TSTP Solution File: SWW261+1 by SRASS---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : SWW261+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art03.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 : Mon Mar 7 01:35:12 EST 2011
% Result : Theorem 212.56s
% Output : Solution 212.56s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Reading problem from /tmp/SystemOnTPTP25899/SWW261+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% WARNING: TreeLimitedRun lost 0.57s, total lost is 0.57s
% found
% SZS status THM for /tmp/SystemOnTPTP25899/SWW261+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP25899/SWW261+1.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=60 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 60s
% TreeLimitedRun: WC time limit is 120s
% TreeLimitedRun: PID is 26135
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.01 WC
% PrfWatch: 1.50 CPU 2.06 WC
% PrfWatch: 3.28 CPU 4.07 WC
% PrfWatch: 5.27 CPU 6.08 WC
% PrfWatch: 7.26 CPU 8.08 WC
% PrfWatch: 9.25 CPU 10.09 WC
% PrfWatch: 11.25 CPU 12.09 WC
% PrfWatch: 13.23 CPU 14.10 WC
% PrfWatch: 15.22 CPU 16.10 WC
% PrfWatch: 17.21 CPU 18.11 WC
% PrfWatch: 19.20 CPU 20.11 WC
% PrfWatch: 21.19 CPU 22.12 WC
% PrfWatch: 23.18 CPU 24.12 WC
% PrfWatch: 25.17 CPU 26.13 WC
% PrfWatch: 27.16 CPU 28.13 WC
% PrfWatch: 29.15 CPU 30.14 WC
% PrfWatch: 31.14 CPU 32.14 WC
% # Preprocessing time : 0.198 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 33.11 CPU 34.14 WC
% PrfWatch: 35.09 CPU 36.15 WC
% PrfWatch: 37.09 CPU 38.15 WC
% PrfWatch: 39.08 CPU 40.16 WC
% PrfWatch: 41.08 CPU 42.16 WC
% PrfWatch: 43.07 CPU 44.17 WC
% PrfWatch: 45.06 CPU 46.17 WC
% # SZS output start CNFRefutation.
% fof(1, axiom,![X1]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),file('/tmp/SRASS.s.p', fact_real__le__refl)).
% fof(2, axiom,![X1]:![X2]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)),file('/tmp/SRASS.s.p', fact_real__le__linear)).
% fof(3, axiom,![X3]:![X4]:![X5]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X4)=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X3)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X3))),file('/tmp/SRASS.s.p', fact_real__le__trans)).
% fof(4, 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/SRASS.s.p', fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096)).
% fof(6, axiom,![X6]:![X7]:![X8]:(class_RealVector_Oreal__normed__algebra(X8)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7)),c_RealVector_Onorm__class_Onorm(X8,X6)))),file('/tmp/SRASS.s.p', fact_norm__mult__ineq)).
% fof(7, axiom,![X1]:![X2]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),file('/tmp/SRASS.s.p', fact_real__mult__commute)).
% fof(27, axiom,![X20]:![X21]:![X22]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X22)=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X20))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20))),file('/tmp/SRASS.s.p', fact_real__mult__le__cancel__iff2)).
% fof(28, axiom,![X6]:![X7]:![X8]:(class_RealVector_Oreal__normed__div__algebra(X8)=>c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X6))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7)),c_RealVector_Onorm__class_Onorm(X8,X6))),file('/tmp/SRASS.s.p', fact_norm__mult)).
% fof(31, axiom,![X25]:![X26]:![X27]:(~(X27=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X27)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X27)<=>X26=X25)),file('/tmp/SRASS.s.p', fact_real__mult__right__cancel)).
% fof(32, axiom,![X25]:![X26]:![X27]:(~(X27=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X25)<=>X26=X25)),file('/tmp/SRASS.s.p', fact_real__mult__left__cancel)).
% fof(43, axiom,~(v_w____=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),file('/tmp/SRASS.s.p', fact_w0)).
% fof(44, axiom,![X2]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X2)=X2,file('/tmp/SRASS.s.p', fact_real__mult__1)).
% fof(48, axiom,![X7]:![X8]:(class_RealVector_Oreal__normed__vector(X8)=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7))),file('/tmp/SRASS.s.p', fact_norm__ge__zero)).
% fof(54, axiom,![X6]:![X7]:![X30]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X30,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6)))=>X7=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),file('/tmp/SRASS.s.p', fact_rabs__ratiotest__lemma)).
% fof(74, axiom,c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),file('/tmp/SRASS.s.p', fact_t_I1_J)).
% fof(79, axiom,![X20]:![X21]:(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20)<=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)&~(X21=X20))),file('/tmp/SRASS.s.p', fact_real__less__def)).
% fof(81, axiom,![X29]:c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X29)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X29),file('/tmp/SRASS.s.p', fact_real__norm__def)).
% fof(82, axiom,![X21]:![X8]:(class_RealVector_Oreal__normed__vector(X8)=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X21),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<=>X21=c_Groups_Ozero__class_Ozero(X8))),file('/tmp/SRASS.s.p', fact_norm__le__zero__iff)).
% fof(86, axiom,c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),file('/tmp/SRASS.s.p', fact_t_I2_J)).
% fof(89, axiom,![X29]:![X8]:(class_RealVector_Oreal__normed__algebra__1(X8)=>c_RealVector_Onorm__class_Onorm(X8,c_RealVector_Oof__real(X8,X29))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X29)),file('/tmp/SRASS.s.p', fact_norm__of__real)).
% fof(103, axiom,class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra)).
% fof(105, axiom,class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__RealVector_Oreal__normed__vector)).
% fof(106, axiom,class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__RealVector_Oreal__algebra__1)).
% fof(114, axiom,![X24]:![X23]:![X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X24)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X23)),file('/tmp/SRASS.s.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)).
% fof(122, axiom,class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),file('/tmp/SRASS.s.p', arity_Complex__Ocomplex__Rings_Ocomm__semiring__1)).
% fof(133, axiom,class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),file('/tmp/SRASS.s.p', arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1)).
% fof(134, axiom,class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),file('/tmp/SRASS.s.p', arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra)).
% fof(137, axiom,class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),file('/tmp/SRASS.s.p', arity_Complex__Ocomplex__RealVector_Oreal__normed__vector)).
% fof(194, axiom,class_Rings_Olinordered__idom(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__Rings_Olinordered__idom)).
% fof(195, axiom,class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__Rings_Ocomm__semiring__1)).
% fof(206, axiom,class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero)).
% fof(210, axiom,class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1)).
% fof(212, axiom,class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs)).
% fof(214, axiom,class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__Groups_Olinordered__ab__group__add)).
% fof(223, axiom,class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__Groups_Oordered__ab__group__add)).
% fof(226, axiom,class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__Fields_Ofield__inverse__zero)).
% fof(243, axiom,class_Orderings_Opreorder(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__Orderings_Opreorder)).
% fof(249, axiom,class_Groups_Ogroup__add(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__Groups_Ogroup__add)).
% fof(252, axiom,class_Orderings_Oorder(tc_RealDef_Oreal),file('/tmp/SRASS.s.p', arity_RealDef__Oreal__Orderings_Oorder)).
% fof(274, axiom,![X2]:![X6]:![X7]:![X8]:(class_Orderings_Opreorder(X8)=>(c_Orderings_Oord__class_Oless__eq(X8,X7,X6)=>(c_Orderings_Oord__class_Oless__eq(X8,X6,X2)=>c_Orderings_Oord__class_Oless__eq(X8,X7,X2)))),file('/tmp/SRASS.s.p', fact_order__trans)).
% fof(302, axiom,![X8]:(class_RealVector_Oreal__algebra__1(X8)=>c_RealVector_Oof__real(X8,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(X8)),file('/tmp/SRASS.s.p', fact_of__real__1)).
% fof(333, axiom,![X23]:![X8]:(class_Rings_Ocomm__semiring__1(X8)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),c_Groups_Oone__class_Oone(X8))=X23),file('/tmp/SRASS.s.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)).
% fof(383, axiom,![X23]:![X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23)=>c_Groups_Oabs__class_Oabs(X8,X23)=X23)),file('/tmp/SRASS.s.p', fact_abs__of__nonneg)).
% fof(390, axiom,![X21]:![X8]:(class_RealVector_Oreal__normed__vector(X8)=>(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X21))<=>~(X21=c_Groups_Ozero__class_Ozero(X8)))),file('/tmp/SRASS.s.p', fact_zero__less__norm__iff)).
