TSTP Solution File: SWW234+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWW234+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Mar 6 15:14:16 EST 2011
% Result : Theorem 80.02s
% Output : CNFRefutation 80.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 58
% Syntax : Number of formulae : 319 ( 86 unt; 0 def)
% Number of atoms : 754 ( 215 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 751 ( 316 ~; 319 |; 53 &)
% ( 17 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 422 ( 5 sgn 259 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(44,axiom,
! [X19,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X19)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X19)
| X10 = X19 ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_less__eq__real__def) ).
fof(47,axiom,
! [X18] :
( c_RealDef_Oreal(tc_Nat_Onat,X18) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__of__nat__zero__iff) ).
fof(53,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(56,axiom,
! [X7,X8,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7)))
=> X8 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_rabs__ratiotest__lemma) ).
fof(63,axiom,
! [X12,X4,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X12)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),c_Groups_Ouminus__class_Ouminus(X5,X4)) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_le__imp__neg__le) ).
fof(91,axiom,
! [X8] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__sgn__pos) ).
fof(107,axiom,
! [X12,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X12),X12) = X4 ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_add__diff__cancel) ).
fof(108,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_h) ).
fof(114,axiom,
! [X6] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X6)) = X6,
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_natceiling__real__of__nat) ).
fof(116,axiom,
! [X11,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X11)),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_le__add1) ).
fof(140,axiom,
! [X8] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X8,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X8))),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__natfloor__gt__diff__one) ).
fof(160,axiom,
! [X8] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X8)),X8) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__natfloor__le) ).
fof(167,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X6),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_le__refl) ).
fof(186,axiom,
! [X19,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__add__le__0__iff) ).
fof(212,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> c_Groups_Oabs__class_Oabs(X5,X4) = c_Groups_Ouminus__class_Ouminus(X5,X4) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_abs__of__neg) ).
fof(353,axiom,
! [X57,X36] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X36,X57) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X36,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X57)),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__diff__def) ).
fof(371,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4)) = X4 ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_minus__minus) ).
fof(373,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(382,axiom,
! [X17,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X17),c_Groups_Ozero__class_Ozero(X5))
<=> X17 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_abs__le__zero__iff) ).
fof(440,axiom,
! [X8] :
( ( X8 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X8 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__sgn__def) ).
fof(453,axiom,
! [X6] : c_Nat_OSuc(X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_Suc__eq__plus1) ).
fof(461,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(463,axiom,
! [X24,X23,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X24) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__le__trans) ).
fof(486,axiom,
! [X19,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X19)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X10,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__le__eq__diff) ).
fof(533,axiom,
! [X13,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,X13) = c_Groups_Oplus__class_Oplus(X5,X13,X4) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(538,axiom,
! [X8] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X8)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X8)),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_complex__mod__minus__le__complex__mod) ).
fof(584,axiom,
! [X4] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4) = X4 ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_abs__real__def) ).
fof(585,axiom,
! [X8] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X8,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X8),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_natfloor__add__one) ).
fof(619,axiom,
! [X36] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X36) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X36),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__norm__def) ).
fof(625,axiom,
! [X19,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X19,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__add__less__0__iff) ).
fof(633,axiom,
! [X19,X10] :
( 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,X10,X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10),X19) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__0__le__add__iff) ).
fof(637,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(646,axiom,
! [X19,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X10,X19)
<=> c_Orderings_Oord__class_Oless__eq(X5,X19,X10) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_linorder__not__less) ).
fof(661,axiom,
! [X6,X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X11),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_nat__add__commute) ).
fof(774,axiom,
! [X19,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X19))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10),X19) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__0__less__add__iff) ).
fof(781,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',conj_0) ).
fof(806,axiom,
! [X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X10))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X10) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_le__natfloor__eq__one) ).
fof(835,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_less__Suc0) ).
fof(862,axiom,
! [X7,X8] :
( X8 != X7
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X8) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_linorder__neqE__nat) ).
fof(864,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) = X6,
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_plus__nat_Oadd__0) ).
fof(872,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_RealVector_Onorm__class_Onorm(X5,X10) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X10 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_norm__eq__zero) ).
fof(874,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> c_Groups_Oabs__class_Oabs(X5,X4) = X4 ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_abs__of__pos) ).
fof(893,axiom,
! [X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_natceiling__le__eq__one) ).
fof(947,axiom,
! [X19,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X10,X19)
<=> c_Orderings_Oord__class_Oless(X5,X19,X10) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_linorder__not__le) ).
fof(994,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',arity_Nat__Onat__Orderings_Olinorder) ).
fof(1008,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(1039,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(1072,axiom,
! [X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oabs__class_Oabs(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(X5) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_abs__one) ).
fof(1077,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(1090,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(1109,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__zero__not__eq__one) ).
fof(1129,axiom,
! [X17,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X17),X17)
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_minus__le__self__iff) ).
