TSTP Solution File: SWW203+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW203+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 : Sun May 5 11:34:40 EDT 2024
% Result : Theorem 93.67s 13.74s
% Output : Refutation 93.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 45
% Syntax : Number of formulae : 216 ( 188 unt; 0 def)
% Number of atoms : 244 ( 177 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 49 ( 21 ~; 14 |; 0 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 7 con; 0-3 aty)
% Number of variables : 254 ( 254 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f372677,plain,
$false,
inference(resolution,[],[f139215,f5684]) ).
fof(f5684,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))))),
inference(backward_demodulation,[],[f5681,f4075]) ).
fof(f4075,plain,
! [X0,X1] : c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X1),c_Complex_ORe(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] : c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X1),c_Complex_ORe(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Re_Odiff) ).
fof(f5681,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))))),
inference(backward_demodulation,[],[f5649,f4073]) ).
fof(f4073,plain,
! [X0,X1] : c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),c_Complex_OIm(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] : c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),c_Complex_OIm(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Im_Odiff) ).
fof(f5649,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(backward_demodulation,[],[f5630,f5648]) ).
fof(f5648,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
inference(forward_demodulation,[],[f3968,f3878]) ).
fof(f3878,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f523]) ).
fof(f523,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
fof(f3968,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(cnf_transformation,[],[f1289]) ).
fof(f1289,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(rectify,[],[f182]) ).
fof(f182,axiom,
! [X16] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X16) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(X16),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(X16),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cmod__def) ).
fof(f5630,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(backward_demodulation,[],[f3653,f3878]) ).
fof(f3653,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(cnf_transformation,[],[f1204]) ).
fof(f1204,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(flattening,[],[f1203]) ).
fof(f1203,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(negated_conjecture,[],[f1202]) ).
fof(f1202,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f139215,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))))),
inference(backward_demodulation,[],[f9590,f139214]) ).
fof(f139214,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)),
inference(forward_demodulation,[],[f139059,f9585]) ).
fof(f9585,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X0)),
inference(resolution,[],[f4141,f3663]) ).
fof(f3663,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1163]) ).
fof(f1163,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f4141,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X0)) ),
inference(cnf_transformation,[],[f2178]) ).
fof(f2178,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X0))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(ennf_transformation,[],[f1405]) ).
fof(f1405,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra__1(X1)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X0)) ),
inference(rectify,[],[f550]) ).
fof(f550,axiom,
! [X43,X6] :
( class_RealVector_Oreal__normed__algebra__1(X6)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X43) = c_RealVector_Onorm__class_Onorm(X6,c_RealVector_Oof__real(X6,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__of__real) ).
fof(f139059,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X0)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)),
inference(superposition,[],[f139004,f21408]) ).
fof(f21408,plain,
! [X0] : c_RealVector_Oof__real(tc_Complex_Ocomplex,X0) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0),c_Complex_Oii),
inference(superposition,[],[f21340,f3955]) ).
fof(f3955,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_RealVector_Oof__real(tc_Complex_Ocomplex,X0)) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0),
inference(cnf_transformation,[],[f1276]) ).
fof(f1276,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_RealVector_Oof__real(tc_Complex_Ocomplex,X0)) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0),
inference(rectify,[],[f673]) ).
fof(f673,axiom,
! [X43] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_RealVector_Oof__real(tc_Complex_Ocomplex,X43)) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_i__complex__of__real) ).
fof(f21340,plain,
! [X0] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X0),c_Complex_Oii) = X0,
inference(forward_demodulation,[],[f21312,f6251]) ).
fof(f6251,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = X0,
inference(resolution,[],[f4240,f3758]) ).
fof(f3758,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1190]) ).
fof(f1190,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(f4240,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2258]) ).
fof(f2258,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1476]) ).
fof(f1476,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
inference(rectify,[],[f584]) ).
fof(f584,axiom,
! [X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Ouminus__class_Ouminus(X6,X5)) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(f21312,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X0),c_Complex_Oii),
inference(superposition,[],[f18330,f3951]) ).
fof(f3951,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X0)),
inference(cnf_transformation,[],[f1272]) ).