% fof(413, axiom,![X58]:![X21]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X21),X58)<=>(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X58),X21)&c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X58))),file('/tmp/SRASS.s.p', fact_abs__le__interval__iff)).
% fof(421, axiom,![X21]:![X8]:(class_RealVector_Oreal__normed__vector(X8)=>(c_RealVector_Onorm__class_Onorm(X8,X21)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<=>X21=c_Groups_Ozero__class_Ozero(X8))),file('/tmp/SRASS.s.p', fact_norm__eq__zero)).
% fof(514, axiom,![X7]:(~(X7=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X7)),X7)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),file('/tmp/SRASS.s.p', fact_real__mult__inverse__left)).
% fof(558, axiom,![X24]:![X23]:![X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,X23),X24)=>c_Orderings_Oord__class_Oless__eq(X8,X23,X24))),file('/tmp/SRASS.s.p', fact_abs__le__D1)).
% fof(561, axiom,![X23]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X23))&(~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))=>c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23)=X23)),file('/tmp/SRASS.s.p', fact_abs__real__def)).
% fof(570, axiom,![X8]:(class_RealVector_Oreal__normed__algebra__1(X8)=>c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oone__class_Oone(X8))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),file('/tmp/SRASS.s.p', fact_norm__one)).
% fof(578, axiom,![X25]:![X26]:![X8]:(class_Groups_Oordered__ab__group__add(X8)=>(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X25)<=>c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),X26))),file('/tmp/SRASS.s.p', fact_minus__le__iff)).
% fof(616, axiom,![X20]:![X21]:![X8]:(class_Orderings_Opreorder(X8)=>(c_Orderings_Oord__class_Oless(X8,X21,X20)<=>(c_Orderings_Oord__class_Oless__eq(X8,X21,X20)&~(c_Orderings_Oord__class_Oless__eq(X8,X20,X21))))),file('/tmp/SRASS.s.p', fact_less__le__not__le)).
% fof(637, axiom,![X23]:![X8]:(class_Groups_Ogroup__add(X8)=>c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ouminus__class_Ouminus(X8,X23))=X23),file('/tmp/SRASS.s.p', fact_minus__minus)).
% fof(665, axiom,![X23]:![X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>(c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Ozero__class_Ozero(X8))=>c_Groups_Oabs__class_Oabs(X8,X23)=c_Groups_Ouminus__class_Ouminus(X8,X23))),file('/tmp/SRASS.s.p', fact_abs__of__nonpos)).
% fof(687, axiom,![X3]:![X8]:(class_Rings_Olinordered__idom(X8)=>c_Groups_Oabs__class_Oabs(X8,X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X3),c_Groups_Osgn__class_Osgn(X8,X3))),file('/tmp/SRASS.s.p', fact_abs__sgn)).
% fof(757, axiom,![X21]:![X20]:![X8]:(class_Orderings_Oorder(X8)=>(c_Orderings_Oord__class_Oless__eq(X8,X20,X21)=>(c_Orderings_Oord__class_Oless__eq(X8,X21,X20)<=>X21=X20))),file('/tmp/SRASS.s.p', fact_order__antisym__conv)).
% fof(787, axiom,![X23]:![X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X23)=>c_Groups_Oabs__class_Oabs(X8,X23)=X23)),file('/tmp/SRASS.s.p', fact_abs__of__pos)).
% fof(1055, axiom,![X26]:![X8]:(class_Groups_Olinordered__ab__group__add(X8)=>(X26=c_Groups_Ouminus__class_Ouminus(X8,X26)<=>X26=c_Groups_Ozero__class_Ozero(X8))),file('/tmp/SRASS.s.p', fact_equal__neg__zero)).
% fof(1079, axiom,![X21]:![X8]:(class_Fields_Olinordered__field__inverse__zero(X8)=>(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X21))<=>(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X21)&c_Orderings_Oord__class_Oless__eq(X8,X21,c_Groups_Oone__class_Oone(X8))))),file('/tmp/SRASS.s.p', fact_one__le__inverse__iff)).
% fof(1150, axiom,![X21]:![X8]:(class_Fields_Ofield__inverse__zero(X8)=>(c_Rings_Oinverse__class_Oinverse(X8,X21)=c_Groups_Oone__class_Oone(X8)<=>X21=c_Groups_Oone__class_Oone(X8))),file('/tmp/SRASS.s.p', fact_inverse__eq__1__iff)).
% fof(1178, axiom,![X23]:![X8]:(class_Groups_Oordered__ab__group__add__abs(X8)=>c_Groups_Oabs__class_Oabs(X8,c_Groups_Ouminus__class_Ouminus(X8,X23))=c_Groups_Oabs__class_Oabs(X8,X23)),file('/tmp/SRASS.s.p', fact_abs__minus__cancel)).
% fof(1182, axiom,![X23]:![X8]:(class_Fields_Olinordered__field__inverse__zero(X8)=>c_Groups_Oabs__class_Oabs(X8,c_Rings_Oinverse__class_Oinverse(X8,X23))=c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Oabs__class_Oabs(X8,X23))),file('/tmp/SRASS.s.p', fact_abs__inverse)).
% fof(1288, 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/SRASS.s.p', conj_0)).
% 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)],[1288])).
% fof(1313, plain,![X23]:((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=>c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X23))&(~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))=>c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23)=X23)),inference(fof_simplification,[status(thm)],[561,theory(equality)])).
% fof(1319, plain,![X20]:![X21]:![X8]:(class_Orderings_Opreorder(X8)=>(c_Orderings_Oord__class_Oless(X8,X21,X20)<=>(c_Orderings_Oord__class_Oless__eq(X8,X21,X20)&~(c_Orderings_Oord__class_Oless__eq(X8,X20,X21))))),inference(fof_simplification,[status(thm)],[616,theory(equality)])).
% fof(1347, 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)])).
% fof(1348, plain,![X2]:c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X2),inference(variable_rename,[status(thm)],[1])).
% cnf(1349,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1)),inference(split_conjunct,[status(thm)],[1348])).
% fof(1350, plain,![X3]:![X4]:(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X3)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X4)),inference(variable_rename,[status(thm)],[2])).
% cnf(1351,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)],[1350])).
% fof(1352, plain,![X3]:![X4]:![X5]:(~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X4))|(~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X3))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X3))),inference(fof_nnf,[status(thm)],[3])).
% fof(1353, plain,![X6]:![X7]:![X8]:(~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X7))|(~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,X6))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X6))),inference(variable_rename,[status(thm)],[1352])).
% cnf(1354,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)],[1353])).
% cnf(1355,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)],[4])).
% fof(1358, plain,![X6]:![X7]:![X8]:(~(class_RealVector_Oreal__normed__algebra(X8))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7)),c_RealVector_Onorm__class_Onorm(X8,X6)))),inference(fof_nnf,[status(thm)],[6])).
% fof(1359, plain,![X9]:![X10]:![X11]:(~(class_RealVector_Oreal__normed__algebra(X11))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X11,X10)),c_RealVector_Onorm__class_Onorm(X11,X9)))),inference(variable_rename,[status(thm)],[1358])).
% cnf(1360,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)],[1359])).
% fof(1361, plain,![X3]:![X4]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X4),inference(variable_rename,[status(thm)],[7])).
% cnf(1362,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)],[1361])).
% fof(1436, plain,![X20]:![X21]:![X22]:(~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X22))|((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X20)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20))&(~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X20))))),inference(fof_nnf,[status(thm)],[27])).
% fof(1437, plain,![X23]:![X24]:![X25]:(~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X25))|((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X23)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X23))&(~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X23))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X23))))),inference(variable_rename,[status(thm)],[1436])).
% fof(1438, plain,![X23]:![X24]:![X25]:(((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X23)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X23))|~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X25)))&((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X23))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X23)))|~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X25)))),inference(distribute,[status(thm)],[1437])).
% cnf(1439,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)),inference(split_conjunct,[status(thm)],[1438])).
% fof(1441, plain,![X6]:![X7]:![X8]:(~(class_RealVector_Oreal__normed__div__algebra(X8))|c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X6))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7)),c_RealVector_Onorm__class_Onorm(X8,X6))),inference(fof_nnf,[status(thm)],[28])).
% fof(1442, plain,![X9]:![X10]:![X11]:(~(class_RealVector_Oreal__normed__div__algebra(X11))|c_RealVector_Onorm__class_Onorm(X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),X9))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X11,X10)),c_RealVector_Onorm__class_Onorm(X11,X9))),inference(variable_rename,[status(thm)],[1441])).
