TSTP Solution File: SWW207+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWW207+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 15:02:24 EST 2011
% Result : Theorem 11.16s
% Output : CNFRefutation 11.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 32
% Syntax : Number of formulae : 183 ( 92 unt; 0 def)
% Number of atoms : 334 ( 82 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 269 ( 118 ~; 113 |; 19 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 11 con; 0-2 aty)
% Number of variables : 181 ( 6 sgn 108 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(15,axiom,
! [X3,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X3))
=> c_Groups_Oabs__class_Oabs(X4,X3) = X3 ) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_abs__of__nonneg) ).
fof(57,conjecture,
? [X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X31))
& ! [X32] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X32)))))),X31)) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',conj_0) ).
fof(146,axiom,
! [X27,X23] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23),X27))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27),X23))
=> X23 = X27 ) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_real__le__antisym) ).
fof(162,axiom,
! [X3,X4] :
( class_Groups_Omonoid__mult(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Oone__class_Oone(X4)) = X3 ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_mult__1__right) ).
fof(214,axiom,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_complex__Re__one) ).
fof(223,axiom,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_complex__Re__i) ).
fof(308,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(350,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(444,axiom,
! [X6] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X6))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X6))),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_abs__Im__le__cmod) ).
fof(454,axiom,
! [X22,X21,X20] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20),X21))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21),X22))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20),X22)) ) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_real__le__trans) ).
fof(483,axiom,
? [X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X31))
& ! [X40] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X40))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X40)),X31))) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_Re_Ononneg__bounded) ).
fof(511,axiom,
! [X3] : hAPP(c_Complex_OIm,c_Complex_Ocis(X3)) = c_Transcendental_Osin(X3),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_Im__cis) ).
fof(548,axiom,
! [X23] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X23),hAPP(c_Complex_OIm,X23)) = X23,
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_complex__surj) ).
fof(607,axiom,
! [X38] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X38) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X38),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_real__norm__def) ).
fof(633,axiom,
! [X24,X8,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X8),X24))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X24),X8)) ) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_linorder__not__less) ).
fof(679,axiom,
! [X27,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X27) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X23),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_real__mult__commute) ).
fof(683,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_rp) ).
fof(774,axiom,
! [X8,X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X4,X8)))
<=> X8 != c_Groups_Ozero__class_Ozero(X4) ) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_zero__less__norm__iff) ).
fof(793,axiom,
! [X32] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X32))),v_r)),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_assms) ).
fof(824,axiom,
! [X3] : c_Complex_Ocis(X3) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_cis__rcis__eq) ).
fof(897,axiom,
! [X3] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X3),c_Transcendental_Osin(X3))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_cmod__unit__one) ).
fof(935,axiom,
! [X24,X8,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X8),X24))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X24),X8)) ) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_linorder__not__le) ).
fof(999,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(1042,axiom,
! [X4] :
( class_Rings_Olinordered__semidom(X4)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4)),c_Groups_Oone__class_Oone(X4))) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_zero__less__one) ).
fof(1051,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(1066,axiom,
! [X4] :
( class_RealVector_Oreal__normed__algebra__1(X4)
=> c_RealVector_Onorm__class_Onorm(X4,c_Groups_Oone__class_Oone(X4)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_norm__one) ).
fof(1072,axiom,
! [X3,X38] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X38,X3)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X38),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_complex__mod__rcis) ).
fof(1145,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(1151,axiom,
? [X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X31))
& ! [X40] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X40))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X40)),X31))) ),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_Im_Ononneg__bounded) ).
fof(1190,axiom,
! [X3] : hAPP(c_Complex_ORe,c_Complex_Ocis(X3)) = c_Transcendental_Ocos(X3),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_Re__cis) ).
fof(1201,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(1259,axiom,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/tmp/tmpfp4_dF/sel_SWW207+1.p_1',fact_complex__Im__i) ).
fof(1270,negated_conjecture,
~ ? [X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X31))
& ! [X32] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X32)))))),X31)) ),
inference(assume_negation,[status(cth)],[57]) ).
fof(1297,plain,
! [X24,X8,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X8),X24))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X24),X8)) ) ),
inference(fof_simplification,[status(thm)],[633,theory(equality)]) ).
