%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWW230+1 : TPTP v9.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.knzCLQULmW true
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 05:02:27 PM UTC 2025
% Result : Theorem 185.34s 27.10s
% Output : Refutation 185.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of formulae : 92 ( 68 unt; 0 typ; 0 def)
% Number of atoms : 130 ( 42 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1647 ( 38 ~; 25 |; 0 &;1571 @)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 36 usr; 12 con; 0-3 aty)
% Number of variables : 89 ( 0 ^; 89 !; 0 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: $i > $i > $i ).
thf(v_s_____type,type,
v_s____: $i ).
thf(v_f_____type,type,
v_f____: $i ).
thf(v_z_____type,type,
v_z____: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_RealDef_Oreal_type,type,
c_RealDef_Oreal: $i > $i > $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(v_p_type,type,
v_p: $i ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
thf(v_g_____type,type,
v_g____: $i > $i ).
thf(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Rings_Odivision__ring_type,type,
class_Rings_Odivision__ring: $i > $o ).
thf(c_Rings_Oinverse__class_Odivide_type,type,
c_Rings_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(v_N1_____type,type,
v_N1____: $i ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(v_N2_____type,type,
v_N2____: $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
thf(class_Rings_Oordered__comm__semiring_type,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: $i > $i > $i ).
thf(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: $i > $i > $i > $i ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(class_Fields_Olinordered__field_type,type,
class_Fields_Olinordered__field: $i > $o ).
thf(c_Int_OPls_type,type,
c_Int_OPls: $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal ).
thf(zip_derived_cl1676,plain,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
inference(cnf,[status(esa)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
thf(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [V_a_2: $i,T_a: $i] :
( ( class_Groups_Olinordered__ab__group__add @ T_a )
=> ( ( c_Orderings_Oord__class_Oless__eq @ T_a @ ( c_Groups_Ozero__class_Ozero @ T_a ) @ ( c_Groups_Oplus__class_Oplus @ T_a @ V_a_2 @ V_a_2 ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ T_a @ ( c_Groups_Ozero__class_Ozero @ T_a ) @ V_a_2 ) ) ) ).
thf(zip_derived_cl1503,plain,
! [X0: $i,X1: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ X0 @ ( c_Groups_Ozero__class_Ozero @ X0 ) @ X1 )
| ( c_Orderings_Oord__class_Oless__eq @ X0 @ ( c_Groups_Ozero__class_Ozero @ X0 ) @ ( c_Groups_Oplus__class_Oplus @ X0 @ X1 @ X1 ) )
| ~ ( class_Groups_Olinordered__ab__group__add @ X0 ) ),
inference(cnf,[status(esa)],[fact_zero__le__double__add__iff__zero__le__single__add]) ).
thf(zip_derived_cl5302,plain,
! [X0: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ X0 @ X0 ) )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ X0 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl1676,zip_derived_cl1503]) ).
thf(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal ).
thf(zip_derived_cl1684,plain,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
inference(cnf,[status(esa)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]) ).
thf(fact_comm__mult__left__mono,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Oordered__comm__semiring @ T_a )
=> ( ( c_Orderings_Oord__class_Oless__eq @ T_a @ V_a @ V_b )
=> ( ( c_Orderings_Oord__class_Oless__eq @ T_a @ ( c_Groups_Ozero__class_Ozero @ T_a ) @ V_c )
=> ( c_Orderings_Oord__class_Oless__eq @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_c @ V_a ) @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_c @ V_b ) ) ) ) ) ).
thf(zip_derived_cl1022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ X0 @ X1 @ X2 )
| ( c_Orderings_Oord__class_Oless__eq @ X0 @ ( c_Groups_Otimes__class_Otimes @ X0 @ X3 @ X1 ) @ ( c_Groups_Otimes__class_Otimes @ X0 @ X3 @ X2 ) )
| ~ ( c_Orderings_Oord__class_Oless__eq @ X0 @ ( c_Groups_Ozero__class_Ozero @ X0 ) @ X3 )
| ~ ( class_Rings_Oordered__comm__semiring @ X0 ) ),
inference(cnf,[status(esa)],[fact_comm__mult__left__mono]) ).