% cnf(1443,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)],[1442])).
% fof(1449, plain,![X25]:![X26]:![X27]:(X27=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|((~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X27)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X27))|X26=X25)&(~(X26=X25)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X27)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X27)))),inference(fof_nnf,[status(thm)],[31])).
% fof(1450, plain,![X28]:![X29]:![X30]:(X30=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|((~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X29),X30)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X28),X30))|X29=X28)&(~(X29=X28)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X29),X30)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X28),X30)))),inference(variable_rename,[status(thm)],[1449])).
% fof(1451, plain,![X28]:![X29]:![X30]:(((~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X29),X30)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X28),X30))|X29=X28)|X30=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))&((~(X29=X28)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X29),X30)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X28),X30))|X30=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(distribute,[status(thm)],[1450])).
% cnf(1453,plain,(X1=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1)),inference(split_conjunct,[status(thm)],[1451])).
% fof(1454, plain,![X25]:![X26]:![X27]:(X27=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|((~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X25))|X26=X25)&(~(X26=X25)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X27),X25)))),inference(fof_nnf,[status(thm)],[32])).
% fof(1455, plain,![X28]:![X29]:![X30]:(X30=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|((~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X28))|X29=X28)&(~(X29=X28)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X28)))),inference(variable_rename,[status(thm)],[1454])).
% fof(1456, plain,![X28]:![X29]:![X30]:(((~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X28))|X29=X28)|X30=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))&((~(X29=X28)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X28))|X30=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(distribute,[status(thm)],[1455])).
% cnf(1458,plain,(X1=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3)),inference(split_conjunct,[status(thm)],[1456])).
% cnf(1507,plain,(v_w____!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),inference(split_conjunct,[status(thm)],[43])).
% fof(1508, plain,![X3]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X3)=X3,inference(variable_rename,[status(thm)],[44])).
% cnf(1509,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)],[1508])).
% fof(1521, plain,![X7]:![X8]:(~(class_RealVector_Oreal__normed__vector(X8))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7))),inference(fof_nnf,[status(thm)],[48])).
% fof(1522, plain,![X9]:![X10]:(~(class_RealVector_Oreal__normed__vector(X10))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X9))),inference(variable_rename,[status(thm)],[1521])).
% cnf(1523,plain,(c_Orderings_Oord__class_Oless__eq(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(split_conjunct,[status(thm)],[1522])).
% fof(1548, plain,![X6]:![X7]:![X30]:(~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X30,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|(~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6))))|X7=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(fof_nnf,[status(thm)],[54])).
% fof(1549, plain,![X31]:![X32]:![X33]:(~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X33,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|(~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X33),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X31))))|X32=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(variable_rename,[status(thm)],[1548])).
% cnf(1550,plain,(X1=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3)))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(split_conjunct,[status(thm)],[1549])).
% cnf(1624,plain,(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)),inference(split_conjunct,[status(thm)],[74])).
% fof(1639, plain,![X20]:![X21]:((~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20))|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)&~(X21=X20)))&((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20))|X21=X20)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20))),inference(fof_nnf,[status(thm)],[79])).
% fof(1640, plain,![X22]:![X23]:((~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,X22))|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)&~(X23=X22)))&((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22))|X23=X22)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,X22))),inference(variable_rename,[status(thm)],[1639])).
% fof(1641, plain,![X22]:![X23]:(((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)|~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,X22)))&(~(X23=X22)|~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,X22))))&((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22))|X23=X22)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,X22))),inference(distribute,[status(thm)],[1640])).
% cnf(1643,plain,(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)|X1!=X2),inference(split_conjunct,[status(thm)],[1641])).
% fof(1646, plain,![X30]:c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X30)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X30),inference(variable_rename,[status(thm)],[81])).
% cnf(1647,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),inference(split_conjunct,[status(thm)],[1646])).
% fof(1648, plain,![X21]:![X8]:(~(class_RealVector_Oreal__normed__vector(X8))|((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X21),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|X21=c_Groups_Ozero__class_Ozero(X8))&(~(X21=c_Groups_Ozero__class_Ozero(X8))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X21),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),inference(fof_nnf,[status(thm)],[82])).
% fof(1649, plain,![X22]:![X23]:(~(class_RealVector_Oreal__normed__vector(X23))|((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X23,X22),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|X22=c_Groups_Ozero__class_Ozero(X23))&(~(X22=c_Groups_Ozero__class_Ozero(X23))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X23,X22),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),inference(variable_rename,[status(thm)],[1648])).
% fof(1650, plain,![X22]:![X23]:(((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X23,X22),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|X22=c_Groups_Ozero__class_Ozero(X23))|~(class_RealVector_Oreal__normed__vector(X23)))&((~(X22=c_Groups_Ozero__class_Ozero(X23))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X23,X22),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|~(class_RealVector_Oreal__normed__vector(X23)))),inference(distribute,[status(thm)],[1649])).
% cnf(1652,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)],[1650])).
% cnf(1665,plain,(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),inference(split_conjunct,[status(thm)],[86])).
% fof(1670, plain,![X29]:![X8]:(~(class_RealVector_Oreal__normed__algebra__1(X8))|c_RealVector_Onorm__class_Onorm(X8,c_RealVector_Oof__real(X8,X29))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X29)),inference(fof_nnf,[status(thm)],[89])).
% fof(1671, plain,![X30]:![X31]:(~(class_RealVector_Oreal__normed__algebra__1(X31))|c_RealVector_Onorm__class_Onorm(X31,c_RealVector_Oof__real(X31,X30))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X30)),inference(variable_rename,[status(thm)],[1670])).
% cnf(1672,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)],[1671])).
% cnf(1720,plain,(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[103])).
% cnf(1722,plain,(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[105])).
% cnf(1723,plain,(class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[106])).
% fof(1745, plain,![X24]:![X23]:![X8]:(~(class_Rings_Ocomm__semiring__1(X8))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X24)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X24),X23)),inference(fof_nnf,[status(thm)],[114])).
% fof(1746, plain,![X25]:![X26]:![X27]:(~(class_Rings_Ocomm__semiring__1(X27))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X25)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X25),X26)),inference(variable_rename,[status(thm)],[1745])).
% cnf(1747,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)],[1746])).
% cnf(1767,plain,(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),inference(split_conjunct,[status(thm)],[122])).
% cnf(1786,plain,(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)),inference(split_conjunct,[status(thm)],[133])).
% cnf(1787,plain,(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)),inference(split_conjunct,[status(thm)],[134])).
% cnf(1790,plain,(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)),inference(split_conjunct,[status(thm)],[137])).
% cnf(1898,plain,(class_Rings_Olinordered__idom(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[194])).
% cnf(1899,plain,(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[195])).
% cnf(1922,plain,(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[206])).
% cnf(1926,plain,(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[210])).
% cnf(1928,plain,(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[212])).
% cnf(1930,plain,(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[214])).
% cnf(1939,plain,(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[223])).
% cnf(1942,plain,(class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[226])).
% cnf(1959,plain,(class_Orderings_Opreorder(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[243])).
% cnf(1965,plain,(class_Groups_Ogroup__add(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[249])).
% cnf(1968,plain,(class_Orderings_Oorder(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[252])).
% fof(1999, plain,![X2]:![X6]:![X7]:![X8]:(~(class_Orderings_Opreorder(X8))|(~(c_Orderings_Oord__class_Oless__eq(X8,X7,X6))|(~(c_Orderings_Oord__class_Oless__eq(X8,X6,X2))|c_Orderings_Oord__class_Oless__eq(X8,X7,X2)))),inference(fof_nnf,[status(thm)],[274])).
% fof(2000, plain,![X9]:![X10]:![X11]:![X12]:(~(class_Orderings_Opreorder(X12))|(~(c_Orderings_Oord__class_Oless__eq(X12,X11,X10))|(~(c_Orderings_Oord__class_Oless__eq(X12,X10,X9))|c_Orderings_Oord__class_Oless__eq(X12,X11,X9)))),inference(variable_rename,[status(thm)],[1999])).
% cnf(2001,plain,(c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X4,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X4)|~class_Orderings_Opreorder(X1)),inference(split_conjunct,[status(thm)],[2000])).
% fof(2089, plain,![X8]:(~(class_RealVector_Oreal__algebra__1(X8))|c_RealVector_Oof__real(X8,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(X8)),inference(fof_nnf,[status(thm)],[302])).