fof(1311,plain,
! [X24,X8,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X8),X24))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X24),X8)) ) ),
inference(fof_simplification,[status(thm)],[935,theory(equality)]) ).
fof(1369,plain,
! [X3,X4] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4)),X3))
| c_Groups_Oabs__class_Oabs(X4,X3) = X3 ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(1370,plain,
! [X5,X6] :
( ~ class_Groups_Oordered__ab__group__add__abs(X6)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6)),X5))
| c_Groups_Oabs__class_Oabs(X6,X5) = X5 ),
inference(variable_rename,[status(thm)],[1369]) ).
cnf(1371,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ hBOOL(hAPP(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)],[1370]) ).
fof(1485,negated_conjecture,
! [X31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X31))
| ? [X32] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X32)))))),X31)) ),
inference(fof_nnf,[status(thm)],[1270]) ).
fof(1486,negated_conjecture,
! [X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X33))
| ? [X34] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X34)))))),X33)) ),
inference(variable_rename,[status(thm)],[1485]) ).
fof(1487,negated_conjecture,
! [X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X33))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk1_1(X33))))))),X33)) ),
inference(skolemize,[status(esa)],[1486]) ).
cnf(1488,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk1_1(X1))))))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[1487]) ).
fof(1749,plain,
! [X27,X23] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23),X27))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27),X23))
| X23 = X27 ),
inference(fof_nnf,[status(thm)],[146]) ).
fof(1750,plain,
! [X28,X29] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X29),X28))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X28),X29))
| X29 = X28 ),
inference(variable_rename,[status(thm)],[1749]) ).
cnf(1751,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[1750]) ).
fof(1810,plain,
! [X3,X4] :
( ~ class_Groups_Omonoid__mult(X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Oone__class_Oone(X4)) = X3 ),
inference(fof_nnf,[status(thm)],[162]) ).
fof(1811,plain,
! [X5,X6] :
( ~ class_Groups_Omonoid__mult(X6)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Oone__class_Oone(X6)) = X5 ),
inference(variable_rename,[status(thm)],[1810]) ).
cnf(1812,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[1811]) ).
cnf(1986,plain,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[214]) ).
cnf(2021,plain,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[223]) ).
cnf(2288,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[308]) ).
cnf(2402,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[350]) ).
fof(2649,plain,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X7))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7))),
inference(variable_rename,[status(thm)],[444]) ).
cnf(2650,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(split_conjunct,[status(thm)],[2649]) ).
fof(2679,plain,
! [X22,X21,X20] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20),X21))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21),X22))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20),X22)) ),
inference(fof_nnf,[status(thm)],[454]) ).
fof(2680,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25),X24))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24),X23))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25),X23)) ),
inference(variable_rename,[status(thm)],[2679]) ).
cnf(2681,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3)) ),
inference(split_conjunct,[status(thm)],[2680]) ).
fof(2751,plain,
? [X41] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X41))
& ! [X42] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X42))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X42)),X41))) ),
inference(variable_rename,[status(thm)],[483]) ).
fof(2752,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk19_0))
& ! [X42] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X42))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X42)),esk19_0))) ),
inference(skolemize,[status(esa)],[2751]) ).
fof(2753,plain,
! [X42] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X42))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X42)),esk19_0)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk19_0)) ),
inference(shift_quantors,[status(thm)],[2752]) ).
cnf(2754,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk19_0)),
inference(split_conjunct,[status(thm)],[2753]) ).
cnf(2755,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),esk19_0))),
inference(split_conjunct,[status(thm)],[2753]) ).
fof(2827,plain,
! [X4] : hAPP(c_Complex_OIm,c_Complex_Ocis(X4)) = c_Transcendental_Osin(X4),
inference(variable_rename,[status(thm)],[511]) ).
cnf(2828,plain,
hAPP(c_Complex_OIm,c_Complex_Ocis(X1)) = c_Transcendental_Osin(X1),
inference(split_conjunct,[status(thm)],[2827]) ).
fof(2937,plain,
! [X24] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X24),hAPP(c_Complex_OIm,X24)) = X24,
inference(variable_rename,[status(thm)],[548]) ).
cnf(2938,plain,
c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X1),hAPP(c_Complex_OIm,X1)) = X1,
inference(split_conjunct,[status(thm)],[2937]) ).
fof(3116,plain,
! [X39] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X39) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X39),
inference(variable_rename,[status(thm)],[607]) ).