thf(zip_derived_cl4435,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ X2 )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ X2 @ X1 ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ X2 @ X0 ) )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ X1 @ X0 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl1684,zip_derived_cl1022]) ).
thf(zip_derived_cl1676_001,plain,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
inference(cnf,[status(esa)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
thf(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_a_2: $i,T_a: $i] :
( ( class_Groups_Olinordered__ab__group__add @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ ( c_Groups_Ozero__class_Ozero @ T_a ) @ ( c_Groups_Oplus__class_Oplus @ T_a @ V_a_2 @ V_a_2 ) )
<=> ( c_Orderings_Oord__class_Oless @ T_a @ ( c_Groups_Ozero__class_Ozero @ T_a ) @ V_a_2 ) ) ) ).
thf(zip_derived_cl1505,plain,
! [X0: $i,X1: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ X0 @ ( c_Groups_Ozero__class_Ozero @ X0 ) @ X1 )
| ( c_Orderings_Oord__class_Oless @ X0 @ ( c_Groups_Ozero__class_Ozero @ X0 ) @ ( c_Groups_Oplus__class_Oplus @ X0 @ X1 @ X1 ) )
| ~ ( class_Groups_Olinordered__ab__group__add @ X0 ) ),
inference(cnf,[status(esa)],[fact_zero__less__double__add__iff__zero__less__single__add]) ).
thf(zip_derived_cl5304,plain,
! [X0: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ X0 @ X0 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ X0 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl1676,zip_derived_cl1505]) ).
thf(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field @ tc_RealDef_Oreal ).
thf(zip_derived_cl1694,plain,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
inference(cnf,[status(esa)],[arity_RealDef__Oreal__Fields_Olinordered__field]) ).
thf(fact_pos__divide__le__eq,axiom,
! [V_a_2: $i,V_b_2: $i,V_c_2: $i,T_a: $i] :
( ( class_Fields_Olinordered__field @ T_a )
=> ( ( c_Orderings_Oord__class_Oless @ T_a @ ( c_Groups_Ozero__class_Ozero @ T_a ) @ V_c_2 )
=> ( ( c_Orderings_Oord__class_Oless__eq @ T_a @ ( c_Rings_Oinverse__class_Odivide @ T_a @ V_b_2 @ V_c_2 ) @ V_a_2 )
<=> ( c_Orderings_Oord__class_Oless__eq @ T_a @ V_b_2 @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_a_2 @ V_c_2 ) ) ) ) ) ).
thf(zip_derived_cl1381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ X0 @ ( c_Groups_Ozero__class_Ozero @ X0 ) @ X1 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ X0 @ X2 @ ( c_Groups_Otimes__class_Otimes @ X0 @ X3 @ X1 ) )
| ( c_Orderings_Oord__class_Oless__eq @ X0 @ ( c_Rings_Oinverse__class_Odivide @ X0 @ X2 @ X1 ) @ X3 )
| ~ ( class_Fields_Olinordered__field @ X0 ) ),
inference(cnf,[status(esa)],[fact_pos__divide__le__eq]) ).
thf(zip_derived_cl5948,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ X2 @ X0 ) @ X1 )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ X2 @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ X1 @ X0 ) )
| ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ X0 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl1694,zip_derived_cl1381]) ).
thf(fact_one__add__one__is__two,axiom,
! [T_a: $i] :
( ( class_Int_Onumber__ring @ T_a )
=> ( ( c_Groups_Oplus__class_Oplus @ T_a @ ( c_Groups_Oone__class_Oone @ T_a ) @ ( c_Groups_Oone__class_Oone @ T_a ) )
= ( c_Int_Onumber__class_Onumber__of @ T_a @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ).
thf(zip_derived_cl502,plain,
! [X0: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ X0 @ ( c_Groups_Oone__class_Oone @ X0 ) @ ( c_Groups_Oone__class_Oone @ X0 ) )
= ( c_Int_Onumber__class_Onumber__of @ X0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
| ~ ( class_Int_Onumber__ring @ X0 ) ),
inference(cnf,[status(esa)],[fact_one__add__one__is__two]) ).