% fof(2090, plain,![X9]:(~(class_RealVector_Oreal__algebra__1(X9))|c_RealVector_Oof__real(X9,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(X9)),inference(variable_rename,[status(thm)],[2089])).
% cnf(2091,plain,(c_RealVector_Oof__real(X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(X1)|~class_RealVector_Oreal__algebra__1(X1)),inference(split_conjunct,[status(thm)],[2090])).
% fof(2199, plain,![X23]:![X8]:(~(class_Rings_Ocomm__semiring__1(X8))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),c_Groups_Oone__class_Oone(X8))=X23),inference(fof_nnf,[status(thm)],[333])).
% fof(2200, plain,![X24]:![X25]:(~(class_Rings_Ocomm__semiring__1(X25))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),c_Groups_Oone__class_Oone(X25))=X24),inference(variable_rename,[status(thm)],[2199])).
% cnf(2201,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Rings_Ocomm__semiring__1(X1)),inference(split_conjunct,[status(thm)],[2200])).
% fof(2365, plain,![X23]:![X8]:(~(class_Groups_Oordered__ab__group__add__abs(X8))|(~(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23))|c_Groups_Oabs__class_Oabs(X8,X23)=X23)),inference(fof_nnf,[status(thm)],[383])).
% fof(2366, plain,![X24]:![X25]:(~(class_Groups_Oordered__ab__group__add__abs(X25))|(~(c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25),X24))|c_Groups_Oabs__class_Oabs(X25,X24)=X24)),inference(variable_rename,[status(thm)],[2365])).
% cnf(2367,plain,(c_Groups_Oabs__class_Oabs(X1,X2)=X2|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)),inference(split_conjunct,[status(thm)],[2366])).
% fof(2388, plain,![X21]:![X8]:(~(class_RealVector_Oreal__normed__vector(X8))|((~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X21)))|~(X21=c_Groups_Ozero__class_Ozero(X8)))&(X21=c_Groups_Ozero__class_Ozero(X8)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X21))))),inference(fof_nnf,[status(thm)],[390])).
% fof(2389, plain,![X22]:![X23]:(~(class_RealVector_Oreal__normed__vector(X23))|((~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X23,X22)))|~(X22=c_Groups_Ozero__class_Ozero(X23)))&(X22=c_Groups_Ozero__class_Ozero(X23)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X23,X22))))),inference(variable_rename,[status(thm)],[2388])).
% fof(2390, plain,![X22]:![X23]:(((~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X23,X22)))|~(X22=c_Groups_Ozero__class_Ozero(X23)))|~(class_RealVector_Oreal__normed__vector(X23)))&((X22=c_Groups_Ozero__class_Ozero(X23)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X23,X22)))|~(class_RealVector_Oreal__normed__vector(X23)))),inference(distribute,[status(thm)],[2389])).
% cnf(2392,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)],[2390])).
% fof(2470, plain,![X58]:![X21]:((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X21),X58))|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X58),X21)&c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X58)))&((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X58),X21))|~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X58)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X21),X58))),inference(fof_nnf,[status(thm)],[413])).
% fof(2471, plain,![X59]:![X60]:((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X60),X59))|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X59),X60)&c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X60,X59)))&((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X59),X60))|~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X60,X59)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X60),X59))),inference(variable_rename,[status(thm)],[2470])).
% fof(2472, plain,![X59]:![X60]:(((c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X59),X60)|~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X60),X59)))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X60,X59)|~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X60),X59))))&((~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X59),X60))|~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X60,X59)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X60),X59))),inference(distribute,[status(thm)],[2471])).
% cnf(2474,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2)),inference(split_conjunct,[status(thm)],[2472])).
% cnf(2475,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2)),inference(split_conjunct,[status(thm)],[2472])).
% fof(2493, plain,![X21]:![X8]:(~(class_RealVector_Oreal__normed__vector(X8))|((~(c_RealVector_Onorm__class_Onorm(X8,X21)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|X21=c_Groups_Ozero__class_Ozero(X8))&(~(X21=c_Groups_Ozero__class_Ozero(X8))|c_RealVector_Onorm__class_Onorm(X8,X21)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),inference(fof_nnf,[status(thm)],[421])).
% fof(2494, plain,![X22]:![X23]:(~(class_RealVector_Oreal__normed__vector(X23))|((~(c_RealVector_Onorm__class_Onorm(X23,X22)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|X22=c_Groups_Ozero__class_Ozero(X23))&(~(X22=c_Groups_Ozero__class_Ozero(X23))|c_RealVector_Onorm__class_Onorm(X23,X22)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),inference(variable_rename,[status(thm)],[2493])).
% fof(2495, plain,![X22]:![X23]:(((~(c_RealVector_Onorm__class_Onorm(X23,X22)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|X22=c_Groups_Ozero__class_Ozero(X23))|~(class_RealVector_Oreal__normed__vector(X23)))&((~(X22=c_Groups_Ozero__class_Ozero(X23))|c_RealVector_Onorm__class_Onorm(X23,X22)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~(class_RealVector_Oreal__normed__vector(X23)))),inference(distribute,[status(thm)],[2494])).
% cnf(2496,plain,(c_RealVector_Onorm__class_Onorm(X1,X2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~class_RealVector_Oreal__normed__vector(X1)|X2!=c_Groups_Ozero__class_Ozero(X1)),inference(split_conjunct,[status(thm)],[2495])).
% fof(2789, plain,![X7]:(X7=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X7)),X7)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(fof_nnf,[status(thm)],[514])).
% fof(2790, plain,![X8]:(X8=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X8)),X8)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(variable_rename,[status(thm)],[2789])).
% cnf(2791,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X1)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|X1=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(split_conjunct,[status(thm)],[2790])).
% fof(2941, plain,![X24]:![X23]:![X8]:(~(class_Groups_Oordered__ab__group__add__abs(X8))|(~(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,X23),X24))|c_Orderings_Oord__class_Oless__eq(X8,X23,X24))),inference(fof_nnf,[status(thm)],[558])).
% fof(2942, plain,![X25]:![X26]:![X27]:(~(class_Groups_Oordered__ab__group__add__abs(X27))|(~(c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Oabs__class_Oabs(X27,X26),X25))|c_Orderings_Oord__class_Oless__eq(X27,X26,X25))),inference(variable_rename,[status(thm)],[2941])).
% cnf(2943,plain,(c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)|~class_Groups_Oordered__ab__group__add__abs(X1)),inference(split_conjunct,[status(thm)],[2942])).
% fof(2954, plain,![X23]:((~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X23))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23)=X23)),inference(fof_nnf,[status(thm)],[1313])).
% fof(2955, plain,![X24]:((~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X24)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X24))&(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X24)=X24)),inference(variable_rename,[status(thm)],[2954])).
% cnf(2956,plain,(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)=X1|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(split_conjunct,[status(thm)],[2955])).
% fof(2981, plain,![X8]:(~(class_RealVector_Oreal__normed__algebra__1(X8))|c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oone__class_Oone(X8))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(fof_nnf,[status(thm)],[570])).
% fof(2982, plain,![X9]:(~(class_RealVector_Oreal__normed__algebra__1(X9))|c_RealVector_Onorm__class_Onorm(X9,c_Groups_Oone__class_Oone(X9))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(variable_rename,[status(thm)],[2981])).
% cnf(2983,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)],[2982])).
% fof(3007, plain,![X25]:![X26]:![X8]:(~(class_Groups_Oordered__ab__group__add(X8))|((~(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X25))|c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),X26))&(~(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X25),X26))|c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),X25)))),inference(fof_nnf,[status(thm)],[578])).
% fof(3008, plain,![X27]:![X28]:![X29]:(~(class_Groups_Oordered__ab__group__add(X29))|((~(c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),X27))|c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X27),X28))&(~(c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X27),X28))|c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),X27)))),inference(variable_rename,[status(thm)],[3007])).
% fof(3009, plain,![X27]:![X28]:![X29]:(((~(c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),X27))|c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X27),X28))|~(class_Groups_Oordered__ab__group__add(X29)))&((~(c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X27),X28))|c_Orderings_Oord__class_Oless__eq(X29,c_Groups_Ouminus__class_Ouminus(X29,X28),X27))|~(class_Groups_Oordered__ab__group__add(X29)))),inference(distribute,[status(thm)],[3008])).
% cnf(3010,plain,(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)|~class_Groups_Oordered__ab__group__add(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)),inference(split_conjunct,[status(thm)],[3009])).