fof(1148,axiom,
! [X25,X7,X8] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X25,X8),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X25,X7)) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__add__left__mono) ).
fof(1159,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(1166,axiom,
! [X49,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X49)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X49,X25) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_real__le__linear) ).
fof(1173,axiom,
! [X8,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ouminus__class_Ouminus(X5,X8)) = c_RealVector_Onorm__class_Onorm(X5,X8) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_norm__minus__cancel) ).
fof(1225,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> c_Groups_Oabs__class_Oabs(X5,X4) = c_Groups_Ouminus__class_Ouminus(X5,X4) ) ),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',fact_abs__of__nonpos) ).
fof(1263,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/tmp/tmpSiDW5O/sel_SWW234+1.p_2',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(1275,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(assume_negation,[status(cth)],[781]) ).
fof(1295,plain,
! [X8] :
( ( X8 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X8 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ),
inference(fof_simplification,[status(thm)],[440,theory(equality)]) ).
fof(1301,plain,
! [X4] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4) = X4 ) ),
inference(fof_simplification,[status(thm)],[584,theory(equality)]) ).
fof(1304,plain,
! [X19,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X10,X19)
<=> c_Orderings_Oord__class_Oless__eq(X5,X19,X10) ) ),
inference(fof_simplification,[status(thm)],[646,theory(equality)]) ).
fof(1314,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(fof_simplification,[status(thm)],[1275,theory(equality)]) ).
fof(1318,plain,
! [X7,X8] :
( X8 != X7
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X8) ) ),
inference(fof_simplification,[status(thm)],[862,theory(equality)]) ).
fof(1324,plain,
! [X19,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X10,X19)
<=> c_Orderings_Oord__class_Oless(X5,X19,X10) ) ),
inference(fof_simplification,[status(thm)],[947,theory(equality)]) ).
fof(1473,plain,
! [X19,X10] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X19)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X19)
| X10 = X19 )
& ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X19)
& X10 != X19 )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X19) ) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(1474,plain,
! [X20,X21] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20)
| X21 = X20 )
& ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20)
& X21 != X20 )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20) ) ),
inference(variable_rename,[status(thm)],[1473]) ).
fof(1475,plain,
! [X20,X21] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20)
| X21 = X20 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20) )
& ( X21 != X20
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20) ) ),
inference(distribute,[status(thm)],[1474]) ).
cnf(1477,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[1475]) ).
fof(1484,plain,
! [X18] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X18) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X18) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(1485,plain,
! [X19] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X19) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X19) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[1484]) ).
cnf(1486,plain,
( c_RealDef_Oreal(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[1485]) ).
cnf(1505,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[53]) ).
fof(1510,plain,
! [X7,X8,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7)))
| X8 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[56]) ).
fof(1511,plain,
! [X14,X15,X16] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X14)))
| X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[1510]) ).
cnf(1512,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[1511]) ).
fof(1526,plain,
! [X12,X4,X5] :
( ~ class_Groups_Oordered__ab__group__add(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X4,X12)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),c_Groups_Ouminus__class_Ouminus(X5,X4)) ),
inference(fof_nnf,[status(thm)],[63]) ).
fof(1527,plain,
! [X13,X14,X15] :
( ~ class_Groups_Oordered__ab__group__add(X15)
| ~ c_Orderings_Oord__class_Oless__eq(X15,X14,X13)
| c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Ouminus__class_Ouminus(X15,X13),c_Groups_Ouminus__class_Ouminus(X15,X14)) ),
inference(variable_rename,[status(thm)],[1526]) ).
cnf(1528,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[1527]) ).
fof(1630,plain,
! [X8] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[91]) ).
fof(1631,plain,
! [X9] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[1630]) ).
cnf(1632,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[1631]) ).
fof(1680,plain,
! [X12,X4,X5] :
( ~ class_Groups_Ogroup__add(X5)
| c_Groups_Ominus__class_Ominus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X12),X12) = X4 ),
inference(fof_nnf,[status(thm)],[107]) ).
fof(1681,plain,
! [X13,X14,X15] :
( ~ class_Groups_Ogroup__add(X15)
| c_Groups_Ominus__class_Ominus(X15,c_Groups_Oplus__class_Oplus(X15,X14,X13),X13) = X14 ),
inference(variable_rename,[status(thm)],[1680]) ).
cnf(1682,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[1681]) ).
cnf(1683,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[108]) ).
fof(1696,plain,
! [X7] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X7)) = X7,
inference(variable_rename,[status(thm)],[114]) ).
cnf(1697,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[1696]) ).
fof(1701,plain,
! [X12,X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X12)),
inference(variable_rename,[status(thm)],[116]) ).
cnf(1702,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[1701]) ).
fof(1774,plain,
! [X9] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X9,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X9))),
inference(variable_rename,[status(thm)],[140]) ).
cnf(1775,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))),
inference(split_conjunct,[status(thm)],[1774]) ).