thf(fact_one__is__num__one,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ).
thf(zip_derived_cl543,plain,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
inference(cnf,[status(esa)],[fact_one__is__num__one]) ).
thf(fact_number__of__is__id,axiom,
! [V_k: $i] :
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ V_k )
= V_k ) ).
thf(zip_derived_cl452,plain,
! [X0: $i] :
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ X0 )
= X0 ),
inference(cnf,[status(esa)],[fact_number__of__is__id]) ).
thf(zip_derived_cl9913,plain,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( c_Int_OBit1 @ c_Int_OPls ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl543,zip_derived_cl452]) ).
thf(zip_derived_cl16679,plain,
! [X0: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ X0 @ ( c_Groups_Oone__class_Oone @ X0 ) @ ( c_Groups_Oone__class_Oone @ X0 ) )
= ( c_Int_Onumber__class_Onumber__of @ X0 @ ( c_Int_OBit0 @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
| ~ ( class_Int_Onumber__ring @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl502,zip_derived_cl9913]) ).
thf(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ),
inference('cnf.neg',[status(esa)],[conj_0]) ).
thf(zip_derived_cl1760,plain,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9913_002,plain,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( c_Int_OBit1 @ c_Int_OPls ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl543,zip_derived_cl452]) ).
thf(fact_real__norm__def,axiom,
! [V_r: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ V_r )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ V_r ) ) ).
thf(zip_derived_cl939,plain,
! [X0: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ X0 )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ X0 ) ),
inference(cnf,[status(esa)],[fact_real__norm__def]) ).
thf(fact_abs__minus__add__cancel,axiom,
! [V_y: $i,V_x: $i] :
( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ V_x @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ V_y ) ) )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ V_y @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ V_x ) ) ) ) ).
thf(zip_derived_cl433,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ X1 @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ X0 ) ) )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ X0 @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ X1 ) ) ) ),
inference(cnf,[status(esa)],[fact_abs__minus__add__cancel]) ).
thf(fact_real__diff__def,axiom,
! [V_s: $i,V_r: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ V_r @ V_s )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ V_r @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ V_s ) ) ) ).
thf(zip_derived_cl431,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ X0 @ X1 )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ X0 @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ X1 ) ) ),
inference(cnf,[status(esa)],[fact_real__diff__def]) ).
thf(zip_derived_cl939_003,plain,
! [X0: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ X0 )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ X0 ) ),
inference(cnf,[status(esa)],[fact_real__norm__def]) ).
thf(zip_derived_cl431_004,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ X0 @ X1 )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ X0 @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ X1 ) ) ),
inference(cnf,[status(esa)],[fact_real__diff__def]) ).
thf(zip_derived_cl939_005,plain,
! [X0: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ X0 )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ X0 ) ),
inference(cnf,[status(esa)],[fact_real__norm__def]) ).
thf(zip_derived_cl14968,plain,
! [X0: $i,X1: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ X1 @ X0 ) )
= ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl433,zip_derived_cl431,zip_derived_cl939,zip_derived_cl431,zip_derived_cl939]) ).
thf(zip_derived_cl9913_006,plain,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( c_Int_OBit1 @ c_Int_OPls ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl543,zip_derived_cl452]) ).
thf(zip_derived_cl939_007,plain,
! [X0: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ X0 )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ X0 ) ),
inference(cnf,[status(esa)],[fact_real__norm__def]) ).
thf(zip_derived_cl14968_008,plain,
! [X0: $i,X1: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ X1 @ X0 ) )
= ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl433,zip_derived_cl431,zip_derived_cl939,zip_derived_cl431,zip_derived_cl939]) ).
thf(zip_derived_cl69907,plain,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1760,zip_derived_cl9913,zip_derived_cl939,zip_derived_cl14968,zip_derived_cl9913,zip_derived_cl939,zip_derived_cl14968]) ).
