TSTP Solution File: SWW265+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWW265+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:38:40 EDT 2023
% Result : Theorem 215.76s 29.40s
% Output : CNFRefutation 215.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 87 ( 29 unt; 0 def)
% Number of atoms : 204 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 200 ( 83 ~; 89 |; 2 &)
% ( 6 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 136 ( 1 sgn; 99 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_w0) ).
fof(f20,axiom,
! [X13,X14,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X13))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(f23,axiom,
! [X14,X9] :
( class_RealVector_Oreal__normed__vector(X9)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X9,X14))
<=> c_Groups_Ozero__class_Ozero(X9) != X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(f36,axiom,
! [X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X25)
=> X24 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(f37,axiom,
! [X26,X27,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,X27)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27,X26)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(f38,axiom,
! [X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X25)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(f40,axiom,
! [X28,X29,X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X29)),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X29),X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(f41,axiom,
! [X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X24),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(f60,axiom,
! [X4,X10,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X10)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X10),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(f75,axiom,
! [X7,X5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(f1142,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(f1192,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1289,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),v_m____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f1290,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(f1291,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
inference(negated_conjecture,[],[f1290]) ).
fof(f1300,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(rectify,[],[f20]) ).
fof(f1303,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 ) ),
inference(rectify,[],[f23]) ).
fof(f1314,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
=> X0 = X1 ) ),
inference(rectify,[],[f36]) ).
fof(f1315,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ) ),
inference(rectify,[],[f37]) ).
fof(f1316,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(rectify,[],[f38]) ).
fof(f1318,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0)),
inference(rectify,[],[f40]) ).
fof(f1319,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
inference(rectify,[],[f41]) ).
fof(f1337,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
inference(rectify,[],[f60]) ).
fof(f1352,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0)) ) ),
inference(rectify,[],[f75]) ).
fof(f2298,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
inference(flattening,[],[f1291]) ).
fof(f2312,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(ennf_transformation,[],[f1300]) ).
fof(f2316,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1303]) ).
fof(f2329,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f1314]) ).
fof(f2330,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(flattening,[],[f2329]) ).
fof(f2331,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(ennf_transformation,[],[f1315]) ).
fof(f2332,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(flattening,[],[f2331]) ).
fof(f2351,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1337]) ).
fof(f2352,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2351]) ).
fof(f2376,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(ennf_transformation,[],[f1352]) ).
fof(f2377,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(flattening,[],[f2376]) ).
fof(f3427,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(nnf_transformation,[],[f2312]) ).
fof(f3428,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0 )
& ( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(nnf_transformation,[],[f2316]) ).
fof(f3788,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f6]) ).
fof(f3806,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(cnf_transformation,[],[f3427]) ).
fof(f3807,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(cnf_transformation,[],[f3427]) ).
fof(f3811,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f3428]) ).
fof(f3828,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2330]) ).
fof(f3829,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(cnf_transformation,[],[f2332]) ).
fof(f3830,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f1316]) ).
fof(f3832,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0)),
inference(cnf_transformation,[],[f1318]) ).
fof(f3833,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
inference(cnf_transformation,[],[f1319]) ).
fof(f3861,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2352]) ).
fof(f3881,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(cnf_transformation,[],[f2377]) ).
fof(f5279,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1142]) ).
fof(f5329,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1192]) ).
fof(f5426,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),v_m____),
inference(cnf_transformation,[],[f1289]) ).
fof(f5427,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
inference(cnf_transformation,[],[f2298]) ).
cnf(c_54,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_w____,
inference(cnf_transformation,[],[f3788]) ).
cnf(c_72,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2)) ),
inference(cnf_transformation,[],[f3807]) ).
cnf(c_73,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(cnf_transformation,[],[f3806]) ).
cnf(c_76,plain,
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Groups_Ozero__class_Ozero(X0) = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X1)) ),
inference(cnf_transformation,[],[f3811]) ).
cnf(c_94,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f3828]) ).
cnf(c_95,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(cnf_transformation,[],[f3829]) ).
cnf(c_96,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3830]) ).
cnf(c_98,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),
inference(cnf_transformation,[],[f3832]) ).
cnf(c_99,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0),
inference(cnf_transformation,[],[f3833]) ).
cnf(c_124,plain,
( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Rings_Olinordered__semidom(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) ),
inference(cnf_transformation,[],[f3861]) ).
cnf(c_143,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0)) ),
inference(cnf_transformation,[],[f3881]) ).