fof(1835,plain,
! [X8] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X8)),X8) ),
inference(fof_nnf,[status(thm)],[160]) ).
fof(1836,plain,
! [X9] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X9)),X9) ),
inference(variable_rename,[status(thm)],[1835]) ).
cnf(1837,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[1836]) ).
fof(1860,plain,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X7),
inference(variable_rename,[status(thm)],[167]) ).
cnf(1861,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[1860]) ).
fof(1925,plain,
! [X19,X10] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[186]) ).
fof(1926,plain,
! [X20,X21] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[1925]) ).
cnf(1927,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(split_conjunct,[status(thm)],[1926]) ).
fof(2003,plain,
! [X4,X5] :
( ~ class_Groups_Oordered__ab__group__add__abs(X5)
| ~ c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
| c_Groups_Oabs__class_Oabs(X5,X4) = c_Groups_Ouminus__class_Ouminus(X5,X4) ),
inference(fof_nnf,[status(thm)],[212]) ).
fof(2004,plain,
! [X6,X7] :
( ~ class_Groups_Oordered__ab__group__add__abs(X7)
| ~ c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
| c_Groups_Oabs__class_Oabs(X7,X6) = c_Groups_Ouminus__class_Ouminus(X7,X6) ),
inference(variable_rename,[status(thm)],[2003]) ).
cnf(2005,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[2004]) ).
fof(2468,plain,
! [X58,X59] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X59,X58) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X59,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X58)),
inference(variable_rename,[status(thm)],[353]) ).
cnf(2469,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[2468]) ).
fof(2519,plain,
! [X4,X5] :
( ~ class_Groups_Ogroup__add(X5)
| c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4)) = X4 ),
inference(fof_nnf,[status(thm)],[371]) ).
fof(2520,plain,
! [X6,X7] :
( ~ class_Groups_Ogroup__add(X7)
| c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ouminus__class_Ouminus(X7,X6)) = X6 ),
inference(variable_rename,[status(thm)],[2519]) ).
cnf(2521,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[2520]) ).
cnf(2527,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[373]) ).
fof(2550,plain,
! [X17,X5] :
( ~ class_Groups_Oordered__ab__group__add__abs(X5)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X17),c_Groups_Ozero__class_Ozero(X5))
| X17 = c_Groups_Ozero__class_Ozero(X5) )
& ( X17 != c_Groups_Ozero__class_Ozero(X5)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X17),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
inference(fof_nnf,[status(thm)],[382]) ).
fof(2551,plain,
! [X18,X19] :
( ~ class_Groups_Oordered__ab__group__add__abs(X19)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oabs__class_Oabs(X19,X18),c_Groups_Ozero__class_Ozero(X19))
| X18 = c_Groups_Ozero__class_Ozero(X19) )
& ( X18 != c_Groups_Ozero__class_Ozero(X19)
| c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oabs__class_Oabs(X19,X18),c_Groups_Ozero__class_Ozero(X19)) ) ) ),
inference(variable_rename,[status(thm)],[2550]) ).
fof(2552,plain,
! [X18,X19] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oabs__class_Oabs(X19,X18),c_Groups_Ozero__class_Ozero(X19))
| X18 = c_Groups_Ozero__class_Ozero(X19)
| ~ class_Groups_Oordered__ab__group__add__abs(X19) )
& ( X18 != c_Groups_Ozero__class_Ozero(X19)
| c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Oabs__class_Oabs(X19,X18),c_Groups_Ozero__class_Ozero(X19))
| ~ class_Groups_Oordered__ab__group__add__abs(X19) ) ),
inference(distribute,[status(thm)],[2551]) ).
cnf(2554,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[2552]) ).
fof(2732,plain,
! [X8] :
( ( X8 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X8 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X8) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ),
inference(fof_nnf,[status(thm)],[1295]) ).
fof(2733,plain,
! [X9] :
( ( X9 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X9 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ),
inference(variable_rename,[status(thm)],[2732]) ).
fof(2734,plain,
! [X9] :
( ( X9 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X9 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
| c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| X9 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[2733]) ).
cnf(2737,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[2734]) ).
fof(2765,plain,
! [X7] : c_Nat_OSuc(X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[453]) ).
cnf(2766,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[2765]) ).
cnf(2784,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[461]) ).
fof(2788,plain,
! [X24,X23,X22] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X23)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X24)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X24) ),
inference(fof_nnf,[status(thm)],[463]) ).
fof(2789,plain,
! [X25,X26,X27] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X26)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X25)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X25) ),
inference(variable_rename,[status(thm)],[2788]) ).
cnf(2790,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
inference(split_conjunct,[status(thm)],[2789]) ).
fof(2858,plain,
! [X19,X10] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X19)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X10,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X10,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X19) ) ),
inference(fof_nnf,[status(thm)],[486]) ).