% fof(3122, plain,![X20]:![X21]:![X8]:(~(class_Orderings_Opreorder(X8))|((~(c_Orderings_Oord__class_Oless(X8,X21,X20))|(c_Orderings_Oord__class_Oless__eq(X8,X21,X20)&~(c_Orderings_Oord__class_Oless__eq(X8,X20,X21))))&((~(c_Orderings_Oord__class_Oless__eq(X8,X21,X20))|c_Orderings_Oord__class_Oless__eq(X8,X20,X21))|c_Orderings_Oord__class_Oless(X8,X21,X20)))),inference(fof_nnf,[status(thm)],[1319])).
% fof(3123, plain,![X22]:![X23]:![X24]:(~(class_Orderings_Opreorder(X24))|((~(c_Orderings_Oord__class_Oless(X24,X23,X22))|(c_Orderings_Oord__class_Oless__eq(X24,X23,X22)&~(c_Orderings_Oord__class_Oless__eq(X24,X22,X23))))&((~(c_Orderings_Oord__class_Oless__eq(X24,X23,X22))|c_Orderings_Oord__class_Oless__eq(X24,X22,X23))|c_Orderings_Oord__class_Oless(X24,X23,X22)))),inference(variable_rename,[status(thm)],[3122])).
% fof(3124, plain,![X22]:![X23]:![X24]:((((c_Orderings_Oord__class_Oless__eq(X24,X23,X22)|~(c_Orderings_Oord__class_Oless(X24,X23,X22)))|~(class_Orderings_Opreorder(X24)))&((~(c_Orderings_Oord__class_Oless__eq(X24,X22,X23))|~(c_Orderings_Oord__class_Oless(X24,X23,X22)))|~(class_Orderings_Opreorder(X24))))&(((~(c_Orderings_Oord__class_Oless__eq(X24,X23,X22))|c_Orderings_Oord__class_Oless__eq(X24,X22,X23))|c_Orderings_Oord__class_Oless(X24,X23,X22))|~(class_Orderings_Opreorder(X24)))),inference(distribute,[status(thm)],[3123])).
% cnf(3126,plain,(~class_Orderings_Opreorder(X1)|~c_Orderings_Oord__class_Oless(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)),inference(split_conjunct,[status(thm)],[3124])).
% fof(3202, plain,![X23]:![X8]:(~(class_Groups_Ogroup__add(X8))|c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ouminus__class_Ouminus(X8,X23))=X23),inference(fof_nnf,[status(thm)],[637])).
% fof(3203, plain,![X24]:![X25]:(~(class_Groups_Ogroup__add(X25))|c_Groups_Ouminus__class_Ouminus(X25,c_Groups_Ouminus__class_Ouminus(X25,X24))=X24),inference(variable_rename,[status(thm)],[3202])).
% cnf(3204,plain,(c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))=X2|~class_Groups_Ogroup__add(X1)),inference(split_conjunct,[status(thm)],[3203])).
% fof(3305, plain,![X23]:![X8]:(~(class_Groups_Oordered__ab__group__add__abs(X8))|(~(c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Ozero__class_Ozero(X8)))|c_Groups_Oabs__class_Oabs(X8,X23)=c_Groups_Ouminus__class_Ouminus(X8,X23))),inference(fof_nnf,[status(thm)],[665])).
% fof(3306, plain,![X24]:![X25]:(~(class_Groups_Oordered__ab__group__add__abs(X25))|(~(c_Orderings_Oord__class_Oless__eq(X25,X24,c_Groups_Ozero__class_Ozero(X25)))|c_Groups_Oabs__class_Oabs(X25,X24)=c_Groups_Ouminus__class_Ouminus(X25,X24))),inference(variable_rename,[status(thm)],[3305])).
% cnf(3307,plain,(c_Groups_Oabs__class_Oabs(X1,X2)=c_Groups_Ouminus__class_Ouminus(X1,X2)|~c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))|~class_Groups_Oordered__ab__group__add__abs(X1)),inference(split_conjunct,[status(thm)],[3306])).
% fof(3374, plain,![X3]:![X8]:(~(class_Rings_Olinordered__idom(X8))|c_Groups_Oabs__class_Oabs(X8,X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X3),c_Groups_Osgn__class_Osgn(X8,X3))),inference(fof_nnf,[status(thm)],[687])).
% fof(3375, plain,![X9]:![X10]:(~(class_Rings_Olinordered__idom(X10))|c_Groups_Oabs__class_Oabs(X10,X9)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),c_Groups_Osgn__class_Osgn(X10,X9))),inference(variable_rename,[status(thm)],[3374])).
% cnf(3376,plain,(c_Groups_Oabs__class_Oabs(X1,X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2))|~class_Rings_Olinordered__idom(X1)),inference(split_conjunct,[status(thm)],[3375])).
% fof(3616, plain,![X21]:![X20]:![X8]:(~(class_Orderings_Oorder(X8))|(~(c_Orderings_Oord__class_Oless__eq(X8,X20,X21))|((~(c_Orderings_Oord__class_Oless__eq(X8,X21,X20))|X21=X20)&(~(X21=X20)|c_Orderings_Oord__class_Oless__eq(X8,X21,X20))))),inference(fof_nnf,[status(thm)],[757])).
% fof(3617, plain,![X22]:![X23]:![X24]:(~(class_Orderings_Oorder(X24))|(~(c_Orderings_Oord__class_Oless__eq(X24,X23,X22))|((~(c_Orderings_Oord__class_Oless__eq(X24,X22,X23))|X22=X23)&(~(X22=X23)|c_Orderings_Oord__class_Oless__eq(X24,X22,X23))))),inference(variable_rename,[status(thm)],[3616])).
% fof(3618, plain,![X22]:![X23]:![X24]:((((~(c_Orderings_Oord__class_Oless__eq(X24,X22,X23))|X22=X23)|~(c_Orderings_Oord__class_Oless__eq(X24,X23,X22)))|~(class_Orderings_Oorder(X24)))&(((~(X22=X23)|c_Orderings_Oord__class_Oless__eq(X24,X22,X23))|~(c_Orderings_Oord__class_Oless__eq(X24,X23,X22)))|~(class_Orderings_Oorder(X24)))),inference(distribute,[status(thm)],[3617])).
% cnf(3620,plain,(X3=X2|~class_Orderings_Oorder(X1)|~c_Orderings_Oord__class_Oless__eq(X1,X2,X3)|~c_Orderings_Oord__class_Oless__eq(X1,X3,X2)),inference(split_conjunct,[status(thm)],[3618])).
% fof(3713, plain,![X23]:![X8]:(~(class_Groups_Oordered__ab__group__add__abs(X8))|(~(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X23))|c_Groups_Oabs__class_Oabs(X8,X23)=X23)),inference(fof_nnf,[status(thm)],[787])).
% fof(3714, plain,![X24]:![X25]:(~(class_Groups_Oordered__ab__group__add__abs(X25))|(~(c_Orderings_Oord__class_Oless(X25,c_Groups_Ozero__class_Ozero(X25),X24))|c_Groups_Oabs__class_Oabs(X25,X24)=X24)),inference(variable_rename,[status(thm)],[3713])).
% cnf(3715,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)],[3714])).
% fof(4415, plain,![X26]:![X8]:(~(class_Groups_Olinordered__ab__group__add(X8))|((~(X26=c_Groups_Ouminus__class_Ouminus(X8,X26))|X26=c_Groups_Ozero__class_Ozero(X8))&(~(X26=c_Groups_Ozero__class_Ozero(X8))|X26=c_Groups_Ouminus__class_Ouminus(X8,X26)))),inference(fof_nnf,[status(thm)],[1055])).
% fof(4416, plain,![X27]:![X28]:(~(class_Groups_Olinordered__ab__group__add(X28))|((~(X27=c_Groups_Ouminus__class_Ouminus(X28,X27))|X27=c_Groups_Ozero__class_Ozero(X28))&(~(X27=c_Groups_Ozero__class_Ozero(X28))|X27=c_Groups_Ouminus__class_Ouminus(X28,X27)))),inference(variable_rename,[status(thm)],[4415])).
% fof(4417, plain,![X27]:![X28]:(((~(X27=c_Groups_Ouminus__class_Ouminus(X28,X27))|X27=c_Groups_Ozero__class_Ozero(X28))|~(class_Groups_Olinordered__ab__group__add(X28)))&((~(X27=c_Groups_Ozero__class_Ozero(X28))|X27=c_Groups_Ouminus__class_Ouminus(X28,X27))|~(class_Groups_Olinordered__ab__group__add(X28)))),inference(distribute,[status(thm)],[4416])).