cnf(c_1505,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f5279]) ).
cnf(c_1555,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f5329]) ).
cnf(c_1652,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),v_m____),
inference(cnf_transformation,[],[f5426]) ).
cnf(c_1653,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
inference(cnf_transformation,[],[f5427]) ).
cnf(c_3415,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_4040,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)))),
inference(demodulation,[status(thm)],[c_1653,c_98,c_99]) ).
cnf(c_8551,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
inference(superposition,[status(thm)],[c_96,c_4040]) ).
cnf(c_8839,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) ),
inference(superposition,[status(thm)],[c_8551,c_95]) ).
cnf(c_9115,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) ),
inference(superposition,[status(thm)],[c_8839,c_95]) ).
cnf(c_11837,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),X1) ),
inference(superposition,[status(thm)],[c_96,c_9115]) ).
cnf(c_16887,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2)) ),
inference(superposition,[status(thm)],[c_72,c_11837]) ).
cnf(c_20568,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),v_m____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_21907,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))) ),
inference(instantiation,[status(thm)],[c_143]) ).
cnf(c_232405,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))) ),
inference(superposition,[status(thm)],[c_8551,c_16887]) ).
cnf(c_288096,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))) ),
inference(superposition,[status(thm)],[c_232405,c_73]) ).
cnf(c_290546,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))) ),
inference(superposition,[status(thm)],[c_288096,c_94]) ).
cnf(c_292564,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))) ),
inference(superposition,[status(thm)],[c_72,c_290546]) ).
cnf(c_294090,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)) ),
inference(instantiation,[status(thm)],[c_124]) ).
cnf(c_294200,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(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____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) ),
inference(superposition,[status(thm)],[c_96,c_292564]) ).
cnf(c_294202,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(global_subsumption_just,[status(thm)],[c_294200,c_1505,c_1652,c_1653,c_20568,c_21907,c_294090]) ).
cnf(c_438506,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_442340,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_438506,c_1555,c_3415]) ).
cnf(c_442343,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_w____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(instantiation,[status(thm)],[c_442340]) ).
cnf(c_442344,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_442343,c_294202,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW265+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 19:10:44 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 215.76/29.40 % SZS status Started for theBenchmark.p
% 215.76/29.40 % SZS status Theorem for theBenchmark.p
% 215.76/29.40
% 215.76/29.40 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 215.76/29.40
% 215.76/29.40 ------ iProver source info
% 215.76/29.40
% 215.76/29.40 git: date: 2023-05-31 18:12:56 +0000
% 215.76/29.40 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 215.76/29.40 git: non_committed_changes: false
% 215.76/29.40 git: last_make_outside_of_git: false
% 215.76/29.40
% 215.76/29.40 ------ Parsing...
% 215.76/29.40 ------ Clausification by vclausify_rel & Parsing by iProver...
% 215.76/29.40
% 215.76/29.40 ------ Preprocessing... sf_s rm: 50 0s sf_e sf_s rm: 5 0s sf_e
% 215.76/29.40
% 215.76/29.40 ------ Preprocessing...
% 215.76/29.40
% 215.76/29.40 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 215.76/29.40 ------ Proving...
% 215.76/29.40 ------ Problem Properties
% 215.76/29.40
% 215.76/29.40
% 215.76/29.40 clauses 1361
% 215.76/29.40 conjectures 1
% 215.76/29.40 EPR 266
% 215.76/29.40 Horn 1258
% 215.76/29.40 unary 405
% 215.76/29.40 binary 491
% 215.76/29.40 lits 3021
% 215.76/29.40 lits eq 690
% 215.76/29.40 fd_pure 0
% 215.76/29.40 fd_pseudo 0
% 215.76/29.40 fd_cond 30
% 215.76/29.40 fd_pseudo_cond 118
% 215.76/29.40 AC symbols 0
% 215.76/29.40
% 215.76/29.40 ------ Input Options Time Limit: Unbounded
% 215.76/29.40
% 215.76/29.40
% 215.76/29.40 ------
% 215.76/29.40 Current options:
% 215.76/29.40 ------
% 215.76/29.40
% 215.76/29.40
% 215.76/29.40
% 215.76/29.40
% 215.76/29.40 ------ Proving...
% 215.76/29.40
% 215.76/29.40
% 215.76/29.40 % SZS status Theorem for theBenchmark.p
% 215.76/29.40
% 215.76/29.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 215.76/29.40
% 215.76/29.41
%------------------------------------------------------------------------------