TSTP Solution File: SWW261+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWW261+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 15:28:48 EST 2011
% Result : Theorem 81.73s
% Output : CNFRefutation 81.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 73 ( 35 unt; 0 def)
% Number of atoms : 128 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 98 ( 43 ~; 46 |; 0 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(110,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(160,axiom,
! [X34,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X34,X26)
=> X26 = X34 ) ),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact_real__le__antisym) ).
fof(204,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096) ).
fof(256,axiom,
! [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X26) = X26,
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact_real__mult__1) ).
fof(361,axiom,
! [X6,X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),c_RealVector_Onorm__class_Onorm(X5,X6))) ),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact_norm__mult__ineq) ).
fof(476,axiom,
! [X23,X22,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X23) ) ),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact_real__le__trans) ).
fof(542,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(646,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(701,axiom,
! [X34,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X34) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X34),X26),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact_real__mult__commute) ).
fof(766,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(793,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),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',conj_0) ).
fof(891,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/tmp5m420R/sel_SWW261+1.p_2',fact_abs__of__pos) ).
fof(919,axiom,
! [X8,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X8) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X4) ),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(984,axiom,
! [X46,X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_RealVector_Oof__real(X5,X46)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X46) ),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact_norm__of__real) ).
fof(1117,axiom,
! [X46] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X46) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X46),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact_real__norm__def) ).
fof(1184,axiom,
! [X34,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X34)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X34,X26) ),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact_real__le__linear) ).
fof(1239,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
file('/tmp/tmp5m420R/sel_SWW261+1.p_2',fact_t_I1_J) ).
fof(1289,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),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(assume_negation,[status(cth)],[793]) ).
fof(1324,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),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(fof_simplification,[status(thm)],[1289,theory(equality)]) ).
cnf(1668,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[110]) ).
fof(1806,plain,
! [X34,X26] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X34)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X34,X26)
| X26 = X34 ),
inference(fof_nnf,[status(thm)],[160]) ).
fof(1807,plain,
! [X35,X36] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,X35)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X35,X36)
| X36 = X35 ),
inference(variable_rename,[status(thm)],[1806]) ).
cnf(1808,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)],[1807]) ).
cnf(1953,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),
inference(split_conjunct,[status(thm)],[204]) ).
fof(2121,plain,
! [X27] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X27) = X27,
inference(variable_rename,[status(thm)],[256]) ).
cnf(2122,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(split_conjunct,[status(thm)],[2121]) ).
fof(2447,plain,
! [X6,X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)),c_RealVector_Onorm__class_Onorm(X5,X6))) ),
inference(fof_nnf,[status(thm)],[361]) ).
fof(2448,plain,
! [X8,X9,X10] :
( ~ class_RealVector_Oreal__normed__algebra(X10)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X9)),c_RealVector_Onorm__class_Onorm(X10,X8))) ),
inference(variable_rename,[status(thm)],[2447]) ).
cnf(2449,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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__algebra(X1) ),
inference(split_conjunct,[status(thm)],[2448]) ).
fof(2769,plain,
! [X23,X22,X21] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X22)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X23)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X23) ),
inference(fof_nnf,[status(thm)],[476]) ).
fof(2770,plain,
! [X24,X25,X26] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X25)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X24)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X24) ),
inference(variable_rename,[status(thm)],[2769]) ).
cnf(2771,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)],[2770]) ).
cnf(2946,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[542]) ).
cnf(3244,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[646]) ).
fof(3406,plain,
! [X35,X36] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X35),X36),
inference(variable_rename,[status(thm)],[701]) ).
cnf(3407,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)],[3406]) ).
cnf(3590,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[766]) ).
cnf(3670,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),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(split_conjunct,[status(thm)],[1324]) ).
fof(3967,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)],[891]) ).
fof(3968,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)],[3967]) ).
cnf(3969,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)],[3968]) ).
