff(c_266933,plain,
! [V_a_5102] : ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a_5102,tc_RealDef_Oreal),V_a_5102,tc_RealDef_Oreal) = v_r ),
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_266724]) ).
tff(c_267002,plain,
! [V_a_2372] :
( ( c_HOL_Oplus__class_Oplus(V_a_2372,c_HOL_Ouminus__class_Ouminus(V_a_2372,tc_RealDef_Oreal),tc_RealDef_Oreal) = v_r )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_1496,c_266933]) ).
tff(c_267041,plain,
! [V_a_2372] : ( c_HOL_Oplus__class_Oplus(V_a_2372,c_HOL_Ouminus__class_Ouminus(V_a_2372,tc_RealDef_Oreal),tc_RealDef_Oreal) = v_r ),
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_267002]) ).
tff(c_267234,plain,
! [V_a_5107,V_b_5108,T_a_5109] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a_5107,V_b_5108,T_a_5109),V_b_5108,T_a_5109) = V_a_5107 )
| ~ class_OrderedGroup_Ogroup__add(T_a_5109) ),
inference(cnfTransformation,[status(thm)],[f_563]) ).
tff(c_267258,plain,
! [V_a_2372] :
( ( c_HOL_Ominus__class_Ominus(v_r,c_HOL_Ouminus__class_Ouminus(V_a_2372,tc_RealDef_Oreal),tc_RealDef_Oreal) = V_a_2372 )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_267041,c_267234]) ).
tff(c_267333,plain,
! [V_a_5110] : ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a_5110,tc_RealDef_Oreal),tc_RealDef_Oreal) = V_a_5110 ),
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_264450,c_267258]) ).
tff(c_267370,plain,
! [V_a_5110,V_b_2352] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_5110,tc_RealDef_Oreal) = V_b_2352 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_2352,tc_RealDef_Oreal) != V_a_5110 )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_267333,c_1478]) ).
tff(c_308280,plain,
! [V_b_2352] : ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b_2352,tc_RealDef_Oreal),tc_RealDef_Oreal) = V_b_2352 ),
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_267370]) ).
tff(c_1424,plain,
! [V_w_2296] : c_lessequals(V_w_2296,V_w_2296,tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_6047]) ).
tff(c_1746,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_6470]) ).
tff(c_264324,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r,
inference(demodulation,[status(thm),theory(equality)],[c_264322,c_264322,c_5138]) ).
tff(c_1436,plain,
! [T_a_2306] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a_2306),T_a_2306) = c_HOL_Ozero__class_Ozero(T_a_2306) )
| ~ class_OrderedGroup_Ogroup__add(T_a_2306) ),
inference(cnfTransformation,[status(thm)],[f_6080]) ).
tff(c_264440,plain,
( ( c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_264322,c_1436]) ).
tff(c_264504,plain,
c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) = v_r,
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_264322,c_264440]) ).
tff(c_264583,plain,
! [V_b_2352] :
( ( v_r = V_b_2352 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_2352,tc_RealDef_Oreal) != v_r )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_264504,c_1478]) ).
tff(c_265409,plain,
! [V_b_5033] :
( ( v_r = V_b_5033 )
| ( c_HOL_Ouminus__class_Ouminus(V_b_5033,tc_RealDef_Oreal) != v_r ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_264583]) ).
tff(c_265420,plain,
! [V_a_2372] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_2372,tc_RealDef_Oreal) = v_r )
| ( v_r != V_a_2372 )
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
inference(superposition,[status(thm),theory(equality)],[c_1496,c_265409]) ).
tff(c_265536,plain,
! [V_a_5039] :
( ( c_HOL_Ouminus__class_Ouminus(V_a_5039,tc_RealDef_Oreal) = v_r )
| ( v_r != V_a_5039 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_265420]) ).
tff(c_920,plain,
! [V_a_1541,T_a_1540] :
( ( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_1541,T_a_1540),T_a_1540) = c_HOL_Oabs__class_Oabs(V_a_1541,T_a_1540) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_1540) ),
inference(cnfTransformation,[status(thm)],[f_3885]) ).
tff(c_265542,plain,
! [V_a_5039] :
( ( c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(V_a_5039,tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( v_r != V_a_5039 ) ),
inference(superposition,[status(thm),theory(equality)],[c_265536,c_920]) ).