% cnf(4418,plain,(X2=c_Groups_Ouminus__class_Ouminus(X1,X2)|~class_Groups_Olinordered__ab__group__add(X1)|X2!=c_Groups_Ozero__class_Ozero(X1)),inference(split_conjunct,[status(thm)],[4417])).
% fof(4509, plain,![X21]:![X8]:(~(class_Fields_Olinordered__field__inverse__zero(X8))|((~(c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X21)))|(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X21)&c_Orderings_Oord__class_Oless__eq(X8,X21,c_Groups_Oone__class_Oone(X8))))&((~(c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X21))|~(c_Orderings_Oord__class_Oless__eq(X8,X21,c_Groups_Oone__class_Oone(X8))))|c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X21))))),inference(fof_nnf,[status(thm)],[1079])).
% fof(4510, plain,![X22]:![X23]:(~(class_Fields_Olinordered__field__inverse__zero(X23))|((~(c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Oone__class_Oone(X23),c_Rings_Oinverse__class_Oinverse(X23,X22)))|(c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),X22)&c_Orderings_Oord__class_Oless__eq(X23,X22,c_Groups_Oone__class_Oone(X23))))&((~(c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),X22))|~(c_Orderings_Oord__class_Oless__eq(X23,X22,c_Groups_Oone__class_Oone(X23))))|c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Oone__class_Oone(X23),c_Rings_Oinverse__class_Oinverse(X23,X22))))),inference(variable_rename,[status(thm)],[4509])).
% fof(4511, plain,![X22]:![X23]:((((c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),X22)|~(c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Oone__class_Oone(X23),c_Rings_Oinverse__class_Oinverse(X23,X22))))|~(class_Fields_Olinordered__field__inverse__zero(X23)))&((c_Orderings_Oord__class_Oless__eq(X23,X22,c_Groups_Oone__class_Oone(X23))|~(c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Oone__class_Oone(X23),c_Rings_Oinverse__class_Oinverse(X23,X22))))|~(class_Fields_Olinordered__field__inverse__zero(X23))))&(((~(c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),X22))|~(c_Orderings_Oord__class_Oless__eq(X23,X22,c_Groups_Oone__class_Oone(X23))))|c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Oone__class_Oone(X23),c_Rings_Oinverse__class_Oinverse(X23,X22)))|~(class_Fields_Olinordered__field__inverse__zero(X23)))),inference(distribute,[status(thm)],[4510])).
% cnf(4513,plain,(c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))|~class_Fields_Olinordered__field__inverse__zero(X1)|~c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))),inference(split_conjunct,[status(thm)],[4511])).
% fof(4708, plain,![X21]:![X8]:(~(class_Fields_Ofield__inverse__zero(X8))|((~(c_Rings_Oinverse__class_Oinverse(X8,X21)=c_Groups_Oone__class_Oone(X8))|X21=c_Groups_Oone__class_Oone(X8))&(~(X21=c_Groups_Oone__class_Oone(X8))|c_Rings_Oinverse__class_Oinverse(X8,X21)=c_Groups_Oone__class_Oone(X8)))),inference(fof_nnf,[status(thm)],[1150])).
% fof(4709, plain,![X22]:![X23]:(~(class_Fields_Ofield__inverse__zero(X23))|((~(c_Rings_Oinverse__class_Oinverse(X23,X22)=c_Groups_Oone__class_Oone(X23))|X22=c_Groups_Oone__class_Oone(X23))&(~(X22=c_Groups_Oone__class_Oone(X23))|c_Rings_Oinverse__class_Oinverse(X23,X22)=c_Groups_Oone__class_Oone(X23)))),inference(variable_rename,[status(thm)],[4708])).
% fof(4710, plain,![X22]:![X23]:(((~(c_Rings_Oinverse__class_Oinverse(X23,X22)=c_Groups_Oone__class_Oone(X23))|X22=c_Groups_Oone__class_Oone(X23))|~(class_Fields_Ofield__inverse__zero(X23)))&((~(X22=c_Groups_Oone__class_Oone(X23))|c_Rings_Oinverse__class_Oinverse(X23,X22)=c_Groups_Oone__class_Oone(X23))|~(class_Fields_Ofield__inverse__zero(X23)))),inference(distribute,[status(thm)],[4709])).
% cnf(4711,plain,(c_Rings_Oinverse__class_Oinverse(X1,X2)=c_Groups_Oone__class_Oone(X1)|~class_Fields_Ofield__inverse__zero(X1)|X2!=c_Groups_Oone__class_Oone(X1)),inference(split_conjunct,[status(thm)],[4710])).
% fof(4799, plain,![X23]:![X8]:(~(class_Groups_Oordered__ab__group__add__abs(X8))|c_Groups_Oabs__class_Oabs(X8,c_Groups_Ouminus__class_Ouminus(X8,X23))=c_Groups_Oabs__class_Oabs(X8,X23)),inference(fof_nnf,[status(thm)],[1178])).
% fof(4800, plain,![X24]:![X25]:(~(class_Groups_Oordered__ab__group__add__abs(X25))|c_Groups_Oabs__class_Oabs(X25,c_Groups_Ouminus__class_Ouminus(X25,X24))=c_Groups_Oabs__class_Oabs(X25,X24)),inference(variable_rename,[status(thm)],[4799])).
% cnf(4801,plain,(c_Groups_Oabs__class_Oabs(X1,c_Groups_Ouminus__class_Ouminus(X1,X2))=c_Groups_Oabs__class_Oabs(X1,X2)|~class_Groups_Oordered__ab__group__add__abs(X1)),inference(split_conjunct,[status(thm)],[4800])).
% fof(4815, plain,![X23]:![X8]:(~(class_Fields_Olinordered__field__inverse__zero(X8))|c_Groups_Oabs__class_Oabs(X8,c_Rings_Oinverse__class_Oinverse(X8,X23))=c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Oabs__class_Oabs(X8,X23))),inference(fof_nnf,[status(thm)],[1182])).
% fof(4816, plain,![X24]:![X25]:(~(class_Fields_Olinordered__field__inverse__zero(X25))|c_Groups_Oabs__class_Oabs(X25,c_Rings_Oinverse__class_Oinverse(X25,X24))=c_Rings_Oinverse__class_Oinverse(X25,c_Groups_Oabs__class_Oabs(X25,X24))),inference(variable_rename,[status(thm)],[4815])).
% cnf(4817,plain,(c_Groups_Oabs__class_Oabs(X1,c_Rings_Oinverse__class_Oinverse(X1,X2))=c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oabs__class_Oabs(X1,X2))|~class_Fields_Olinordered__field__inverse__zero(X1)),inference(split_conjunct,[status(thm)],[4816])).
% cnf(5180,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)],[1347])).
% cnf(5181,plain,(~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1)),inference(er,[status(thm)],[1643,theory(equality)])).
% cnf(5182,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)],[1355,1509,theory(equality)])).
% cnf(5227,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),X2)),inference(rw,[status(thm)],[2474,1647,theory(equality)])).
% cnf(5228,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1))),inference(spm,[status(thm)],[5227,1349,theory(equality)])).
% cnf(5240,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)],[5180,1351,theory(equality)])).
% cnf(5259,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),inference(spm,[status(thm)],[1523,1790,theory(equality)])).
% cnf(5292,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)),inference(spm,[status(thm)],[1354,1351,theory(equality)])).
% cnf(5312,plain,(c_RealVector_Oof__real(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(spm,[status(thm)],[2091,1723,theory(equality)])).
% cnf(5320,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(spm,[status(thm)],[2983,1926,theory(equality)])).
% cnf(5329,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2),X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),X2)),inference(rw,[status(thm)],[2475,1647,theory(equality)])).
% cnf(5330,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)),X1)),inference(spm,[status(thm)],[5329,1349,theory(equality)])).
% cnf(5340,plain,(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)=X1|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X1),inference(spm,[status(thm)],[4418,1930,theory(equality)])).
% cnf(5398,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=X1|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(rw,[status(thm)],[2956,1647,theory(equality)])).
% cnf(5402,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)),inference(spm,[status(thm)],[5329,5398,theory(equality)])).
% cnf(5503,plain,(~class_Orderings_Opreorder(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_t____)),inference(spm,[status(thm)],[3126,1665,theory(equality)])).
% cnf(5522,plain,($false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_t____)),inference(rw,[status(thm)],[5503,1959,theory(equality)])).