fof(2859,plain,
! [X20,X21] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X21,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X21,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20) ) ),
inference(variable_rename,[status(thm)],[2858]) ).
cnf(2861,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[2859]) ).
fof(3001,plain,
! [X13,X4,X5] :
( ~ class_Rings_Ocomm__semiring__1(X5)
| c_Groups_Oplus__class_Oplus(X5,X4,X13) = c_Groups_Oplus__class_Oplus(X5,X13,X4) ),
inference(fof_nnf,[status(thm)],[533]) ).
fof(3002,plain,
! [X14,X15,X16] :
( ~ class_Rings_Ocomm__semiring__1(X16)
| c_Groups_Oplus__class_Oplus(X16,X15,X14) = c_Groups_Oplus__class_Oplus(X16,X14,X15) ),
inference(variable_rename,[status(thm)],[3001]) ).
cnf(3003,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[3002]) ).
fof(3016,plain,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9)),
inference(variable_rename,[status(thm)],[538]) ).
cnf(3017,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(split_conjunct,[status(thm)],[3016]) ).
fof(3145,plain,
! [X4] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4) = X4 ) ),
inference(fof_nnf,[status(thm)],[1301]) ).
fof(3146,plain,
! [X5] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5) = X5 ) ),
inference(variable_rename,[status(thm)],[3145]) ).
cnf(3148,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[3146]) ).
fof(3149,plain,
! [X8] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X8,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X8),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(fof_nnf,[status(thm)],[585]) ).
fof(3150,plain,
! [X9] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[3149]) ).
cnf(3151,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[3150]) ).
fof(3243,plain,
! [X37] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X37) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X37),
inference(variable_rename,[status(thm)],[619]) ).
cnf(3244,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[3243]) ).
fof(3261,plain,
! [X19,X10] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X19,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X19,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[625]) ).
fof(3262,plain,
! [X20,X21] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[3261]) ).
cnf(3264,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[3262]) ).
fof(3285,plain,
! [X19,X10] :
( ( ~ 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,X10,X19))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10),X19) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10),X19)
| 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,X10,X19)) ) ),
inference(fof_nnf,[status(thm)],[633]) ).
fof(3286,plain,
! [X20,X21] :
( ( ~ 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,X21,X20))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21),X20) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21),X20)
| 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,X21,X20)) ) ),
inference(variable_rename,[status(thm)],[3285]) ).
cnf(3288,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
| ~ 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,X1,X2)) ),
inference(split_conjunct,[status(thm)],[3286]) ).
cnf(3296,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[637]) ).
fof(3321,plain,
! [X19,X10,X5] :
( ~ class_Orderings_Olinorder(X5)
| ( ( c_Orderings_Oord__class_Oless(X5,X10,X19)
| c_Orderings_Oord__class_Oless__eq(X5,X19,X10) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5,X19,X10)
| ~ c_Orderings_Oord__class_Oless(X5,X10,X19) ) ) ),
inference(fof_nnf,[status(thm)],[1304]) ).
fof(3322,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| ( ( c_Orderings_Oord__class_Oless(X22,X21,X20)
| c_Orderings_Oord__class_Oless__eq(X22,X20,X21) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X22,X20,X21)
| ~ c_Orderings_Oord__class_Oless(X22,X21,X20) ) ) ),
inference(variable_rename,[status(thm)],[3321]) ).
fof(3323,plain,
! [X20,X21,X22] :
( ( c_Orderings_Oord__class_Oless(X22,X21,X20)
| c_Orderings_Oord__class_Oless__eq(X22,X20,X21)
| ~ class_Orderings_Olinorder(X22) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X22,X20,X21)
| ~ c_Orderings_Oord__class_Oless(X22,X21,X20)
| ~ class_Orderings_Olinorder(X22) ) ),
inference(distribute,[status(thm)],[3322]) ).
cnf(3325,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[3323]) ).
fof(3365,plain,
! [X12,X13] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X12) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X13),
inference(variable_rename,[status(thm)],[661]) ).
cnf(3366,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[3365]) ).
fof(3700,plain,
! [X19,X10] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X19))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10),X19) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10),X19)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X19)) ) ),
inference(fof_nnf,[status(thm)],[774]) ).
fof(3701,plain,
! [X20,X21] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21),X20) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21),X20)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20)) ) ),
inference(variable_rename,[status(thm)],[3700]) ).
cnf(3702,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,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
inference(split_conjunct,[status(thm)],[3701]) ).
cnf(3722,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[1314]) ).
fof(3801,plain,
! [X10] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X10))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X10) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X10)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X10)) ) ),
inference(fof_nnf,[status(thm)],[806]) ).
fof(3802,plain,
! [X11] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X11))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X11)) ) ),
inference(variable_rename,[status(thm)],[3801]) ).
cnf(3804,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1)) ),
inference(split_conjunct,[status(thm)],[3802]) ).