tff(c_265655,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r,
inference(demodulation,[status(thm),theory(equality)],[c_1614,c_264324,c_265542]) ).
tff(c_1776,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_6485]) ).
tff(c_416,plain,
! [T_a_662] :
( ( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a_662) = c_HOL_Ozero__class_Ozero(T_a_662) )
| ~ class_RealVector_Oreal__algebra__1(T_a_662) ),
inference(cnfTransformation,[status(thm)],[f_1666]) ).
tff(c_265889,plain,
! [T_a_5047] :
( ( c_RealVector_Oof__real(v_r,T_a_5047) = c_HOL_Ozero__class_Ozero(T_a_5047) )
| ~ class_RealVector_Oreal__algebra__1(T_a_5047) ),
inference(demodulation,[status(thm),theory(equality)],[c_264322,c_416]) ).
tff(c_265898,plain,
c_RealVector_Oof__real(v_r,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[c_1776,c_265889]) ).
tff(c_1116,plain,
! [V_r_1837,T_a_1836] :
( ( c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(V_r_1837,T_a_1836),T_a_1836) = c_HOL_Oabs__class_Oabs(V_r_1837,tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__normed__algebra__1(T_a_1836) ),
inference(cnfTransformation,[status(thm)],[f_4778]) ).
tff(c_265919,plain,
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) )
| ~ class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_265898,c_1116]) ).
tff(c_265927,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = v_r,
inference(demodulation,[status(thm),theory(equality)],[c_1746,c_265655,c_265919]) ).
tff(c_1752,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_6473]) ).
tff(c_266037,plain,
! [V_y_5053,V_x_5054,T_a_5055] :
( ( c_HOL_Oplus__class_Oplus(V_y_5053,V_x_5054,T_a_5055) = c_HOL_Oplus__class_Oplus(V_x_5054,V_y_5053,T_a_5055) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a_5055) ),
inference(cnfTransformation,[status(thm)],[f_4831]) ).
tff(c_270314,plain,
! [V_y_5186,V_x_5187] : ( c_HOL_Oplus__class_Oplus(V_y_5186,V_x_5187,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(V_x_5187,V_y_5186,tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1752,c_266037]) ).
tff(c_270450,plain,
! [V_a_2218] :
( ( c_HOL_Oplus__class_Oplus(V_a_2218,c_HOL_Ouminus__class_Ouminus(V_a_2218,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1354,c_270314]) ).
tff(c_282080,plain,
! [V_a_5382] : ( c_HOL_Oplus__class_Oplus(V_a_5382,c_HOL_Ouminus__class_Ouminus(V_a_5382,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1778,c_270450]) ).
tff(c_1334,plain,
! [V_b_2195,T_a_2193,V_a_2194] :
( ( c_HOL_Ouminus__class_Ouminus(V_b_2195,T_a_2193) = V_a_2194 )
| ( c_HOL_Oplus__class_Oplus(V_a_2194,V_b_2195,T_a_2193) != c_HOL_Ozero__class_Ozero(T_a_2193) )
| ~ class_OrderedGroup_Ogroup__add(T_a_2193) ),
inference(cnfTransformation,[status(thm)],[f_5765]) ).
tff(c_282119,plain,
! [V_a_5382] :
( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a_5382,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = V_a_5382 )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_282080,c_1334]) ).
tff(c_282465,plain,
! [V_a_5386] : ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a_5386,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = V_a_5386 ),
inference(demodulation,[status(thm),theory(equality)],[c_1794,c_282119]) ).
tff(c_282538,plain,
! [V_a_5386] :
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_a_5386,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(V_a_5386,tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_282465,c_1438]) ).
tff(c_300556,plain,
! [V_a_5636] : ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_a_5636,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(V_a_5636,tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1760,c_282538]) ).
tff(c_300616,plain,
! [V_a_2372] :
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(V_a_2372,tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_a_2372 ) ),
inference(superposition,[status(thm),theory(equality)],[c_4565,c_300556]) ).
tff(c_300671,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = v_r,
inference(demodulation,[status(thm),theory(equality)],[c_265927,c_300616]) ).
tff(c_545059,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_308280,c_1424,c_300671,c_1508]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ALG372-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Apr 6 08:18:02 EDT 2025
% 0.13/0.35 % CPUTime :
% 172.93/143.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 172.94/143.14
% 172.94/143.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------