cnf(3117,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[3116]) ).
fof(3191,plain,
! [X24,X8,X4] :
( ~ class_Orderings_Olinorder(X4)
| ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X8),X24))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X24),X8)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X24),X8))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X8),X24)) ) ) ),
inference(fof_nnf,[status(thm)],[1297]) ).
fof(3192,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Olinorder(X27)
| ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X27,X26),X25))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,X25),X26)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,X25),X26))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X27,X26),X25)) ) ) ),
inference(variable_rename,[status(thm)],[3191]) ).
fof(3193,plain,
! [X25,X26,X27] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X27,X26),X25))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,X25),X26))
| ~ class_Orderings_Olinorder(X27) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,X25),X26))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X27,X26),X25))
| ~ class_Orderings_Olinorder(X27) ) ),
inference(distribute,[status(thm)],[3192]) ).
cnf(3195,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[3193]) ).
fof(3346,plain,
! [X28,X29] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X29),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X28),X29),
inference(variable_rename,[status(thm)],[679]) ).
cnf(3347,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[3346]) ).
cnf(3357,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(split_conjunct,[status(thm)],[683]) ).
fof(3619,plain,
! [X8,X4] :
( ~ class_RealVector_Oreal__normed__vector(X4)
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X4,X8)))
| X8 != c_Groups_Ozero__class_Ozero(X4) )
& ( X8 = c_Groups_Ozero__class_Ozero(X4)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X4,X8))) ) ) ),
inference(fof_nnf,[status(thm)],[774]) ).
fof(3620,plain,
! [X9,X10] :
( ~ class_RealVector_Oreal__normed__vector(X10)
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X10,X9)))
| X9 != c_Groups_Ozero__class_Ozero(X10) )
& ( X9 = c_Groups_Ozero__class_Ozero(X10)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X10,X9))) ) ) ),
inference(variable_rename,[status(thm)],[3619]) ).
fof(3621,plain,
! [X9,X10] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X10,X9)))
| X9 != c_Groups_Ozero__class_Ozero(X10)
| ~ class_RealVector_Oreal__normed__vector(X10) )
& ( X9 = c_Groups_Ozero__class_Ozero(X10)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X10,X9)))
| ~ class_RealVector_Oreal__normed__vector(X10) ) ),
inference(distribute,[status(thm)],[3620]) ).
cnf(3622,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(X1,X2)))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[3621]) ).
fof(3674,plain,
! [X33] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X33))),v_r)),
inference(variable_rename,[status(thm)],[793]) ).
cnf(3675,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X1))),v_r)),
inference(split_conjunct,[status(thm)],[3674]) ).
fof(3767,plain,
! [X4] : c_Complex_Ocis(X4) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4),
inference(variable_rename,[status(thm)],[824]) ).
cnf(3768,plain,
c_Complex_Ocis(X1) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),
inference(split_conjunct,[status(thm)],[3767]) ).
fof(4017,plain,
! [X4] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X4),c_Transcendental_Osin(X4))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(variable_rename,[status(thm)],[897]) ).
cnf(4018,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(X1),c_Transcendental_Osin(X1))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[4017]) ).
fof(4127,plain,
! [X24,X8,X4] :
( ~ class_Orderings_Olinorder(X4)
| ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X8),X24))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X24),X8)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X24),X8))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X8),X24)) ) ) ),
inference(fof_nnf,[status(thm)],[1311]) ).
fof(4128,plain,
! [X25,X26,X27] :
( ~ class_Orderings_Olinorder(X27)
| ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,X26),X25))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X27,X25),X26)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X27,X25),X26))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,X26),X25)) ) ) ),
inference(variable_rename,[status(thm)],[4127]) ).
fof(4129,plain,
! [X25,X26,X27] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,X26),X25))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X27,X25),X26))
| ~ class_Orderings_Olinorder(X27) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X27,X25),X26))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X27,X26),X25))
| ~ class_Orderings_Olinorder(X27) ) ),
inference(distribute,[status(thm)],[4128]) ).
cnf(4130,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
inference(split_conjunct,[status(thm)],[4129]) ).
cnf(4301,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[999]) ).