fof(3890,plain,
! [X18] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X18 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(fof_nnf,[status(thm)],[835]) ).
fof(3891,plain,
! [X19] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[3890]) ).
cnf(3893,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[3891]) ).
fof(3978,plain,
! [X7,X8] :
( X8 = X7
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X7)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X8) ),
inference(fof_nnf,[status(thm)],[1318]) ).
fof(3979,plain,
! [X9,X10] :
( X10 = X9
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X9)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X10) ),
inference(variable_rename,[status(thm)],[3978]) ).
cnf(3980,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[3979]) ).
fof(3986,plain,
! [X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7) = X7,
inference(variable_rename,[status(thm)],[864]) ).
cnf(3987,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(split_conjunct,[status(thm)],[3986]) ).
fof(4016,plain,
! [X10,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ( ( c_RealVector_Onorm__class_Onorm(X5,X10) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X10 = c_Groups_Ozero__class_Ozero(X5) )
& ( X10 != c_Groups_Ozero__class_Ozero(X5)
| c_RealVector_Onorm__class_Onorm(X5,X10) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(fof_nnf,[status(thm)],[872]) ).
fof(4017,plain,
! [X11,X12] :
( ~ class_RealVector_Oreal__normed__vector(X12)
| ( ( c_RealVector_Onorm__class_Onorm(X12,X11) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X11 = c_Groups_Ozero__class_Ozero(X12) )
& ( X11 != c_Groups_Ozero__class_Ozero(X12)
| c_RealVector_Onorm__class_Onorm(X12,X11) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(variable_rename,[status(thm)],[4016]) ).
fof(4018,plain,
! [X11,X12] :
( ( c_RealVector_Onorm__class_Onorm(X12,X11) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X11 = c_Groups_Ozero__class_Ozero(X12)
| ~ class_RealVector_Oreal__normed__vector(X12) )
& ( X11 != c_Groups_Ozero__class_Ozero(X12)
| c_RealVector_Onorm__class_Onorm(X12,X11) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X12) ) ),
inference(distribute,[status(thm)],[4017]) ).
cnf(4019,plain,
( c_RealVector_Onorm__class_Onorm(X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[4018]) ).
fof(4023,plain,
! [X4,X5] :
( ~ class_Groups_Oordered__ab__group__add__abs(X5)
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
| c_Groups_Oabs__class_Oabs(X5,X4) = X4 ),
inference(fof_nnf,[status(thm)],[874]) ).
fof(4024,plain,
! [X6,X7] :
( ~ class_Groups_Oordered__ab__group__add__abs(X7)
| ~ c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
| c_Groups_Oabs__class_Oabs(X7,X6) = X6 ),
inference(variable_rename,[status(thm)],[4023]) ).
cnf(4025,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[4024]) ).
fof(4083,plain,
! [X10] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[893]) ).
fof(4084,plain,
! [X11] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X11),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X11),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[4083]) ).
cnf(4085,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[4084]) ).
fof(4250,plain,
! [X19,X10,X5] :
( ~ class_Orderings_Olinorder(X5)
| ( ( c_Orderings_Oord__class_Oless__eq(X5,X10,X19)
| c_Orderings_Oord__class_Oless(X5,X19,X10) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X19,X10)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X10,X19) ) ) ),
inference(fof_nnf,[status(thm)],[1324]) ).
fof(4251,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| ( ( c_Orderings_Oord__class_Oless__eq(X22,X21,X20)
| c_Orderings_Oord__class_Oless(X22,X20,X21) )
& ( ~ c_Orderings_Oord__class_Oless(X22,X20,X21)
| ~ c_Orderings_Oord__class_Oless__eq(X22,X21,X20) ) ) ),
inference(variable_rename,[status(thm)],[4250]) ).
fof(4252,plain,
! [X20,X21,X22] :
( ( c_Orderings_Oord__class_Oless__eq(X22,X21,X20)
| c_Orderings_Oord__class_Oless(X22,X20,X21)
| ~ class_Orderings_Olinorder(X22) )
& ( ~ c_Orderings_Oord__class_Oless(X22,X20,X21)
| ~ c_Orderings_Oord__class_Oless__eq(X22,X21,X20)
| ~ class_Orderings_Olinorder(X22) ) ),
inference(distribute,[status(thm)],[4251]) ).
cnf(4253,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[4252]) ).
cnf(4379,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[994]) ).
fof(4416,plain,
! [X4,X5] :
( ~ class_Rings_Ocomm__semiring__1(X5)
| c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
inference(fof_nnf,[status(thm)],[1008]) ).
fof(4417,plain,
! [X6,X7] :
( ~ class_Rings_Ocomm__semiring__1(X7)
| c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = X6 ),
inference(variable_rename,[status(thm)],[4416]) ).
cnf(4418,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[4417]) ).
cnf(4508,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1039]) ).