thf(zip_derived_cl69920,plain,
( ~ ( class_Int_Onumber__ring @ tc_RealDef_Oreal )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16679,zip_derived_cl69907]) ).
thf(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring @ tc_RealDef_Oreal ).
thf(zip_derived_cl1714,plain,
class_Int_Onumber__ring @ tc_RealDef_Oreal,
inference(cnf,[status(esa)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
thf(zip_derived_cl69933,plain,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl69920,zip_derived_cl1714]) ).
thf(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring @ tc_RealDef_Oreal ).
thf(zip_derived_cl1703,plain,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
inference(cnf,[status(esa)],[arity_RealDef__Oreal__Rings_Odivision__ring]) ).
thf(fact_times__divide__eq__right,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Odivision__ring @ T_a )
=> ( ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ ( c_Rings_Oinverse__class_Odivide @ T_a @ V_b @ V_c ) )
= ( c_Rings_Oinverse__class_Odivide @ T_a @ ( c_Groups_Otimes__class_Otimes @ T_a @ V_a @ V_b ) @ V_c ) ) ) ).
thf(zip_derived_cl977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( c_Groups_Otimes__class_Otimes @ X0 @ X1 @ ( c_Rings_Oinverse__class_Odivide @ X0 @ X2 @ X3 ) )
= ( c_Rings_Oinverse__class_Odivide @ X0 @ ( c_Groups_Otimes__class_Otimes @ X0 @ X1 @ X2 ) @ X3 ) )
| ~ ( class_Rings_Odivision__ring @ X0 ) ),
inference(cnf,[status(esa)],[fact_times__divide__eq__right]) ).
thf(zip_derived_cl5581,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ X2 @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ X1 @ X0 ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ X2 @ X1 ) @ X0 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl1703,zip_derived_cl977]) ).
thf(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex ).
thf(zip_derived_cl1730,plain,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
thf(fact_norm__minus__commute,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( class_RealVector_Oreal__normed__vector @ T_a )
=> ( ( c_RealVector_Onorm__class_Onorm @ T_a @ ( c_Groups_Ominus__class_Ominus @ T_a @ V_a @ V_b ) )
= ( c_RealVector_Onorm__class_Onorm @ T_a @ ( c_Groups_Ominus__class_Ominus @ T_a @ V_b @ V_a ) ) ) ) ).
thf(zip_derived_cl992,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( c_RealVector_Onorm__class_Onorm @ X0 @ ( c_Groups_Ominus__class_Ominus @ X0 @ X2 @ X1 ) )
= ( c_RealVector_Onorm__class_Onorm @ X0 @ ( c_Groups_Ominus__class_Ominus @ X0 @ X1 @ X2 ) ) )
| ~ ( class_RealVector_Oreal__normed__vector @ X0 ) ),
inference(cnf,[status(esa)],[fact_norm__minus__commute]) ).
thf(zip_derived_cl5348,plain,
! [X0: $i,X1: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ X1 @ X0 ) )
= ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ X0 @ X1 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl1730,zip_derived_cl992]) ).
thf(zip_derived_cl113977,plain,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl69933,zip_derived_cl5581,zip_derived_cl5348]) ).
thf(zip_derived_cl113979,plain,
( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5948,zip_derived_cl113977]) ).
thf(fact_real__mult__commute,axiom,
! [V_w: $i,V_z: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_z @ V_w )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ V_w @ V_z ) ) ).
thf(zip_derived_cl294,plain,
! [X0: $i,X1: $i] :
( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ X1 @ X0 )
= ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[fact_real__mult__commute]) ).
thf(zip_derived_cl114008,plain,
( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl113979,zip_derived_cl294]) ).
thf(zip_derived_cl116525,plain,
( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5304,zip_derived_cl114008]) ).
thf(fact_numeral__1__eq__Suc__0,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ).
thf(zip_derived_cl908,plain,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(cnf,[status(esa)],[fact_numeral__1__eq__Suc__0]) ).
thf(fact_nat__numeral__1__eq__1,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ).