fof(4434,plain,
! [X4] :
( ~ class_Rings_Olinordered__semidom(X4)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4)),c_Groups_Oone__class_Oone(X4))) ),
inference(fof_nnf,[status(thm)],[1042]) ).
fof(4435,plain,
! [X5] :
( ~ class_Rings_Olinordered__semidom(X5)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oone__class_Oone(X5))) ),
inference(variable_rename,[status(thm)],[4434]) ).
cnf(4436,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[4435]) ).
cnf(4463,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1051]) ).
fof(4515,plain,
! [X4] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4)
| c_RealVector_Onorm__class_Onorm(X4,c_Groups_Oone__class_Oone(X4)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[1066]) ).
fof(4516,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(variable_rename,[status(thm)],[4515]) ).
cnf(4517,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)],[4516]) ).
fof(4535,plain,
! [X39,X40] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X40,X39)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X40),
inference(variable_rename,[status(thm)],[1072]) ).
cnf(4536,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[4535]) ).
cnf(4773,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1145]) ).
fof(4784,plain,
? [X41] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X41))
& ! [X42] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X42))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X42)),X41))) ),
inference(variable_rename,[status(thm)],[1151]) ).
fof(4785,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk62_0))
& ! [X42] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X42))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X42)),esk62_0))) ),
inference(skolemize,[status(esa)],[4784]) ).
fof(4786,plain,
! [X42] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X42))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X42)),esk62_0)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk62_0)) ),
inference(shift_quantors,[status(thm)],[4785]) ).
cnf(4787,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),esk62_0)),
inference(split_conjunct,[status(thm)],[4786]) ).
fof(4926,plain,
! [X4] : hAPP(c_Complex_ORe,c_Complex_Ocis(X4)) = c_Transcendental_Ocos(X4),
inference(variable_rename,[status(thm)],[1190]) ).
cnf(4927,plain,
hAPP(c_Complex_ORe,c_Complex_Ocis(X1)) = c_Transcendental_Ocos(X1),
inference(split_conjunct,[status(thm)],[4926]) ).
cnf(4946,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1201]) ).
cnf(5100,plain,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1259]) ).
cnf(5199,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,c_Complex_Ocis(X1)),c_Transcendental_Osin(X1))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[4018,4927,theory(equality)]),
[unfolding] ).
cnf(5219,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,c_Complex_Ocis(X1)),hAPP(c_Complex_OIm,c_Complex_Ocis(X1)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[5199,2828,theory(equality)]),
[unfolding] ).
cnf(5237,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),hAPP(c_Complex_OIm,c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5219,3768,theory(equality)]),3768,theory(equality)]),
[unfolding] ).
cnf(5428,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),esk62_0)),
inference(rw,[status(thm)],[4787,2021,theory(equality)]) ).
cnf(5429,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),esk19_0)),
inference(rw,[status(thm)],[2754,2021,theory(equality)]) ).
cnf(5430,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r)),
inference(rw,[status(thm)],[3357,2021,theory(equality)]) ).
cnf(5442,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk1_1(X1))))))),X1)) ),
inference(rw,[status(thm)],[1488,2021,theory(equality)]) ).
cnf(5453,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk1_1(X1))))))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
inference(rw,[status(thm)],[5442,3117,theory(equality)]) ).
cnf(5491,plain,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(c_Complex_OIm,c_Complex_Oii),
inference(rw,[status(thm)],[1986,5100,theory(equality)]) ).
cnf(5556,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X1))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(rw,[status(thm)],[2650,3117,theory(equality)]) ).
cnf(5841,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X2)))) ),
inference(spm,[status(thm)],[2681,3675,theory(equality)]) ).
cnf(5866,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1)) = hAPP(c_Complex_OIm,c_Complex_Oii)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(rw,[status(thm)],[4517,5100,theory(equality)]) ).
cnf(5868,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(c_Complex_OIm,c_Complex_Oii),
inference(spm,[status(thm)],[5866,4301,theory(equality)]) ).
cnf(6014,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(spm,[status(thm)],[4436,2288,theory(equality)]) ).
cnf(6018,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(c_Complex_OIm,c_Complex_Oii))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[6014,2021,theory(equality)]),5100,theory(equality)]) ).
cnf(6514,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[4536,3117,theory(equality)]) ).
cnf(7339,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),c_RealVector_Onorm__class_Onorm(X1,X2)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(rw,[status(thm)],[3622,2021,theory(equality)]) ).