fof(f1272,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X0)),
inference(rectify,[],[f695]) ).
fof(f695,axiom,
! [X1] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__mult__minus) ).
fof(f18330,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X0)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii),
inference(backward_demodulation,[],[f7823,f18328]) ).
fof(f18328,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii),
inference(backward_demodulation,[],[f17039,f18327]) ).
fof(f18327,plain,
! [X0] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii) = c_Complex_Ocomplex_OComplex(c_Complex_OIm(X0),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X0))),
inference(backward_demodulation,[],[f18203,f18326]) ).
fof(f18326,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X0)) = c_Complex_OIm(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(forward_demodulation,[],[f18325,f11226]) ).
fof(f11226,plain,
! [X0] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Ocnj(c_Complex_Oii),X0),
inference(superposition,[],[f11222,f8743]) ).
fof(f8743,plain,
! [X0] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Ocnj(c_Complex_Oii)),
inference(superposition,[],[f4054,f5625]) ).
fof(f5625,plain,
c_Complex_Ocnj(c_Complex_Oii) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii),
inference(forward_demodulation,[],[f3872,f3862]) ).
fof(f3862,plain,
c_Complex_Ocnj(c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
inference(cnf_transformation,[],[f694]) ).
fof(f694,axiom,
c_Complex_Ocnj(c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__cnj__i) ).
fof(f3872,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii),
inference(cnf_transformation,[],[f888]) ).
fof(f888,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__i) ).
fof(f4054,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)),
inference(cnf_transformation,[],[f889]) ).
fof(f889,axiom,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__divide__def) ).
fof(f11222,plain,
! [X0,X1] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,X1),
inference(resolution,[],[f4782,f3840]) ).
fof(f3840,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1179]) ).
fof(f1179,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f4782,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Otimes__class_Otimes(X2,X1,X0) = c_Groups_Otimes__class_Otimes(X2,X0,X1) ),
inference(cnf_transformation,[],[f2653]) ).
fof(f2653,plain,
! [X0,X1,X2] :
( c_Groups_Otimes__class_Otimes(X2,X1,X0) = c_Groups_Otimes__class_Otimes(X2,X0,X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1818]) ).
fof(f1818,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,X0) = c_Groups_Otimes__class_Otimes(X2,X0,X1) ),
inference(rectify,[],[f358]) ).
fof(f358,axiom,
! [X3,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Otimes__class_Otimes(X6,X5,X3) = c_Groups_Otimes__class_Otimes(X6,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f18325,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X0)) = c_Complex_OIm(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Ocnj(c_Complex_Oii),X0)),
inference(forward_demodulation,[],[f18297,f13166]) ).
fof(f13166,plain,
! [X0,X1] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Ocnj(X1),X0) = c_Complex_Ocnj(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X1,c_Complex_Ocnj(X0))),
inference(forward_demodulation,[],[f13165,f8744]) ).
fof(f8744,plain,
! [X0,X1] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X1,X0) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)),
inference(superposition,[],[f4054,f6220]) ).
fof(f6220,plain,
! [X0] : c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)) = X0,
inference(resolution,[],[f4146,f3674]) ).
fof(f3674,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1162]) ).
fof(f1162,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(f4146,plain,
! [X0,X1] :
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2184]) ).
fof(f2184,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1410]) ).
fof(f1410,plain,
! [X0,X1] :
( class_Rings_Odivision__ring__inverse__zero(X1)
=> c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0 ),
inference(rectify,[],[f837]) ).
fof(f837,axiom,
! [X5,X6] :
( class_Rings_Odivision__ring__inverse__zero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,c_Rings_Oinverse__class_Oinverse(X6,X5)) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
fof(f13165,plain,
! [X0,X1] : c_Complex_Ocnj(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Ocnj(X0)))) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Ocnj(X1),X0),
inference(forward_demodulation,[],[f13150,f8744]) ).
fof(f13150,plain,
! [X0,X1] : c_Complex_Ocnj(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Ocnj(X0)))) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X1),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)),
inference(superposition,[],[f4069,f6028]) ).
fof(f6028,plain,
! [X0] : c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0) = c_Complex_Ocnj(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Ocnj(X0))),
inference(superposition,[],[f3900,f3938]) ).