thf(zip_derived_cl786,plain,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(cnf,[status(esa)],[fact_nat__numeral__1__eq__1]) ).
thf(zip_derived_cl9070,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl786]) ).
thf(fact_real__of__nat__Suc__gt__zero,axiom,
! [V_n: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ V_n ) ) ) ).
thf(zip_derived_cl148,plain,
! [X0: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ X0 ) ) ),
inference(cnf,[status(esa)],[fact_real__of__nat__Suc__gt__zero]) ).
thf(zip_derived_cl11154,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl9070,zip_derived_cl148]) ).
thf(fact_real__of__nat__1,axiom,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ).
thf(zip_derived_cl542,plain,
( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(cnf,[status(esa)],[fact_real__of__nat__1]) ).
thf(zip_derived_cl11155,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
inference(demod,[status(thm)],[zip_derived_cl11154,zip_derived_cl542]) ).
thf(zip_derived_cl116529,plain,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl116525,zip_derived_cl11155]) ).
thf(zip_derived_cl122209,plain,
( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) )
| ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4435,zip_derived_cl116529]) ).
thf(fact__096abs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_060_061_Aabs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_L_Acmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_A_N_Apoly_Ap_Az_J_096,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) ).
thf(zip_derived_cl2,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ),
inference(cnf,[status(esa)],[fact__096abs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_060_061_Aabs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_L_Acmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_A_N_Apoly_Ap_Az_J_096]) ).
thf(zip_derived_cl939_009,plain,
! [X0: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ X0 )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ X0 ) ),
inference(cnf,[status(esa)],[fact_real__norm__def]) ).
thf(zip_derived_cl939_010,plain,
! [X0: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ X0 )
= ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ X0 ) ),
inference(cnf,[status(esa)],[fact_real__norm__def]) ).
thf(zip_derived_cl9206,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl939,zip_derived_cl939]) ).
thf(zip_derived_cl14968_011,plain,
! [X0: $i,X1: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ X1 @ X0 ) )
= ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl433,zip_derived_cl431,zip_derived_cl939,zip_derived_cl431,zip_derived_cl939]) ).
thf(zip_derived_cl14968_012,plain,
! [X0: $i,X1: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ X1 @ X0 ) )
= ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl433,zip_derived_cl431,zip_derived_cl939,zip_derived_cl431,zip_derived_cl939]) ).
thf(zip_derived_cl5348_013,plain,
! [X0: $i,X1: $i] :
( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ X1 @ X0 ) )
= ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ X0 @ X1 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl1730,zip_derived_cl992]) ).
thf(zip_derived_cl112313,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9206,zip_derived_cl14968,zip_derived_cl14968,zip_derived_cl5348]) ).
thf(zip_derived_cl122234,plain,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(demod,[status(thm)],[zip_derived_cl122209,zip_derived_cl112313]) ).
thf(zip_derived_cl122245,plain,
~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5302,zip_derived_cl122234]) ).
thf(fact_th000_I1_J,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ).
thf(zip_derived_cl448,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
inference(cnf,[status(esa)],[fact_th000_I1_J]) ).
thf(zip_derived_cl122249,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl122245,zip_derived_cl448]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW230+1 : TPTP v9.2.0. Released v5.2.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.knzCLQULmW true
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 1 11:57:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.55/0.65 % Total configuration time : 435
% 0.55/0.65 % Estimated wc time : 1092
% 0.55/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.55/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.55/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 185.34/27.10 % Solved by fo/fo6_bce.sh.
% 185.34/27.10 % BCE start: 1761
% 185.34/27.10 % BCE eliminated: 26
% 185.34/27.10 % PE start: 1735
% 185.34/27.10 logic: eq
% 185.34/27.10 % PE eliminated: -122
% 185.34/27.10 % done 7452 iterations in 26.315s
% 185.34/27.10 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 185.34/27.10 % SZS output start Refutation
% See solution above
% 185.34/27.11
% 185.34/27.11
% 185.34/27.11 % Terminating...
% 185.76/27.14 % Runner terminated.
% 185.76/27.15 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------