fof(4606,plain,
! [X5] :
( ~ class_Rings_Olinordered__idom(X5)
| c_Groups_Oabs__class_Oabs(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(X5) ),
inference(fof_nnf,[status(thm)],[1072]) ).
fof(4607,plain,
! [X6] :
( ~ class_Rings_Olinordered__idom(X6)
| c_Groups_Oabs__class_Oabs(X6,c_Groups_Oone__class_Oone(X6)) = c_Groups_Oone__class_Oone(X6) ),
inference(variable_rename,[status(thm)],[4606]) ).
cnf(4608,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[4607]) ).
fof(4620,plain,
! [X4,X5] :
( ~ class_Rings_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
inference(fof_nnf,[status(thm)],[1077]) ).
fof(4621,plain,
! [X6,X7] :
( ~ class_Rings_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),c_Groups_Oone__class_Oone(X7)) = X6 ),
inference(variable_rename,[status(thm)],[4620]) ).
cnf(4622,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[4621]) ).
cnf(4659,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1090]) ).
cnf(4729,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1109]) ).
fof(4787,plain,
! [X17,X5] :
( ~ class_Groups_Olinordered__ab__group__add(X5)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X17),X17)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X17),X17) ) ) ),
inference(fof_nnf,[status(thm)],[1129]) ).
fof(4788,plain,
! [X18,X19] :
( ~ class_Groups_Olinordered__ab__group__add(X19)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X18),X18)
| c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
| c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X18),X18) ) ) ),
inference(variable_rename,[status(thm)],[4787]) ).
fof(4789,plain,
! [X18,X19] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X18),X18)
| c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
| ~ class_Groups_Olinordered__ab__group__add(X19) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
| c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ouminus__class_Ouminus(X19,X18),X18)
| ~ class_Groups_Olinordered__ab__group__add(X19) ) ),
inference(distribute,[status(thm)],[4788]) ).
cnf(4791,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[4789]) ).
fof(4855,plain,
! [X25,X7,X8] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X7)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X25,X8),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X25,X7)) ),
inference(fof_nnf,[status(thm)],[1148]) ).
fof(4856,plain,
! [X26,X27,X28] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X28,X27)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X26,X28),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X26,X27)) ),
inference(variable_rename,[status(thm)],[4855]) ).
cnf(4857,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[4856]) ).
cnf(4890,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1159]) ).
fof(4904,plain,
! [X50,X51] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X51,X50)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X50,X51) ),
inference(variable_rename,[status(thm)],[1166]) ).
cnf(4905,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[4904]) ).
fof(4923,plain,
! [X8,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ouminus__class_Ouminus(X5,X8)) = c_RealVector_Onorm__class_Onorm(X5,X8) ),
inference(fof_nnf,[status(thm)],[1173]) ).
fof(4924,plain,
! [X9,X10] :
( ~ class_RealVector_Oreal__normed__vector(X10)
| c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)) = c_RealVector_Onorm__class_Onorm(X10,X9) ),
inference(variable_rename,[status(thm)],[4923]) ).
cnf(4925,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[4924]) ).
fof(5086,plain,
! [X4,X5] :
( ~ class_Groups_Oordered__ab__group__add__abs(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Ozero__class_Ozero(X5))
| c_Groups_Oabs__class_Oabs(X5,X4) = c_Groups_Ouminus__class_Ouminus(X5,X4) ),
inference(fof_nnf,[status(thm)],[1225]) ).
fof(5087,plain,
! [X6,X7] :
( ~ class_Groups_Oordered__ab__group__add__abs(X7)
| ~ c_Orderings_Oord__class_Oless__eq(X7,X6,c_Groups_Ozero__class_Ozero(X7))
| c_Groups_Oabs__class_Oabs(X7,X6) = c_Groups_Ouminus__class_Ouminus(X7,X6) ),
inference(variable_rename,[status(thm)],[5086]) ).
cnf(5088,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[5087]) ).
cnf(5198,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1263]) ).
cnf(5279,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[3893,2766,theory(equality)]),
[unfolding] ).
cnf(5448,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 ),
inference(spm,[status(thm)],[1632,2737,theory(equality)]) ).
cnf(5449,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 ),
inference(sr,[status(thm)],[5448,4729,theory(equality)]) ).
cnf(5492,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[4085,1697,theory(equality)]) ).
cnf(5506,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2) ),
inference(spm,[status(thm)],[2790,1477,theory(equality)]) ).
cnf(5507,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
inference(spm,[status(thm)],[2790,4905,theory(equality)]) ).
cnf(5975,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[1683,3148,theory(equality)]) ).
cnf(6006,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ 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,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))) ),
inference(spm,[status(thm)],[1927,3288,theory(equality)]) ).
cnf(6023,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 ),
inference(spm,[status(thm)],[4019,2527,theory(equality)]) ).
cnf(6024,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 ),
inference(rw,[status(thm)],[6023,3244,theory(equality)]) ).
