TSTP Solution File: SWW236+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWW236+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 15:15:02 EST 2011
% Result : Theorem 21.44s
% Output : CNFRefutation 21.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of formulae : 120 ( 43 unt; 0 def)
% Number of atoms : 310 ( 64 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 335 ( 145 ~; 143 |; 26 &)
% ( 8 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 155 ( 0 sgn 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(43,axiom,
! [X29,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X29)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X29)
| X13 = X29 ) ),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_less__eq__real__def) ).
fof(66,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',conj_0) ).
fof(102,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(104,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(111,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_h) ).
fof(149,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(352,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(373,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(388,axiom,
! [X29,X13,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X29)
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X29)
& ~ c_Orderings_Oord__class_Oless__eq(X5,X29,X13) ) ) ),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_less__le__not__le) ).
fof(402,axiom,
! [X19,X18,X17,X5] :
( class_Fields_Olinordered__field(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Odivide(X5,X18,X17),X19)
<=> c_Orderings_Oord__class_Oless__eq(X5,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X19),X17)) ) ) ),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_pos__divide__le__eq) ).
fof(557,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(594,axiom,
! [X48] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X48) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X48),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_real__norm__def) ).
fof(630,axiom,
! [X9,X7,X5] :
( class_RealVector_Oreal__normed__div__algebra(X5)
=> c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),c_RealVector_Onorm__class_Onorm(X5,X9)) ),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_norm__mult) ).
fof(665,axiom,
! [X6,X8] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X8),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X8),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_real__mult__commute) ).
fof(844,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/tmpfUeMLJ/sel_SWW236+1.p_1',fact_abs__of__pos) ).
fof(877,axiom,
! [X14,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X14) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X14),X4) ),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(884,axiom,
! [X13,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X13))
<=> X13 != c_Groups_Ozero__class_Ozero(X5) ) ),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_zero__less__norm__iff) ).
fof(925,axiom,
! [X29,X13,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X13,X29)
<=> c_Orderings_Oord__class_Oless(X5,X29,X13) ) ),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_linorder__not__le) ).
fof(955,axiom,
! [X13,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X13 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_norm__le__zero__iff) ).
fof(1092,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact__0960_A_060_Acmod_Ac_096) ).
fof(1137,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4)) = c_RealVector_Onorm__class_Onorm(X5,X4) ),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_abs__norm__cancel) ).
fof(1144,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(1150,axiom,
! [X6,X8] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X6)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X8) ),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',fact_real__le__linear) ).
fof(1196,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/tmp/tmpfUeMLJ/sel_SWW236+1.p_1',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(1267,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(assume_negation,[status(cth)],[66]) ).
fof(1271,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(fof_simplification,[status(thm)],[1267,theory(equality)]) ).
fof(1290,plain,
! [X29,X13,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X13,X29)
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X29)
& ~ c_Orderings_Oord__class_Oless__eq(X5,X29,X13) ) ) ),
inference(fof_simplification,[status(thm)],[388,theory(equality)]) ).
fof(1314,plain,
! [X29,X13,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X13,X29)
<=> c_Orderings_Oord__class_Oless(X5,X29,X13) ) ),
inference(fof_simplification,[status(thm)],[925,theory(equality)]) ).
fof(1436,plain,
! [X29,X13] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X29)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X29)
| X13 = X29 )
& ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X29)
& X13 != X29 )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X29) ) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(1437,plain,
! [X30,X31] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X31,X30)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X31,X30)
| X31 = X30 )
& ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X31,X30)
& X31 != X30 )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X31,X30) ) ),
inference(variable_rename,[status(thm)],[1436]) ).
fof(1438,plain,
! [X30,X31] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X31,X30)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X31,X30)
| X31 = X30 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X31,X30)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X31,X30) )
& ( X31 != X30
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X31,X30) ) ),
inference(distribute,[status(thm)],[1437]) ).
cnf(1441,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[1438]) ).
cnf(1530,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(split_conjunct,[status(thm)],[1271]) ).
cnf(1658,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(1662,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(1679,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(1793,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[149]) ).
cnf(2472,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[352]) ).
cnf(2539,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[373]) ).
fof(2577,plain,
! [X29,X13,X5] :
( ~ class_Orderings_Opreorder(X5)
| ( ( ~ c_Orderings_Oord__class_Oless(X5,X13,X29)
| ( c_Orderings_Oord__class_Oless__eq(X5,X13,X29)
& ~ c_Orderings_Oord__class_Oless__eq(X5,X29,X13) ) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5,X13,X29)
| c_Orderings_Oord__class_Oless__eq(X5,X29,X13)
| c_Orderings_Oord__class_Oless(X5,X13,X29) ) ) ),
inference(fof_nnf,[status(thm)],[1290]) ).