fof(f3938,plain,
! [X0] : c_Complex_Ocnj(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Ocnj(X0)),
inference(cnf_transformation,[],[f1259]) ).
fof(f1259,plain,
! [X0] : c_Complex_Ocnj(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Ocnj(X0)),
inference(rectify,[],[f779]) ).
fof(f779,axiom,
! [X1] : c_Complex_Ocnj(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X1)) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Ocnj(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__cnj__inverse) ).
fof(f3900,plain,
! [X0] : c_Complex_Ocnj(c_Complex_Ocnj(X0)) = X0,
inference(cnf_transformation,[],[f1221]) ).
fof(f1221,plain,
! [X0] : c_Complex_Ocnj(c_Complex_Ocnj(X0)) = X0,
inference(rectify,[],[f454]) ).
fof(f454,axiom,
! [X16] : c_Complex_Ocnj(c_Complex_Ocnj(X16)) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__cnj__cnj) ).
fof(f4069,plain,
! [X0,X1] : c_Complex_Ocnj(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X1),c_Complex_Ocnj(X0)),
inference(cnf_transformation,[],[f687]) ).
fof(f687,axiom,
! [X0,X1] : c_Complex_Ocnj(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X1),c_Complex_Ocnj(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__cnj__divide) ).
fof(f18297,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X0)) = c_Complex_OIm(c_Complex_Ocnj(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Ocnj(X0)))),
inference(superposition,[],[f3929,f18245]) ).
fof(f18245,plain,
! [X0] : c_Complex_ORe(X0) = c_Complex_OIm(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Ocnj(X0))),
inference(forward_demodulation,[],[f18239,f13170]) ).
fof(f13170,plain,
! [X0] : c_Complex_Ocnj(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Ocnj(X0)),
inference(forward_demodulation,[],[f13152,f11222]) ).
fof(f13152,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Ocnj(X0),c_Complex_Oii) = c_Complex_Ocnj(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(superposition,[],[f4069,f8741]) ).
fof(f8741,plain,
! [X0] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Ocnj(c_Complex_Oii)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii),
inference(superposition,[],[f4054,f6037]) ).
fof(f6037,plain,
c_Complex_Oii = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Ocnj(c_Complex_Oii)),
inference(forward_demodulation,[],[f6027,f3900]) ).
fof(f6027,plain,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Ocnj(c_Complex_Oii)) = c_Complex_Ocnj(c_Complex_Ocnj(c_Complex_Oii)),
inference(superposition,[],[f3938,f5625]) ).
fof(f18239,plain,
! [X0] : c_Complex_ORe(X0) = c_Complex_OIm(c_Complex_Ocnj(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii))),
inference(superposition,[],[f16984,f18230]) ).
fof(f18230,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii),c_Complex_Oii) = X0,
inference(forward_demodulation,[],[f18229,f3923]) ).
fof(f3923,plain,
! [X0] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X0),c_Complex_OIm(X0)) = X0,
inference(cnf_transformation,[],[f1244]) ).
fof(f1244,plain,
! [X0] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X0),c_Complex_OIm(X0)) = X0,
inference(rectify,[],[f504]) ).
fof(f504,axiom,
! [X16] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X16),c_Complex_OIm(X16)) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__surj) ).
fof(f18229,plain,
! [X0] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X0),c_Complex_OIm(X0)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii),c_Complex_Oii),
inference(forward_demodulation,[],[f18228,f3906]) ).
fof(f3906,plain,
! [X0] : c_Complex_ORe(X0) = c_Complex_ORe(c_Complex_Ocnj(X0)),
inference(cnf_transformation,[],[f1227]) ).
fof(f1227,plain,
! [X0] : c_Complex_ORe(X0) = c_Complex_ORe(c_Complex_Ocnj(X0)),
inference(rectify,[],[f451]) ).
fof(f451,axiom,
! [X1] : c_Complex_ORe(X1) = c_Complex_ORe(c_Complex_Ocnj(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__Re__cnj) ).