cnf(6471,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_RComplete_Onatfloor(X1) ),
inference(spm,[status(thm)],[1775,1486,theory(equality)]) ).
cnf(6521,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = X1,
inference(spm,[status(thm)],[2521,2784,theory(equality)]) ).
cnf(6544,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X1,
inference(spm,[status(thm)],[4418,4508,theory(equality)]) ).
cnf(6596,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[3244,4925,theory(equality)]) ).
cnf(6610,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[6596,3244,theory(equality)]) ).
cnf(6611,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| $false ),
inference(rw,[status(thm)],[6610,2527,theory(equality)]) ).
cnf(6612,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
inference(cn,[status(thm)],[6611,theory(equality)]) ).
cnf(6809,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2),X3) ),
inference(spm,[status(thm)],[4857,2469,theory(equality)]) ).
cnf(6925,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,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[3702,3264,theory(equality)]) ).
cnf(6927,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[6925,2469,theory(equality)]) ).
cnf(6928,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[6927,2469,theory(equality)]) ).
cnf(7489,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[5279,3987,theory(equality)]) ).
cnf(7499,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = X1,
inference(spm,[status(thm)],[4622,4508,theory(equality)]) ).
cnf(7745,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[3325,4890,theory(equality)]) ).
cnf(8448,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))
| ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[4791,3017,theory(equality)]) ).
cnf(8469,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))
| $false ),
inference(rw,[status(thm)],[8448,1505,theory(equality)]) ).
cnf(8470,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(cn,[status(thm)],[8469,theory(equality)]) ).
cnf(8559,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[1512,4608,theory(equality)]) ).
cnf(8570,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| $false ),
inference(rw,[status(thm)],[8559,4659,theory(equality)]) ).
cnf(8571,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[8570,theory(equality)]) ).
cnf(9262,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),
inference(spm,[status(thm)],[3003,4508,theory(equality)]) ).
cnf(9272,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X2) = X1,
inference(spm,[status(thm)],[1682,2784,theory(equality)]) ).
cnf(10114,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1)) = c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[3151,3366,theory(equality)]) ).
cnf(10117,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(spm,[status(thm)],[3804,10114,theory(equality)]) ).
cnf(10125,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| $false
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[10117,1702,theory(equality)]) ).
cnf(10126,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(cn,[status(thm)],[10125,theory(equality)]) ).
cnf(10900,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(spm,[status(thm)],[7489,3980,theory(equality)]) ).
cnf(11009,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ 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,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(spm,[status(thm)],[5088,3288,theory(equality)]) ).
cnf(11043,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| $false
| ~ 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,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(rw,[status(thm)],[11009,3296,theory(equality)]) ).
cnf(11044,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ 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,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(cn,[status(thm)],[11043,theory(equality)]) ).
cnf(12804,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1)
| ~ class_Groups_Oordered__ab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(spm,[status(thm)],[4791,1528,theory(equality)]) ).
cnf(103785,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[5975,2469,theory(equality)]) ).
cnf(106783,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ 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,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))) ),
inference(rw,[status(thm)],[6006,2469,theory(equality)]) ).
cnf(106784,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)) ),
inference(rw,[status(thm)],[106783,2469,theory(equality)]) ).
cnf(107463,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____ ),
inference(spm,[status(thm)],[1683,6024,theory(equality)]) ).
cnf(107603,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____ ),
inference(rw,[status(thm)],[107463,6544,theory(equality)]) ).
cnf(107604,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____,
inference(sr,[status(thm)],[107603,3722,theory(equality)]) ).
cnf(196534,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[3722,7745,theory(equality)]) ).
cnf(197118,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(spm,[status(thm)],[5506,196534,theory(equality)]) ).
cnf(197400,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(spm,[status(thm)],[197118,1837,theory(equality)]) ).
cnf(197483,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| $false ),
inference(rw,[status(thm)],[197400,8470,theory(equality)]) ).
cnf(197484,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[197483,theory(equality)]) ).
cnf(198275,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(spm,[status(thm)],[5492,197484,theory(equality)]) ).
cnf(198318,negated_conjecture,
( ~ class_Orderings_Olinorder(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))) ),
inference(spm,[status(thm)],[4253,198275,theory(equality)]) ).
cnf(198346,negated_conjecture,
( $false
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))) ),
inference(rw,[status(thm)],[198318,4379,theory(equality)]) ).
cnf(198347,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
inference(cn,[status(thm)],[198346,theory(equality)]) ).
cnf(228871,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[8571,7499,theory(equality)]) ).
cnf(351321,negated_conjecture,
( c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(spm,[status(thm)],[198347,10900,theory(equality)]) ).
cnf(351433,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(spm,[status(thm)],[3804,351321,theory(equality)]) ).
cnf(351505,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| $false ),
inference(rw,[status(thm)],[351433,1861,theory(equality)]) ).
cnf(351506,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(cn,[status(thm)],[351505,theory(equality)]) ).