cnf(8107,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)],[1812,4463,theory(equality)]) ).
cnf(8112,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(c_Complex_OIm,c_Complex_Oii)) = X1,
inference(rw,[status(thm)],[8107,5100,theory(equality)]) ).
cnf(8641,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X1)) ),
inference(spm,[status(thm)],[3195,4773,theory(equality)]) ).
cnf(9708,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),esk19_0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)))),
inference(rw,[status(thm)],[2755,3347,theory(equality)]) ).
cnf(20655,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5237,5100,theory(equality)]),5100,theory(equality)]),2938,theory(equality)]),6514,theory(equality)]) ).
cnf(20656,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)) = hAPP(c_Complex_OIm,c_Complex_Oii),
inference(rw,[status(thm)],[20655,5100,theory(equality)]) ).
cnf(101278,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk62_0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(spm,[status(thm)],[2681,5428,theory(equality)]) ).
cnf(101279,plain,
( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(spm,[status(thm)],[4130,5428,theory(equality)]) ).
cnf(101289,plain,
( $false
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(rw,[status(thm)],[101279,4773,theory(equality)]) ).
cnf(101290,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),hAPP(c_Complex_ORe,c_Complex_Oii))),
inference(cn,[status(thm)],[101289,theory(equality)]) ).
cnf(101308,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk19_0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(spm,[status(thm)],[2681,5429,theory(equality)]) ).
cnf(101338,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(spm,[status(thm)],[2681,5430,theory(equality)]) ).
cnf(114291,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),esk19_0),hAPP(c_Complex_OIm,c_Complex_Oii)))),
inference(spm,[status(thm)],[9708,5868,theory(equality)]) ).
cnf(114347,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),esk19_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[114291,5491,theory(equality)]),20656,theory(equality)]),8112,theory(equality)]) ).
cnf(114518,plain,
( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk19_0),hAPP(c_Complex_OIm,c_Complex_Oii))) ),
inference(spm,[status(thm)],[4130,114347,theory(equality)]) ).
cnf(114529,plain,
( $false
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk19_0),hAPP(c_Complex_OIm,c_Complex_Oii))) ),
inference(rw,[status(thm)],[114518,4773,theory(equality)]) ).
cnf(114530,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk19_0),hAPP(c_Complex_OIm,c_Complex_Oii))),
inference(cn,[status(thm)],[114529,theory(equality)]) ).
cnf(119873,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),v_r)),
inference(spm,[status(thm)],[5841,5556,theory(equality)]) ).
cnf(119958,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r)),
inference(spm,[status(thm)],[5453,119873,theory(equality)]) ).
cnf(128107,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk62_0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
inference(spm,[status(thm)],[101278,8641,theory(equality)]) ).
cnf(128198,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk19_0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
inference(spm,[status(thm)],[101308,8641,theory(equality)]) ).
cnf(128271,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
inference(spm,[status(thm)],[101338,8641,theory(equality)]) ).
cnf(129995,negated_conjecture,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),esk62_0)),
inference(spm,[status(thm)],[119958,128107,theory(equality)]) ).
cnf(130102,negated_conjecture,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk62_0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r)) ),
inference(spm,[status(thm)],[2681,129995,theory(equality)]) ).
cnf(130387,negated_conjecture,
( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r)) ),
inference(spm,[status(thm)],[4130,130102,theory(equality)]) ).
cnf(130409,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),esk62_0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk1_1(esk62_0))))))),v_r)) ),
inference(spm,[status(thm)],[5453,130102,theory(equality)]) ).
cnf(130416,negated_conjecture,
( $false
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r)) ),
inference(rw,[status(thm)],[130387,4773,theory(equality)]) ).
cnf(130417,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r)) ),
inference(cn,[status(thm)],[130416,theory(equality)]) ).
cnf(130468,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),esk62_0))
| $false ),
inference(rw,[status(thm)],[130409,119873,theory(equality)]) ).
cnf(130469,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),esk62_0)),
inference(cn,[status(thm)],[130468,theory(equality)]) ).
cnf(130658,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1))))),
inference(spm,[status(thm)],[130417,119873,theory(equality)]) ).
cnf(132196,negated_conjecture,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),esk19_0)),
inference(spm,[status(thm)],[119958,128198,theory(equality)]) ).
