TSTP Solution File: SWW233+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWW233+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 15:13:52 EST 2011
% Result : Theorem 8.05s
% Output : CNFRefutation 8.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 26
% Syntax : Number of formulae : 141 ( 42 unt; 0 def)
% Number of atoms : 337 ( 90 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 330 ( 134 ~; 161 |; 14 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 166 ( 1 sgn 107 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(15,axiom,
! [X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> c_Groups_Oabs__class_Oabs(X5,X4) = X4 ) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_abs__of__nonneg) ).
fof(55,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_natceiling__zero) ).
fof(110,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/tmpkqa1J9/sel_SWW233+1.p_1',fact_h) ).
fof(149,axiom,
! [X25,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X24)
=> X24 = X25 ) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_real__le__antisym) ).
fof(169,axiom,
! [X17,X16,X18,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X18,X16),c_Groups_Oplus__class_Oplus(X5,X17,X16))
<=> c_Orderings_Oord__class_Oless__eq(X5,X18,X17) ) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_add__le__cancel__right) ).
fof(210,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_less__eq__nat_Osimps_I1_J) ).
fof(350,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Oone__class_Oone(X5) != c_Groups_Ozero__class_Ozero(X5) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_one__neq__zero) ).
fof(351,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(361,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(436,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(455,axiom,
! [X19,X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,X19)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X19) ) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_real__le__trans) ).
fof(469,axiom,
! [X14,X4,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X4),X14)
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X14) ) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_abs__le__D1) ).
fof(564,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_RealVector_Onorm__class_Onorm(X5,X12) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X12 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_norm__eq__zero) ).
fof(584,axiom,
! [X12,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X12 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_norm__le__zero__iff) ).
fof(757,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',conj_0) ).
fof(866,axiom,
! [X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X12),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_natceiling__le__eq__one) ).
fof(892,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(965,axiom,
! [X17,X18,X16,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X16,X18),c_Groups_Oplus__class_Oplus(X5,X16,X17))
<=> c_Orderings_Oord__class_Oless__eq(X5,X18,X17) ) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_add__le__cancel__left) ).
fof(989,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/tmpkqa1J9/sel_SWW233+1.p_1',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(992,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(1017,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(1060,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_norm__one) ).
fof(1086,axiom,
! [X36] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X36) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X36),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_real__norm__def) ).
fof(1147,axiom,
! [X25,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X25)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X24) ),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',fact_real__le__linear) ).
fof(1192,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(1195,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/tmp/tmpkqa1J9/sel_SWW233+1.p_1',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(1262,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(assume_negation,[status(cth)],[757]) ).
fof(1300,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(fof_simplification,[status(thm)],[1262,theory(equality)]) ).
fof(1371,plain,
! [X4,X5] :
( ~ class_Groups_Oordered__ab__group__add__abs(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
| c_Groups_Oabs__class_Oabs(X5,X4) = X4 ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(1372,plain,
! [X6,X7] :
( ~ class_Groups_Oordered__ab__group__add__abs(X7)
| ~ c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
| c_Groups_Oabs__class_Oabs(X7,X6) = X6 ),
inference(variable_rename,[status(thm)],[1371]) ).
cnf(1373,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[1372]) ).
cnf(1484,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(1664,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)],[110]) ).
fof(1773,plain,
! [X25,X24] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X25)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X24)
| X24 = X25 ),
inference(fof_nnf,[status(thm)],[149]) ).
fof(1774,plain,
! [X26,X27] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X26)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X27)
| X27 = X26 ),
inference(variable_rename,[status(thm)],[1773]) ).
cnf(1775,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[1774]) ).
fof(1853,plain,
! [X17,X16,X18,X5] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X18,X16),c_Groups_Oplus__class_Oplus(X5,X17,X16))
| c_Orderings_Oord__class_Oless__eq(X5,X18,X17) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5,X18,X17)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X18,X16),c_Groups_Oplus__class_Oplus(X5,X17,X16)) ) ) ),
inference(fof_nnf,[status(thm)],[169]) ).
fof(1854,plain,
! [X19,X20,X21,X22] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X22,c_Groups_Oplus__class_Oplus(X22,X21,X20),c_Groups_Oplus__class_Oplus(X22,X19,X20))
| c_Orderings_Oord__class_Oless__eq(X22,X21,X19) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X22,X21,X19)
| c_Orderings_Oord__class_Oless__eq(X22,c_Groups_Oplus__class_Oplus(X22,X21,X20),c_Groups_Oplus__class_Oplus(X22,X19,X20)) ) ) ),
inference(variable_rename,[status(thm)],[1853]) ).