% cnf(5523,plain,(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_t____)),inference(cn,[status(thm)],[5522,theory(equality)])).
% cnf(5717,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=X1),inference(spm,[status(thm)],[2496,1722,theory(equality)])).
% cnf(5737,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)],[1672,1647,theory(equality)])).
% cnf(5738,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)],[5737,1786,theory(equality)])).
% cnf(5739,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Oof__real(tc_RealDef_Oreal,X1))=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)),inference(spm,[status(thm)],[5737,1926,theory(equality)])).
% cnf(5769,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)],[2201,1899,theory(equality)])).
% cnf(5834,plain,(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(rw,[status(thm)],[2791,1362,theory(equality)])).
% cnf(6230,plain,(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))=X1),inference(spm,[status(thm)],[3204,1965,theory(equality)])).
% cnf(6348,plain,(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|X2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1)!=X1),inference(spm,[status(thm)],[1453,1509,theory(equality)])).
% cnf(6512,plain,(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=X1),inference(spm,[status(thm)],[4711,1942,theory(equality)])).
% cnf(6763,plain,(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[1550,1647,theory(equality)]),1647,theory(equality)])).
% cnf(6771,plain,(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=X1|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)),X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(spm,[status(thm)],[6763,1362,theory(equality)])).
% cnf(7350,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)],[1747,1767,theory(equality)])).
% cnf(8161,plain,(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)),inference(spm,[status(thm)],[1647,4801,theory(equality)])).
% cnf(8177,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)),inference(rw,[status(thm)],[8161,1647,theory(equality)])).
% cnf(8178,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|$false),inference(rw,[status(thm)],[8177,1928,theory(equality)])).
% cnf(8179,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),inference(cn,[status(thm)],[8178,theory(equality)])).
% cnf(8250,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)],[3715,1624,theory(equality)])).
% cnf(8285,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)],[8250,1647,theory(equality)])).
% cnf(8286,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____)=v_t____|$false),inference(rw,[status(thm)],[8285,1928,theory(equality)])).
% cnf(8287,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____)=v_t____),inference(cn,[status(thm)],[8286,theory(equality)])).
% cnf(11296,plain,(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1))),inference(spm,[status(thm)],[4817,1922,theory(equality)])).
% cnf(11297,plain,(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1))),inference(rw,[status(thm)],[11296,1647,theory(equality)])).
% cnf(11298,plain,(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1))=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1))),inference(rw,[status(thm)],[11297,1647,theory(equality)])).
% cnf(12772,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2))=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))),inference(spm,[status(thm)],[1443,1720,theory(equality)])).
% cnf(13685,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))|~class_Orderings_Oorder(tc_RealDef_Oreal)|~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)],[3620,1360,theory(equality)])).
% cnf(13744,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))|$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(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(rw,[status(thm)],[13685,1968,theory(equality)])).
% cnf(13745,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(cn,[status(thm)],[13744,theory(equality)])).
% cnf(60495,plain,(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=v_t____|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)|~class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)),inference(spm,[status(thm)],[2392,8287,theory(equality)])).
% cnf(60541,plain,(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=v_t____|$false|~class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)),inference(rw,[status(thm)],[60495,1624,theory(equality)])).
% cnf(60542,plain,(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=v_t____|$false|$false),inference(rw,[status(thm)],[60541,1722,theory(equality)])).
% cnf(60543,plain,(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=v_t____),inference(cn,[status(thm)],[60542,theory(equality)])).
% cnf(60934,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|~class_Orderings_Opreorder(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)))),inference(spm,[status(thm)],[2001,5182,theory(equality)])).
% cnf(60945,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|$false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)))),inference(rw,[status(thm)],[60934,1959,theory(equality)])).
% cnf(60946,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)))),inference(cn,[status(thm)],[60945,theory(equality)])).
% cnf(62410,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Oof__real(tc_RealDef_Oreal,X1),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1))),inference(spm,[status(thm)],[5228,5739,theory(equality)])).
% cnf(62681,plain,(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)|~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)),inference(spm,[status(thm)],[2367,5259,theory(equality)])).
% cnf(62708,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)|~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)),inference(rw,[status(thm)],[62681,1647,theory(equality)])).
% cnf(62709,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)|$false),inference(rw,[status(thm)],[62708,1928,theory(equality)])).
% cnf(62710,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),inference(cn,[status(thm)],[62709,theory(equality)])).
% cnf(67698,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),inference(spm,[status(thm)],[60946,5330,theory(equality)])).
% cnf(67717,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))))|~class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)),inference(spm,[status(thm)],[3010,67698,theory(equality)])).
% cnf(67739,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))))|$false),inference(rw,[status(thm)],[67717,1939,theory(equality)])).
% cnf(67740,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(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____))))),inference(cn,[status(thm)],[67739,theory(equality)])).
% cnf(70270,plain,(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____)=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____))),inference(spm,[status(thm)],[11298,8287,theory(equality)])).
% cnf(83613,plain,(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_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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),inference(spm,[status(thm)],[67740,5340,theory(equality)])).
% cnf(83779,plain,(c_RealVector_Onorm__class_Onorm(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____)|~class_Orderings_Oorder(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(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____))|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(spm,[status(thm)],[3620,83613,theory(equality)])).
% cnf(83792,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(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____))),inference(spm,[status(thm)],[83613,5717,theory(equality)])).
% cnf(83796,plain,(c_RealVector_Onorm__class_Onorm(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____)|$false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(rw,[status(thm)],[83779,1968,theory(equality)])).
% cnf(83797,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(cn,[status(thm)],[83796,theory(equality)])).
% cnf(85760,plain,(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=v_w____|~class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(spm,[status(thm)],[1652,83792,theory(equality)])).
% cnf(85785,plain,(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=v_w____|$false|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(rw,[status(thm)],[85760,1790,theory(equality)])).
% cnf(85786,plain,(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=v_w____|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(cn,[status(thm)],[85785,theory(equality)])).
% cnf(85787,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(sr,[status(thm)],[85786,1507,theory(equality)])).
% cnf(89657,plain,(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)),inference(spm,[status(thm)],[3307,5402,theory(equality)])).
% cnf(89699,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[89657,1647,theory(equality)]),8179,theory(equality)])).
% cnf(89700,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=X1|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)),inference(rw,[status(thm)],[89699,6230,theory(equality)])).
% cnf(89701,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=X1|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|$false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)),inference(rw,[status(thm)],[89700,1928,theory(equality)])).
% cnf(89702,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=X1|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)),inference(cn,[status(thm)],[89701,theory(equality)])).
% cnf(89703,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)=X1|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)),inference(sr,[status(thm)],[89702,5181,theory(equality)])).
% cnf(100064,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1))=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1))),inference(spm,[status(thm)],[12772,8287,theory(equality)])).
% cnf(100875,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)))|~class_Rings_Olinordered__idom(tc_RealDef_Oreal)),inference(spm,[status(thm)],[100064,3376,theory(equality)])).
% cnf(100876,plain,(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____)))|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=v_t____),inference(spm,[status(thm)],[100064,5834,theory(equality)])).
% cnf(100887,plain,(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____)|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(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)],[inference(rw,[status(thm)],[83797,100064,theory(equality)]),62710,theory(equality)])).
% cnf(100888,plain,(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____)|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|$false),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[100887,100064,theory(equality)]),62710,theory(equality)]),5182,theory(equality)])).
% cnf(100889,plain,(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____)|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(cn,[status(thm)],[100888,theory(equality)])).
% cnf(101017,plain,(v_t____=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)))|~class_Rings_Olinordered__idom(tc_RealDef_Oreal)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[100875,1647,theory(equality)]),8287,theory(equality)]),8287,theory(equality)])).
% cnf(101018,plain,(v_t____=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)))|$false),inference(rw,[status(thm)],[101017,1898,theory(equality)])).
% cnf(101019,plain,(v_t____=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)))),inference(cn,[status(thm)],[101018,theory(equality)])).
% cnf(101020,plain,(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____)))|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=v_t____),inference(rw,[status(thm)],[100876,5320,theory(equality)])).
% cnf(101021,plain,(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____))|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=v_t____),inference(rw,[status(thm)],[101020,70270,theory(equality)])).
% cnf(101022,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(sr,[status(thm)],[101021,60543,theory(equality)])).
% cnf(101659,plain,(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(spm,[status(thm)],[85787,100889,theory(equality)])).
% cnf(102086,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1),v_t____)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)))),inference(spm,[status(thm)],[1439,101019,theory(equality)])).