fof(2578,plain,
! [X30,X31,X32] :
( ~ class_Orderings_Opreorder(X32)
| ( ( ~ c_Orderings_Oord__class_Oless(X32,X31,X30)
| ( c_Orderings_Oord__class_Oless__eq(X32,X31,X30)
& ~ c_Orderings_Oord__class_Oless__eq(X32,X30,X31) ) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X32,X31,X30)
| c_Orderings_Oord__class_Oless__eq(X32,X30,X31)
| c_Orderings_Oord__class_Oless(X32,X31,X30) ) ) ),
inference(variable_rename,[status(thm)],[2577]) ).
fof(2579,plain,
! [X30,X31,X32] :
( ( c_Orderings_Oord__class_Oless__eq(X32,X31,X30)
| ~ c_Orderings_Oord__class_Oless(X32,X31,X30)
| ~ class_Orderings_Opreorder(X32) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X32,X30,X31)
| ~ c_Orderings_Oord__class_Oless(X32,X31,X30)
| ~ class_Orderings_Opreorder(X32) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X32,X31,X30)
| c_Orderings_Oord__class_Oless__eq(X32,X30,X31)
| c_Orderings_Oord__class_Oless(X32,X31,X30)
| ~ class_Orderings_Opreorder(X32) ) ),
inference(distribute,[status(thm)],[2578]) ).
cnf(2580,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[2579]) ).
fof(2618,plain,
! [X19,X18,X17,X5] :
( ~ class_Fields_Olinordered__field(X5)
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X17)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Odivide(X5,X18,X17),X19)
| c_Orderings_Oord__class_Oless__eq(X5,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X19),X17)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X19),X17))
| c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Odivide(X5,X18,X17),X19) ) ) ),
inference(fof_nnf,[status(thm)],[402]) ).
fof(2619,plain,
! [X20,X21,X22,X23] :
( ~ class_Fields_Olinordered__field(X23)
| ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),X22)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X23,c_Rings_Oinverse__class_Odivide(X23,X21,X22),X20)
| c_Orderings_Oord__class_Oless__eq(X23,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23),X20),X22)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X23,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23),X20),X22))
| c_Orderings_Oord__class_Oless__eq(X23,c_Rings_Oinverse__class_Odivide(X23,X21,X22),X20) ) ) ),
inference(variable_rename,[status(thm)],[2618]) ).
fof(2620,plain,
! [X20,X21,X22,X23] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X23,c_Rings_Oinverse__class_Odivide(X23,X21,X22),X20)
| c_Orderings_Oord__class_Oless__eq(X23,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23),X20),X22))
| ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),X22)
| ~ class_Fields_Olinordered__field(X23) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X23,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23),X20),X22))
| c_Orderings_Oord__class_Oless__eq(X23,c_Rings_Oinverse__class_Odivide(X23,X21,X22),X20)
| ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),X22)
| ~ class_Fields_Olinordered__field(X23) ) ),
inference(distribute,[status(thm)],[2619]) ).
cnf(2622,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4) ),
inference(split_conjunct,[status(thm)],[2620]) ).
cnf(3064,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[557]) ).
fof(3170,plain,
! [X49] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X49) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X49),
inference(variable_rename,[status(thm)],[594]) ).
cnf(3171,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[3170]) ).
fof(3281,plain,
! [X9,X7,X5] :
( ~ class_RealVector_Oreal__normed__div__algebra(X5)
| c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),c_RealVector_Onorm__class_Onorm(X5,X9)) ),
inference(fof_nnf,[status(thm)],[630]) ).
fof(3282,plain,
! [X10,X11,X12] :
( ~ class_RealVector_Oreal__normed__div__algebra(X12)
| c_RealVector_Onorm__class_Onorm(X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),X11),X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X12,X11)),c_RealVector_Onorm__class_Onorm(X12,X10)) ),
inference(variable_rename,[status(thm)],[3281]) ).
cnf(3283,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[3282]) ).
fof(3395,plain,
! [X9,X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X10),
inference(variable_rename,[status(thm)],[665]) ).
cnf(3396,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)],[3395]) ).
fof(3942,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)],[844]) ).
fof(3943,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)],[3942]) ).
cnf(3944,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)],[3943]) ).