fof(1855,plain,
! [X19,X20,X21,X22] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X22,c_Groups_Oplus__class_Oplus(X22,X21,X20),c_Groups_Oplus__class_Oplus(X22,X19,X20))
| c_Orderings_Oord__class_Oless__eq(X22,X21,X19)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X22,X21,X19)
| c_Orderings_Oord__class_Oless__eq(X22,c_Groups_Oplus__class_Oplus(X22,X21,X20),c_Groups_Oplus__class_Oplus(X22,X19,X20))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22) ) ),
inference(distribute,[status(thm)],[1854]) ).
cnf(1857,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[1855]) ).
fof(1972,plain,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7),
inference(variable_rename,[status(thm)],[210]) ).
cnf(1973,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[1972]) ).
fof(2412,plain,
! [X5] :
( ~ class_Rings_Ozero__neq__one(X5)
| c_Groups_Oone__class_Oone(X5) != c_Groups_Ozero__class_Ozero(X5) ),
inference(fof_nnf,[status(thm)],[350]) ).
fof(2413,plain,
! [X6] :
( ~ class_Rings_Ozero__neq__one(X6)
| c_Groups_Oone__class_Oone(X6) != c_Groups_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[2412]) ).
cnf(2414,plain,
( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[2413]) ).
cnf(2415,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[351]) ).
cnf(2437,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[361]) ).
cnf(2654,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[436]) ).
fof(2700,plain,
! [X19,X20,X21] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,X19)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X19) ),
inference(fof_nnf,[status(thm)],[455]) ).
fof(2701,plain,
! [X22,X23,X24] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X23)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X22) ),
inference(variable_rename,[status(thm)],[2700]) ).
cnf(2702,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)],[2701]) ).
fof(2732,plain,
! [X14,X4,X5] :
( ~ class_Groups_Oordered__ab__group__add__abs(X5)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oabs__class_Oabs(X5,X4),X14)
| c_Orderings_Oord__class_Oless__eq(X5,X4,X14) ),
inference(fof_nnf,[status(thm)],[469]) ).
fof(2733,plain,
! [X15,X16,X17] :
( ~ class_Groups_Oordered__ab__group__add__abs(X17)
| ~ c_Orderings_Oord__class_Oless__eq(X17,c_Groups_Oabs__class_Oabs(X17,X16),X15)
| c_Orderings_Oord__class_Oless__eq(X17,X16,X15) ),
inference(variable_rename,[status(thm)],[2732]) ).
cnf(2734,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[2733]) ).
fof(3009,plain,
! [X12,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ( ( c_RealVector_Onorm__class_Onorm(X5,X12) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X12 = c_Groups_Ozero__class_Ozero(X5) )
& ( X12 != c_Groups_Ozero__class_Ozero(X5)
| c_RealVector_Onorm__class_Onorm(X5,X12) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(fof_nnf,[status(thm)],[564]) ).
fof(3010,plain,
! [X13,X14] :
( ~ class_RealVector_Oreal__normed__vector(X14)
| ( ( c_RealVector_Onorm__class_Onorm(X14,X13) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X13 = c_Groups_Ozero__class_Ozero(X14) )
& ( X13 != c_Groups_Ozero__class_Ozero(X14)
| c_RealVector_Onorm__class_Onorm(X14,X13) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(variable_rename,[status(thm)],[3009]) ).
fof(3011,plain,
! [X13,X14] :
( ( c_RealVector_Onorm__class_Onorm(X14,X13) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X13 = c_Groups_Ozero__class_Ozero(X14)
| ~ class_RealVector_Oreal__normed__vector(X14) )
& ( X13 != c_Groups_Ozero__class_Ozero(X14)
| c_RealVector_Onorm__class_Onorm(X14,X13) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X14) ) ),
inference(distribute,[status(thm)],[3010]) ).
cnf(3012,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)],[3011]) ).
fof(3063,plain,
! [X12,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X12 = c_Groups_Ozero__class_Ozero(X5) )
& ( X12 != c_Groups_Ozero__class_Ozero(X5)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
inference(fof_nnf,[status(thm)],[584]) ).
fof(3064,plain,
! [X13,X14] :
( ~ class_RealVector_Oreal__normed__vector(X14)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X13 = c_Groups_Ozero__class_Ozero(X14) )
& ( X13 != c_Groups_Ozero__class_Ozero(X14)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
inference(variable_rename,[status(thm)],[3063]) ).