fof(4059,plain,
! [X8,X4,X5] :
( ~ class_Rings_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X8) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),X4) ),
inference(fof_nnf,[status(thm)],[919]) ).
fof(4060,plain,
! [X9,X10,X11] :
( ~ class_Rings_Ocomm__semiring__1(X11)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X9),X10) ),
inference(variable_rename,[status(thm)],[4059]) ).
cnf(4061,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)],[4060]) ).
fof(4250,plain,
! [X46,X5] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5)
| c_RealVector_Onorm__class_Onorm(X5,c_RealVector_Oof__real(X5,X46)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X46) ),
inference(fof_nnf,[status(thm)],[984]) ).
fof(4251,plain,
! [X47,X48] :
( ~ class_RealVector_Oreal__normed__algebra__1(X48)
| c_RealVector_Onorm__class_Onorm(X48,c_RealVector_Oof__real(X48,X47)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X47) ),
inference(variable_rename,[status(thm)],[4250]) ).
cnf(4252,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[4251]) ).
fof(4656,plain,
! [X47] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X47) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X47),
inference(variable_rename,[status(thm)],[1117]) ).
cnf(4657,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[4656]) ).
fof(4860,plain,
! [X35,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,X35)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X35,X36) ),
inference(variable_rename,[status(thm)],[1184]) ).
cnf(4861,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)],[4860]) ).
cnf(5030,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
inference(split_conjunct,[status(thm)],[1239]) ).
cnf(5181,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(rw,[status(thm)],[1953,2122,theory(equality)]) ).
cnf(5212,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),
inference(spm,[status(thm)],[3670,4861,theory(equality)]) ).
cnf(5765,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(rw,[status(thm)],[4252,4657,theory(equality)]) ).
cnf(5766,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[5765,2946,theory(equality)]) ).
cnf(7098,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)],[4061,1668,theory(equality)]) ).
cnf(8524,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____) = v_t____
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[3969,5030,theory(equality)]) ).
cnf(8548,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____) = v_t____
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[8524,4657,theory(equality)]) ).
cnf(8549,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____) = v_t____
| $false ),
inference(rw,[status(thm)],[8548,3244,theory(equality)]) ).
cnf(8550,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____) = v_t____,
inference(cn,[status(thm)],[8549,theory(equality)]) ).
cnf(11474,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)) = c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(spm,[status(thm)],[1808,2449,theory(equality)]) ).
cnf(61456,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(spm,[status(thm)],[2771,5212,theory(equality)]) ).
cnf(174210,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_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(rw,[status(thm)],[3670,7098,theory(equality)]) ).
cnf(174218,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(rw,[status(thm)],[61456,7098,theory(equality)]) ).
cnf(490733,negated_conjecture,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(spm,[status(thm)],[11474,174218,theory(equality)]) ).
cnf(491372,negated_conjecture,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))
| ~ class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[490733,5766,theory(equality)]),8550,theory(equality)]),3407,theory(equality)]) ).
cnf(491373,negated_conjecture,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))
| $false
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(rw,[status(thm)],[491372,3590,theory(equality)]) ).
cnf(491374,negated_conjecture,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))
| $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[491373,5766,theory(equality)]),8550,theory(equality)]),3407,theory(equality)]),5181,theory(equality)]) ).
cnf(491375,negated_conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),
inference(cn,[status(thm)],[491374,theory(equality)]) ).
cnf(491691,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[174210,491375,theory(equality)]),5181,theory(equality)]) ).
cnf(491692,negated_conjecture,
$false,
inference(cn,[status(thm)],[491691,theory(equality)]) ).
cnf(491693,negated_conjecture,
$false,
491692,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW261+1.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmp5m420R/sel_SWW261+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmp5m420R/sel_SWW261+1.p_2 with time limit 81
% -prover status Theorem
% Problem SWW261+1.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW261+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW261+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
%
%------------------------------------------------------------------------------