fof(4058,plain,
! [X14,X4,X5] :
( ~ class_Rings_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X14) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X14),X4) ),
inference(fof_nnf,[status(thm)],[877]) ).
fof(4059,plain,
! [X15,X16,X17] :
( ~ class_Rings_Ocomm__semiring__1(X17)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X16),X15) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17),X15),X16) ),
inference(variable_rename,[status(thm)],[4058]) ).
cnf(4060,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[4059]) ).
fof(4094,plain,
! [X13,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X13))
| X13 != c_Groups_Ozero__class_Ozero(X5) )
& ( X13 = c_Groups_Ozero__class_Ozero(X5)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X13)) ) ) ),
inference(fof_nnf,[status(thm)],[884]) ).
fof(4095,plain,
! [X14,X15] :
( ~ class_RealVector_Oreal__normed__vector(X15)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X15,X14))
| X14 != c_Groups_Ozero__class_Ozero(X15) )
& ( X14 = c_Groups_Ozero__class_Ozero(X15)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X15,X14)) ) ) ),
inference(variable_rename,[status(thm)],[4094]) ).
fof(4096,plain,
! [X14,X15] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X15,X14))
| X14 != c_Groups_Ozero__class_Ozero(X15)
| ~ class_RealVector_Oreal__normed__vector(X15) )
& ( X14 = c_Groups_Ozero__class_Ozero(X15)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X15,X14))
| ~ class_RealVector_Oreal__normed__vector(X15) ) ),
inference(distribute,[status(thm)],[4095]) ).
cnf(4098,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)) ),
inference(split_conjunct,[status(thm)],[4096]) ).
fof(4219,plain,
! [X29,X13,X5] :
( ~ class_Orderings_Olinorder(X5)
| ( ( c_Orderings_Oord__class_Oless__eq(X5,X13,X29)
| c_Orderings_Oord__class_Oless(X5,X29,X13) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X29,X13)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X13,X29) ) ) ),
inference(fof_nnf,[status(thm)],[1314]) ).
fof(4220,plain,
! [X30,X31,X32] :
( ~ class_Orderings_Olinorder(X32)
| ( ( c_Orderings_Oord__class_Oless__eq(X32,X31,X30)
| c_Orderings_Oord__class_Oless(X32,X30,X31) )
& ( ~ c_Orderings_Oord__class_Oless(X32,X30,X31)
| ~ c_Orderings_Oord__class_Oless__eq(X32,X31,X30) ) ) ),
inference(variable_rename,[status(thm)],[4219]) ).
fof(4221,plain,
! [X30,X31,X32] :
( ( c_Orderings_Oord__class_Oless__eq(X32,X31,X30)
| c_Orderings_Oord__class_Oless(X32,X30,X31)
| ~ class_Orderings_Olinorder(X32) )
& ( ~ c_Orderings_Oord__class_Oless(X32,X30,X31)
| ~ c_Orderings_Oord__class_Oless__eq(X32,X31,X30)
| ~ class_Orderings_Olinorder(X32) ) ),
inference(distribute,[status(thm)],[4220]) ).
cnf(4222,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)],[4221]) ).
fof(4309,plain,
! [X13,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X13 = c_Groups_Ozero__class_Ozero(X5) )
& ( X13 != c_Groups_Ozero__class_Ozero(X5)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
inference(fof_nnf,[status(thm)],[955]) ).
fof(4310,plain,
! [X14,X15] :
( ~ class_RealVector_Oreal__normed__vector(X15)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X15,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X14 = c_Groups_Ozero__class_Ozero(X15) )
& ( X14 != c_Groups_Ozero__class_Ozero(X15)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X15,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
inference(variable_rename,[status(thm)],[4309]) ).
fof(4311,plain,
! [X14,X15] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X15,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X14 = c_Groups_Ozero__class_Ozero(X15)
| ~ class_RealVector_Oreal__normed__vector(X15) )
& ( X14 != c_Groups_Ozero__class_Ozero(X15)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X15,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X15) ) ),
inference(distribute,[status(thm)],[4310]) ).
cnf(4313,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)],[4311]) ).
cnf(4738,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
inference(split_conjunct,[status(thm)],[1092]) ).
fof(4870,plain,
! [X4,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4)) = c_RealVector_Onorm__class_Onorm(X5,X4) ),
inference(fof_nnf,[status(thm)],[1137]) ).
fof(4871,plain,
! [X6,X7] :
( ~ class_RealVector_Oreal__normed__vector(X7)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6)) = c_RealVector_Onorm__class_Onorm(X7,X6) ),
inference(variable_rename,[status(thm)],[4870]) ).