fof(3065,plain,
! [X13,X14] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X13 = c_Groups_Ozero__class_Ozero(X14)
| ~ class_RealVector_Oreal__normed__vector(X14) )
& ( X13 != c_Groups_Ozero__class_Ozero(X14)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X14) ) ),
inference(distribute,[status(thm)],[3064]) ).
cnf(3067,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[3065]) ).
cnf(3595,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[1300]) ).
fof(3943,plain,
! [X12] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X12),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[866]) ).
fof(3944,plain,
! [X13] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X13),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[3943]) ).
cnf(3946,plain,
( 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_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[3944]) ).
fof(4029,plain,
! [X4,X5] :
( ~ class_Rings_Ocomm__semiring__1(X5)
| c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
inference(fof_nnf,[status(thm)],[892]) ).
fof(4030,plain,
! [X6,X7] :
( ~ class_Rings_Ocomm__semiring__1(X7)
| c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X6) = X6 ),
inference(variable_rename,[status(thm)],[4029]) ).
cnf(4031,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[4030]) ).
fof(4247,plain,
! [X17,X18,X16,X5] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X16,X18),c_Groups_Oplus__class_Oplus(X5,X16,X17))
| c_Orderings_Oord__class_Oless__eq(X5,X18,X17) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5,X18,X17)
| c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X16,X18),c_Groups_Oplus__class_Oplus(X5,X16,X17)) ) ) ),
inference(fof_nnf,[status(thm)],[965]) ).
fof(4248,plain,
! [X19,X20,X21,X22] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X22,c_Groups_Oplus__class_Oplus(X22,X21,X20),c_Groups_Oplus__class_Oplus(X22,X21,X19))
| c_Orderings_Oord__class_Oless__eq(X22,X20,X19) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X22,X20,X19)
| c_Orderings_Oord__class_Oless__eq(X22,c_Groups_Oplus__class_Oplus(X22,X21,X20),c_Groups_Oplus__class_Oplus(X22,X21,X19)) ) ) ),
inference(variable_rename,[status(thm)],[4247]) ).
fof(4249,plain,
! [X19,X20,X21,X22] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X22,c_Groups_Oplus__class_Oplus(X22,X21,X20),c_Groups_Oplus__class_Oplus(X22,X21,X19))
| c_Orderings_Oord__class_Oless__eq(X22,X20,X19)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X22,X20,X19)
| c_Orderings_Oord__class_Oless__eq(X22,c_Groups_Oplus__class_Oplus(X22,X21,X20),c_Groups_Oplus__class_Oplus(X22,X21,X19))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22) ) ),
inference(distribute,[status(thm)],[4248]) ).
cnf(4251,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[4249]) ).
fof(4316,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)],[989]) ).
fof(4317,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)],[4316]) ).
cnf(4318,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)],[4317]) ).
cnf(4324,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[992]) ).
cnf(4405,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1017]) ).
fof(4541,plain,
! [X5] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5)
| c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[1060]) ).
fof(4542,plain,
! [X6] :
( ~ class_RealVector_Oreal__normed__algebra__1(X6)
| c_RealVector_Onorm__class_Onorm(X6,c_Groups_Oone__class_Oone(X6)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[4541]) ).
cnf(4543,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[4542]) ).
fof(4628,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)],[1086]) ).
cnf(4629,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[4628]) ).
fof(4819,plain,
! [X26,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X26)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X27) ),
inference(variable_rename,[status(thm)],[1147]) ).
cnf(4820,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)],[4819]) ).
cnf(4990,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1192]) ).
cnf(4995,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1195]) ).
cnf(5482,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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(rw,[status(thm)],[1664,4629,theory(equality)]) ).
cnf(5483,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[2414,2415,theory(equality)]) ).
cnf(5564,plain,
( 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,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____))) ),
inference(spm,[status(thm)],[2702,5482,theory(equality)]) ).
cnf(5567,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)],[2702,4820,theory(equality)]) ).
cnf(5605,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[4543,4324,theory(equality)]) ).
cnf(5621,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(spm,[status(thm)],[3946,1484,theory(equality)]) ).
cnf(5625,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| $false ),
inference(rw,[status(thm)],[5621,1973,theory(equality)]) ).
cnf(5626,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[5625,theory(equality)]) ).
cnf(5968,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)],[3012,2437,theory(equality)]) ).
cnf(6507,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X1,
inference(spm,[status(thm)],[4318,4405,theory(equality)]) ).
cnf(6544,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = X1,
inference(spm,[status(thm)],[4031,4405,theory(equality)]) ).
cnf(110960,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[3067,5605,theory(equality)]) ).