cnf(351507,negated_conjecture,
c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(sr,[status(thm)],[351506,3722,theory(equality)]) ).
cnf(351633,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[6471,351507,theory(equality)]) ).
cnf(351928,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
inference(spm,[status(thm)],[6928,351633,theory(equality)]) ).
cnf(352491,negated_conjecture,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[4025,351928,theory(equality)]) ).
cnf(352496,negated_conjecture,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(spm,[status(thm)],[5449,351928,theory(equality)]) ).
cnf(352509,negated_conjecture,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| $false ),
inference(rw,[status(thm)],[352491,3296,theory(equality)]) ).
cnf(352510,negated_conjecture,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(cn,[status(thm)],[352509,theory(equality)]) ).
cnf(352892,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[228871,352510,theory(equality)]) ).
cnf(353075,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(sr,[status(thm)],[352892,352496,theory(equality)]) ).
cnf(354896,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),X1) ),
inference(spm,[status(thm)],[353075,6809,theory(equality)]) ).
cnf(357419,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ 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,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(rw,[status(thm)],[11044,6612,theory(equality)]) ).
cnf(357420,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1
| ~ 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,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(rw,[status(thm)],[357419,6521,theory(equality)]) ).
cnf(357421,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[357420,6544,theory(equality)]) ).
cnf(375534,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(spm,[status(thm)],[354896,1528,theory(equality)]) ).
cnf(375754,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(rw,[status(thm)],[375534,2469,theory(equality)]) ).
cnf(375755,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| $false
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(rw,[status(thm)],[375754,5198,theory(equality)]) ).
cnf(375756,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(cn,[status(thm)],[375755,theory(equality)]) ).
cnf(376943,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(spm,[status(thm)],[375756,2861,theory(equality)]) ).
cnf(376944,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(spm,[status(thm)],[375756,106784,theory(equality)]) ).
cnf(376954,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))),
inference(spm,[status(thm)],[376943,1683,theory(equality)]) ).
cnf(386942,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____) ),
inference(spm,[status(thm)],[376954,357421,theory(equality)]) ).
cnf(386956,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_r____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____) ),
inference(rw,[status(thm)],[386942,9262,theory(equality)]) ).
cnf(394749,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____),
inference(csr,[status(thm)],[386956,10126]) ).
cnf(394751,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[394749,4905,theory(equality)]) ).
cnf(394754,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[394749,7745,theory(equality)]) ).
cnf(394758,negated_conjecture,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____)
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[2005,394754,theory(equality)]) ).
cnf(394782,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| $false ),
inference(rw,[status(thm)],[103785,394754,theory(equality)]) ).
cnf(394783,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(cn,[status(thm)],[394782,theory(equality)]) ).
cnf(394790,negated_conjecture,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____)
| $false ),
inference(rw,[status(thm)],[394758,3296,theory(equality)]) ).
cnf(394791,negated_conjecture,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____),
inference(cn,[status(thm)],[394790,theory(equality)]) ).
cnf(395333,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,X1) ),
inference(spm,[status(thm)],[5507,394751,theory(equality)]) ).
cnf(395678,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r____
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[2554,394791,theory(equality)]) ).
cnf(395960,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r____
| $false
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[395678,3296,theory(equality)]) ).
cnf(395961,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[395960,theory(equality)]) ).
cnf(395962,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(sr,[status(thm)],[395961,107604,theory(equality)]) ).
cnf(404032,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(spm,[status(thm)],[376944,9272,theory(equality)]) ).
cnf(404509,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(spm,[status(thm)],[404032,9262,theory(equality)]) ).
cnf(404556,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(spm,[status(thm)],[404509,2469,theory(equality)]) ).
cnf(408379,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____)),
inference(spm,[status(thm)],[395962,395333,theory(equality)]) ).
cnf(450056,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____))
| ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)
| ~ class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[12804,408379,theory(equality)]) ).
cnf(450239,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____))
| $false
| ~ class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[450056,1505,theory(equality)]) ).
cnf(450240,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____))
| $false
| $false ),
inference(rw,[status(thm)],[450239,5198,theory(equality)]) ).
cnf(450241,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____)),
inference(cn,[status(thm)],[450240,theory(equality)]) ).
cnf(480391,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_r____)),
inference(spm,[status(thm)],[404556,394783,theory(equality)]) ).
cnf(480434,negated_conjecture,
$false,
inference(rw,[status(thm)],[480391,450241,theory(equality)]) ).
cnf(480435,negated_conjecture,
$false,
inference(cn,[status(thm)],[480434,theory(equality)]) ).
cnf(480436,negated_conjecture,
$false,
480435,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW234+1.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpSiDW5O/sel_SWW234+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpSiDW5O/sel_SWW234+1.p_2 with time limit 81
% -prover status Theorem
% Problem SWW234+1.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW234+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW234+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------