cnf(132197,negated_conjecture,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,esk62_0),esk19_0)),
inference(spm,[status(thm)],[130469,128198,theory(equality)]) ).
cnf(132322,negated_conjecture,
( esk19_0 = v_r
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,esk19_0),v_r)) ),
inference(spm,[status(thm)],[1751,132196,theory(equality)]) ).
cnf(132357,negated_conjecture,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk19_0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk62_0)) ),
inference(spm,[status(thm)],[2681,132197,theory(equality)]) ).
cnf(132629,negated_conjecture,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),esk19_0))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),X1)) ),
inference(spm,[status(thm)],[132357,8641,theory(equality)]) ).
cnf(132933,negated_conjecture,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,esk19_0) = esk19_0
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[1371,132629,theory(equality)]) ).
cnf(132952,negated_conjecture,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk1_1(esk19_0))))))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),esk19_0)) ),
inference(spm,[status(thm)],[5453,132629,theory(equality)]) ).
cnf(132963,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,esk19_0) = esk19_0
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[132933,3117,theory(equality)]) ).
cnf(132964,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,esk19_0) = esk19_0
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),hAPP(c_Complex_ORe,c_Complex_Oii)))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[132963,2021,theory(equality)]) ).
cnf(132965,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,esk19_0) = esk19_0
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),hAPP(c_Complex_ORe,c_Complex_Oii)))
| $false ),
inference(rw,[status(thm)],[132964,4946,theory(equality)]) ).
cnf(132966,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,esk19_0) = esk19_0
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk62_0),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(cn,[status(thm)],[132965,theory(equality)]) ).
cnf(132967,negated_conjecture,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,esk19_0) = esk19_0,
inference(sr,[status(thm)],[132966,101290,theory(equality)]) ).
cnf(133017,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),esk19_0)),
inference(sr,[status(thm)],[132952,130658,theory(equality)]) ).
cnf(134778,negated_conjecture,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,esk19_0),v_r)),
inference(spm,[status(thm)],[133017,128271,theory(equality)]) ).
cnf(134918,negated_conjecture,
( esk19_0 = v_r
| $false ),
inference(rw,[status(thm)],[132322,134778,theory(equality)]) ).
cnf(134919,negated_conjecture,
esk19_0 = v_r,
inference(cn,[status(thm)],[134918,theory(equality)]) ).
cnf(134951,negated_conjecture,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r) = esk19_0,
inference(rw,[status(thm)],[132967,134919,theory(equality)]) ).
cnf(134952,negated_conjecture,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_r) = v_r,
inference(rw,[status(thm)],[134951,134919,theory(equality)]) ).
cnf(134987,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),hAPP(c_Complex_OIm,c_Complex_Oii))),
inference(rw,[status(thm)],[114530,134919,theory(equality)]) ).
cnf(135331,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r))
| ~ class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[7339,134952,theory(equality)]) ).
cnf(135406,negated_conjecture,
( hAPP(c_Complex_ORe,c_Complex_Oii) = v_r
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r))
| ~ class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[135331,2021,theory(equality)]) ).
cnf(135407,negated_conjecture,
( hAPP(c_Complex_ORe,c_Complex_Oii) = v_r
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r))
| $false ),
inference(rw,[status(thm)],[135406,2402,theory(equality)]) ).
cnf(135408,negated_conjecture,
( hAPP(c_Complex_ORe,c_Complex_Oii) = v_r
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r)) ),
inference(cn,[status(thm)],[135407,theory(equality)]) ).
cnf(135409,negated_conjecture,
hAPP(c_Complex_ORe,c_Complex_Oii) = v_r,
inference(sr,[status(thm)],[135408,119958,theory(equality)]) ).
cnf(135534,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),hAPP(c_Complex_OIm,c_Complex_Oii))),
inference(rw,[status(thm)],[6018,135409,theory(equality)]) ).
cnf(135535,plain,
$false,
inference(sr,[status(thm)],[135534,134987,theory(equality)]) ).
cnf(135536,plain,
$false,
135535,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW207+1.p
% --creating new selector for []
% -running prover on /tmp/tmpfp4_dF/sel_SWW207+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWW207+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW207+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW207+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
%
%------------------------------------------------------------------------------