% cnf(102149,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____))=v_t____|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____))),inference(spm,[status(thm)],[101019,89703,theory(equality)])).
% cnf(102347,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1),v_t____)|$false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)))),inference(rw,[status(thm)],[102086,1624,theory(equality)])).
% cnf(102348,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1),v_t____)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)))),inference(cn,[status(thm)],[102347,theory(equality)])).
% cnf(112869,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Oof__real(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____))),v_t____)),inference(spm,[status(thm)],[102348,62410,theory(equality)])).
% cnf(112982,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_t____)|~class_Orderings_Opreorder(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Oof__real(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____))))),inference(spm,[status(thm)],[2001,112869,theory(equality)])).
% cnf(112998,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_t____)|$false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Oof__real(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____))))),inference(rw,[status(thm)],[112982,1959,theory(equality)])).
% cnf(112999,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,v_t____)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Oof__real(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____))))),inference(cn,[status(thm)],[112998,theory(equality)])).
% cnf(133710,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1),v_t____)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Oof__real(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)))),inference(spm,[status(thm)],[112999,1439,theory(equality)])).
% cnf(133756,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1),v_t____)|$false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Oof__real(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)))),inference(rw,[status(thm)],[133710,1624,theory(equality)])).
% cnf(133757,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1),v_t____)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Oof__real(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)))),inference(cn,[status(thm)],[133756,theory(equality)])).
% cnf(135400,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=X1),inference(spm,[status(thm)],[4513,6512,theory(equality)])).
% cnf(135508,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|$false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=X1),inference(rw,[status(thm)],[135400,1922,theory(equality)])).
% cnf(135509,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|$false|$false|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=X1),inference(rw,[status(thm)],[135508,1349,theory(equality)])).
% cnf(135510,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=X1),inference(cn,[status(thm)],[135509,theory(equality)])).
% cnf(263669,plain,(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=v_t____|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)),X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(spm,[status(thm)],[6771,8287,theory(equality)])).
% cnf(263747,plain,(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)),X2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(sr,[status(thm)],[263669,60543,theory(equality)])).
% cnf(263911,plain,(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(spm,[status(thm)],[263747,8287,theory(equality)])).
% cnf(269322,plain,(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_t____))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~class_Rings_Olinordered__idom(tc_RealDef_Oreal)),inference(spm,[status(thm)],[263911,3376,theory(equality)])).
% cnf(269403,plain,($false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|~class_Rings_Olinordered__idom(tc_RealDef_Oreal)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[269322,1647,theory(equality)]),8287,theory(equality)]),1349,theory(equality)])).
% cnf(269404,plain,($false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|$false),inference(rw,[status(thm)],[269403,1898,theory(equality)])).
% cnf(269405,plain,(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),inference(cn,[status(thm)],[269404,theory(equality)])).
% cnf(269440,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____))),inference(spm,[status(thm)],[269405,1351,theory(equality)])).
% cnf(269498,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____))=v_t____|$false),inference(rw,[status(thm)],[102149,269440,theory(equality)])).
% cnf(269499,plain,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____))=v_t____),inference(cn,[status(thm)],[269498,theory(equality)])).
% cnf(270066,plain,(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=v_t____|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)=X1|v_t____!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1)),inference(spm,[status(thm)],[1458,269499,theory(equality)])).
% cnf(270323,plain,(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1)!=v_t____),inference(sr,[status(thm)],[270066,60543,theory(equality)])).
% cnf(290333,plain,(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_t____)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(spm,[status(thm)],[270323,5769,theory(equality)])).
% cnf(290581,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1),v_t____)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[133757,290333,theory(equality)]),5312,theory(equality)])).
% cnf(297061,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),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))))),inference(rw,[status(thm)],[5240,7350,theory(equality)])).
% cnf(297067,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)],[5180,7350,theory(equality)])).
% cnf(297450,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,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),X1)),inference(spm,[status(thm)],[5292,297061,theory(equality)])).
% cnf(356566,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),inference(spm,[status(thm)],[2943,135510,theory(equality)])).
% cnf(356627,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|$false|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),inference(rw,[status(thm)],[356566,1928,theory(equality)])).
% cnf(356628,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|$false|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)),inference(rw,[status(thm)],[356627,1647,theory(equality)])).
% cnf(356629,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)),inference(cn,[status(thm)],[356628,theory(equality)])).
% cnf(357918,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),X1),v_t____)|c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(spm,[status(thm)],[290581,356629,theory(equality)])).
% cnf(358114,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____)),v_t____)|c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(spm,[status(thm)],[357918,70270,theory(equality)])).
% cnf(358242,plain,(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_t____)|c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(rw,[status(thm)],[358114,101022,theory(equality)])).
% cnf(358243,plain,(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),inference(sr,[status(thm)],[358242,5523,theory(equality)])).
% cnf(358247,plain,(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)!=v_t____),inference(spm,[status(thm)],[358243,6512,theory(equality)])).
% cnf(984174,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____)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),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____))))|~class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)),inference(spm,[status(thm)],[13745,297450,theory(equality)])).
% cnf(986382,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____)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),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____))))|~class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[984174,5738,theory(equality)]),8287,theory(equality)]),1362,theory(equality)])).
% cnf(986383,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____)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)))|~class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[986382,5738,theory(equality)]),8287,theory(equality)]),1362,theory(equality)])).
% cnf(986384,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____)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)))|$false),inference(rw,[status(thm)],[986383,1787,theory(equality)])).
% cnf(986385,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____)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)))),inference(cn,[status(thm)],[986384,theory(equality)])).
% cnf(986393,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,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____)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|~class_Orderings_Oorder(tc_RealDef_Oreal)|~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(spm,[status(thm)],[3620,986385,theory(equality)])).
% cnf(986422,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,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____)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|$false|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),inference(rw,[status(thm)],[986393,1968,theory(equality)])).
% cnf(986423,negated_conjecture,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|$false|$false),inference(rw,[status(thm)],[986422,5182,theory(equality)])).
% cnf(986424,negated_conjecture,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)|c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),inference(cn,[status(thm)],[986423,theory(equality)])).
% cnf(986622,negated_conjecture,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),inference(spm,[status(thm)],[297067,986424,theory(equality)])).
% cnf(986853,negated_conjecture,(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)|$false),inference(rw,[status(thm)],[986622,5182,theory(equality)])).
% cnf(986854,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,v_w____)),inference(cn,[status(thm)],[986853,theory(equality)])).
% cnf(986914,negated_conjecture,(v_t____=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),inference(spm,[status(thm)],[6348,986854,theory(equality)])).
% cnf(987484,negated_conjecture,(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),inference(sr,[status(thm)],[986914,358247,theory(equality)])).
% cnf(987485,negated_conjecture,($false),inference(sr,[status(thm)],[987484,101659,theory(equality)])).
% cnf(987486,negated_conjecture,($false),987485,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 48893
% # ...of these trivial : 1989
% # ...subsumed : 34862
% # ...remaining for further processing: 12042
% # Other redundant clauses eliminated : 484
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 394
% # Backward-rewritten : 2285
% # Generated clauses : 495899
% # ...of the previous two non-trivial : 414530
% # Contextual simplify-reflections : 4185
% # Paramodulations : 495284
% # Factorizations : 21
% # Equation resolutions : 590
% # Current number of processed clauses: 9325
% # Positive orientable unit clauses: 2852
% # Positive unorientable unit clauses: 14
% # Negative unit clauses : 2685
% # Non-unit-clauses : 3774
% # Current number of unprocessed clauses: 300987
% # ...number of literals in the above : 747998
% # Clause-clause subsumption calls (NU) : 480464
% # Rec. Clause-clause subsumption calls : 441307
% # Unit Clause-clause subsumption calls : 228573
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 437943
% # Indexed BW rewrite successes : 1485
% # Backwards rewriting index: 3260 leaves, 3.20+/-20.101 terms/leaf
% # Paramod-from index: 1199 leaves, 3.30+/-17.210 terms/leaf
% # Paramod-into index: 3087 leaves, 3.11+/-20.232 terms/leaf
% # -------------------------------------------------
% # User time : 31.951 s
% # System time : 0.792 s
% # Total time : 32.743 s
% # Maximum resident set size: 0 pages
% PrfWatch: 45.37 CPU 46.51 WC
% FINAL PrfWatch: 45.37 CPU 46.51 WC
% SZS output end Solution for /tmp/SystemOnTPTP25899/SWW261+1.tptp
%
%------------------------------------------------------------------------------