cnf(4872,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[4871]) ).
cnf(4892,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1144]) ).
fof(4907,plain,
! [X9,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X10) ),
inference(variable_rename,[status(thm)],[1150]) ).
cnf(4908,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)],[4907]) ).
cnf(5077,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[1196]) ).
cnf(5503,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(rw,[status(thm)],[1679,3171,theory(equality)]) ).
cnf(5504,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
inference(rw,[status(thm)],[1530,3171,theory(equality)]) ).
cnf(5675,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(rw,[status(thm)],[4872,3171,theory(equality)]) ).
cnf(6098,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(spm,[status(thm)],[4098,5675,theory(equality)]) ).
cnf(6105,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X2)
| $false
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(rw,[status(thm)],[6098,2472,theory(equality)]) ).
cnf(6106,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cn,[status(thm)],[6105,theory(equality)]) ).
cnf(6403,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[1441,4908,theory(equality)]) ).
cnf(7523,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),
inference(spm,[status(thm)],[4060,1662,theory(equality)]) ).
cnf(7537,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[3944,4738,theory(equality)]) ).
cnf(7551,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[7537,3171,theory(equality)]) ).
cnf(7552,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)
| $false ),
inference(rw,[status(thm)],[7551,5077,theory(equality)]) ).
cnf(7553,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),
inference(cn,[status(thm)],[7552,theory(equality)]) ).
cnf(11928,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),
inference(spm,[status(thm)],[3283,2539,theory(equality)]) ).
cnf(87109,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))
| ~ class_Fields_Olinordered__field(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
inference(spm,[status(thm)],[2622,5503,theory(equality)]) ).
cnf(87139,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)))
| ~ class_Fields_Olinordered__field(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
inference(rw,[status(thm)],[87109,3396,theory(equality)]) ).
cnf(87140,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)))
| $false
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
inference(rw,[status(thm)],[87139,1658,theory(equality)]) ).
cnf(87141,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
inference(cn,[status(thm)],[87140,theory(equality)]) ).
cnf(87162,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)
| ~ class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spm,[status(thm)],[4313,7553,theory(equality)]) ).
cnf(87205,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)
| $false
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[87162,2472,theory(equality)]) ).
cnf(87206,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[87205,theory(equality)]) ).
cnf(87278,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(spm,[status(thm)],[5504,4908,theory(equality)]) ).
cnf(87294,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[2580,87278,theory(equality)]) ).
cnf(87318,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| $false ),
inference(rw,[status(thm)],[87294,3064,theory(equality)]) ).
cnf(87319,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))) ),
inference(cn,[status(thm)],[87318,theory(equality)]) ).
cnf(87320,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(sr,[status(thm)],[87319,5504,theory(equality)]) ).
cnf(94525,plain,
( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
inference(spm,[status(thm)],[4222,87141,theory(equality)]) ).
cnf(94540,plain,
( $false
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
inference(rw,[status(thm)],[94525,4892,theory(equality)]) ).
cnf(94541,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
inference(cn,[status(thm)],[94540,theory(equality)]) ).
cnf(101473,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_c____),v_z____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
inference(rw,[status(thm)],[94541,11928,theory(equality)]) ).
cnf(127083,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[6106,4738,theory(equality)]) ).
cnf(127100,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| $false ),
inference(rw,[status(thm)],[127083,1793,theory(equality)]) ).
cnf(127101,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cn,[status(thm)],[127100,theory(equality)]) ).
cnf(136549,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)) ),
inference(spm,[status(thm)],[87206,6403,theory(equality)]) ).
cnf(136779,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
inference(sr,[status(thm)],[136549,127101,theory(equality)]) ).
cnf(136819,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_c____),v_z____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)))
| $false ),
inference(rw,[status(thm)],[101473,136779,theory(equality)]) ).
cnf(136820,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_c____),v_z____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(cn,[status(thm)],[136819,theory(equality)]) ).
cnf(212727,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_c____),v_z____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(rw,[status(thm)],[87320,7523,theory(equality)]) ).
cnf(212728,negated_conjecture,
$false,
inference(sr,[status(thm)],[212727,136820,theory(equality)]) ).
cnf(212729,negated_conjecture,
$false,
212728,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW236+1.p
% --creating new selector for []
% -running prover on /tmp/tmpfUeMLJ/sel_SWW236+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWW236+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW236+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW236+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
%
%------------------------------------------------------------------------------