cnf(110996,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| $false
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[110960,2654,theory(equality)]) ).
cnf(110997,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[110996,theory(equality)]) ).
cnf(110998,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(sr,[status(thm)],[110997,5483,theory(equality)]) ).
cnf(113560,plain,
( 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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____)),X1) ),
inference(spm,[status(thm)],[5567,5482,theory(equality)]) ).
cnf(113566,plain,
( 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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(spm,[status(thm)],[5567,5626,theory(equality)]) ).
cnf(114448,plain,
( 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,X1,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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____ ),
inference(spm,[status(thm)],[5564,5968,theory(equality)]) ).
cnf(114615,plain,
( 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,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____ ),
inference(rw,[status(thm)],[114448,6507,theory(equality)]) ).
cnf(114808,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[2734,114615,theory(equality)]) ).
cnf(114841,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| $false
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[114808,4995,theory(equality)]) ).
cnf(114842,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| $false
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[114841,4629,theory(equality)]) ).
cnf(114843,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[114842,theory(equality)]) ).
cnf(116194,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 ),
inference(spm,[status(thm)],[114843,5968,theory(equality)]) ).
cnf(116210,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____
| $false
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 ),
inference(rw,[status(thm)],[116194,5626,theory(equality)]) ).
cnf(116211,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 ),
inference(cn,[status(thm)],[116210,theory(equality)]) ).
cnf(116216,negated_conjecture,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r____,
inference(spm,[status(thm)],[3595,116211,theory(equality)]) ).
cnf(118250,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____),X1)
| 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____))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[4251,113560,theory(equality)]) ).
cnf(118282,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____),X1)
| 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____))
| $false ),
inference(rw,[status(thm)],[118250,4990,theory(equality)]) ).
cnf(118283,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____),X1)
| 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____)) ),
inference(cn,[status(thm)],[118282,theory(equality)]) ).
cnf(118292,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_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[118283,6507,theory(equality)]) ).
cnf(118345,plain,
( 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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(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)],[1775,118292,theory(equality)]) ).
cnf(118395,plain,
( 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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____),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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(spm,[status(thm)],[118345,113566,theory(equality)]) ).
cnf(118486,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r____
| 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____))
| ~ class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[3067,118395,theory(equality)]) ).
cnf(118513,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r____
| 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____))
| $false ),
inference(rw,[status(thm)],[118486,2437,theory(equality)]) ).
cnf(118514,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r____
| 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(cn,[status(thm)],[118513,theory(equality)]) ).
cnf(118515,plain,
( 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(sr,[status(thm)],[118514,116216,theory(equality)]) ).
cnf(118570,plain,
( 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),X1)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[5567,118515,theory(equality)]) ).
cnf(119007,negated_conjecture,
( 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),v_r____) ),
inference(spm,[status(thm)],[3595,118570,theory(equality)]) ).
cnf(119101,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[3595,119007,theory(equality)]) ).
cnf(119250,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)],[119101,113566]) ).
cnf(119257,negated_conjecture,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____) = v_r____
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[1373,119250,theory(equality)]) ).
cnf(119286,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____) = v_r____
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[119257,4629,theory(equality)]) ).
cnf(119287,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____) = v_r____
| $false ),
inference(rw,[status(thm)],[119286,4995,theory(equality)]) ).
cnf(119288,negated_conjecture,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r____) = v_r____,
inference(cn,[status(thm)],[119287,theory(equality)]) ).
cnf(119382,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),v_r____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(rw,[status(thm)],[5482,119288,theory(equality)]) ).
cnf(122618,plain,
( 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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____),X1) ),
inference(spm,[status(thm)],[5567,119382,theory(equality)]) ).
cnf(124127,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_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,v_r____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[1857,122618,theory(equality)]) ).
cnf(124162,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_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,v_r____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| $false ),
inference(rw,[status(thm)],[124127,4990,theory(equality)]) ).
cnf(124163,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_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,v_r____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(cn,[status(thm)],[124162,theory(equality)]) ).
cnf(124226,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,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),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[124163,6544,theory(equality)]) ).
cnf(124248,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(sr,[status(thm)],[124226,3595,theory(equality)]) ).
cnf(124249,plain,
$false,
inference(sr,[status(thm)],[124248,110998,theory(equality)]) ).
cnf(124250,plain,
$false,
124249,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW233+1.p
% --creating new selector for []
% -running prover on /tmp/tmpkqa1J9/sel_SWW233+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWW233+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW233+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW233+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
%
%------------------------------------------------------------------------------