fof(f18228,plain,
! [X0] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Complex_Ocnj(X0)),c_Complex_OIm(X0)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii),c_Complex_Oii),
inference(forward_demodulation,[],[f18227,f17103]) ).
fof(f17103,plain,
! [X0] : c_Complex_ORe(X0) = c_Complex_OIm(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X0)),
inference(superposition,[],[f16983,f11222]) ).
fof(f16983,plain,
! [X0] : c_Complex_ORe(X0) = c_Complex_OIm(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(superposition,[],[f4037,f16663]) ).
fof(f16663,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii) = c_Complex_Ocomplex_OComplex(c_Complex_OIm(c_Complex_Ocnj(X0)),c_Complex_ORe(X0)),
inference(forward_demodulation,[],[f16647,f3929]) ).
fof(f16647,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii) = c_Complex_Ocomplex_OComplex(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(X0)),c_Complex_ORe(X0)),
inference(superposition,[],[f4081,f3923]) ).
fof(f4081,plain,
! [X0,X1] : c_Complex_Ocomplex_OComplex(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X0),c_Complex_Oii),
inference(cnf_transformation,[],[f1364]) ).
fof(f1364,plain,
! [X0,X1] : c_Complex_Ocomplex_OComplex(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X0),c_Complex_Oii),
inference(rectify,[],[f616]) ).
fof(f616,axiom,
! [X3,X5] : c_Complex_Ocomplex_OComplex(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3),X5) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X5,X3),c_Complex_Oii),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Complex__mult__i) ).
fof(f4037,plain,
! [X0,X1] : c_Complex_OIm(c_Complex_Ocomplex_OComplex(X1,X0)) = X0,
inference(cnf_transformation,[],[f459]) ).
fof(f459,axiom,
! [X0,X1] : c_Complex_OIm(c_Complex_Ocomplex_OComplex(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Im) ).
fof(f18227,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii),c_Complex_Oii) = c_Complex_Ocomplex_OComplex(c_Complex_OIm(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Ocnj(X0))),c_Complex_OIm(X0)),
inference(forward_demodulation,[],[f18216,f13170]) ).
fof(f18216,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii),c_Complex_Oii) = c_Complex_Ocomplex_OComplex(c_Complex_OIm(c_Complex_Ocnj(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii))),c_Complex_OIm(X0)),
inference(superposition,[],[f16663,f18156]) ).
fof(f18156,plain,
! [X0] : c_Complex_OIm(X0) = c_Complex_ORe(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(superposition,[],[f17100,f3900]) ).
fof(f17100,plain,
! [X0] : c_Complex_OIm(c_Complex_Ocnj(X0)) = c_Complex_ORe(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X0),c_Complex_Oii)),
inference(forward_demodulation,[],[f17001,f14068]) ).
fof(f14068,plain,
! [X0] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X0),c_Complex_Oii) = c_Complex_Ocnj(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(superposition,[],[f4072,f8743]) ).
fof(f4072,plain,
! [X0,X1] : c_Complex_Ocnj(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X1,X0)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Ocnj(X1),c_Complex_Ocnj(X0)),
inference(cnf_transformation,[],[f483]) ).
fof(f483,axiom,
! [X0,X1] : c_Complex_Ocnj(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X1,X0)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Ocnj(X1),c_Complex_Ocnj(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__cnj__mult) ).
fof(f17001,plain,
! [X0] : c_Complex_OIm(c_Complex_Ocnj(X0)) = c_Complex_ORe(c_Complex_Ocnj(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii))),
inference(superposition,[],[f6745,f16663]) ).
fof(f6745,plain,
! [X0,X1] : c_Complex_ORe(c_Complex_Ocnj(c_Complex_Ocomplex_OComplex(X0,X1))) = X0,
inference(superposition,[],[f4038,f4052]) ).
fof(f4052,plain,
! [X0,X1] : c_Complex_Ocnj(c_Complex_Ocomplex_OComplex(X1,X0)) = c_Complex_Ocomplex_OComplex(X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(cnf_transformation,[],[f1349]) ).
fof(f1349,plain,
! [X0,X1] : c_Complex_Ocnj(c_Complex_Ocomplex_OComplex(X1,X0)) = c_Complex_Ocomplex_OComplex(X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(rectify,[],[f654]) ).
fof(f654,axiom,
! [X3,X5] : c_Complex_Ocnj(c_Complex_Ocomplex_OComplex(X5,X3)) = c_Complex_Ocomplex_OComplex(X5,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__cnj) ).
fof(f4038,plain,
! [X0,X1] : c_Complex_ORe(c_Complex_Ocomplex_OComplex(X1,X0)) = X1,
inference(cnf_transformation,[],[f460]) ).
fof(f460,axiom,
! [X0,X1] : c_Complex_ORe(c_Complex_Ocomplex_OComplex(X1,X0)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Re) ).
fof(f16984,plain,
! [X0] : c_Complex_OIm(c_Complex_Ocnj(X0)) = c_Complex_ORe(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(superposition,[],[f4038,f16663]) ).
fof(f3929,plain,
! [X0] : c_Complex_OIm(c_Complex_Ocnj(X0)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(X0)),
inference(cnf_transformation,[],[f1250]) ).
fof(f1250,plain,
! [X0] : c_Complex_OIm(c_Complex_Ocnj(X0)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(X0)),
inference(rectify,[],[f653]) ).
fof(f653,axiom,
! [X1] : c_Complex_OIm(c_Complex_Ocnj(X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__Im__cnj) ).
fof(f18203,plain,
! [X0] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii) = c_Complex_Ocomplex_OComplex(c_Complex_OIm(X0),c_Complex_OIm(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii))),
inference(superposition,[],[f3923,f18156]) ).
fof(f17039,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Complex_Ocomplex_OComplex(c_Complex_OIm(X0),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X0))),
inference(forward_demodulation,[],[f17038,f11222]) ).
fof(f17038,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Complex_Oii) = c_Complex_Ocomplex_OComplex(c_Complex_OIm(X0),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X0))),
inference(forward_demodulation,[],[f17037,f3900]) ).
fof(f17037,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Complex_Oii) = c_Complex_Ocomplex_OComplex(c_Complex_OIm(c_Complex_Ocnj(c_Complex_Ocnj(X0))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X0))),
inference(forward_demodulation,[],[f17036,f5638]) ).
fof(f5638,plain,
! [X0] : c_Complex_OIm(c_Complex_Ocnj(X0)) = c_Complex_OIm(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
inference(forward_demodulation,[],[f3943,f3929]) ).
fof(f3943,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(X0)) = c_Complex_OIm(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
inference(cnf_transformation,[],[f1264]) ).
fof(f1264,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(X0)) = c_Complex_OIm(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
inference(rectify,[],[f692]) ).
fof(f692,axiom,
! [X1] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_OIm(X1)) = c_Complex_OIm(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Im_Ominus) ).
fof(f17036,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Complex_Oii) = c_Complex_Ocomplex_OComplex(c_Complex_OIm(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Ocnj(X0))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X0))),
inference(forward_demodulation,[],[f16960,f3940]) ).
fof(f3940,plain,
! [X0] : c_Complex_ORe(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X0)),
inference(cnf_transformation,[],[f1261]) ).
fof(f1261,plain,
! [X0] : c_Complex_ORe(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X0)),
inference(rectify,[],[f691]) ).
fof(f691,axiom,
! [X1] : c_Complex_ORe(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Complex_ORe(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Re_Ominus) ).
fof(f16960,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),c_Complex_Oii) = c_Complex_Ocomplex_OComplex(c_Complex_OIm(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Ocnj(X0))),c_Complex_ORe(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0))),
inference(superposition,[],[f16663,f3939]) ).
fof(f3939,plain,
! [X0] : c_Complex_Ocnj(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Ocnj(X0)),
inference(cnf_transformation,[],[f1260]) ).
fof(f1260,plain,
! [X0] : c_Complex_Ocnj(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Ocnj(X0)),
inference(rectify,[],[f686]) ).
fof(f686,axiom,
! [X1] : c_Complex_Ocnj(c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Ocnj(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cnj_Ominus) ).
fof(f7823,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X0)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
inference(superposition,[],[f3951,f3951]) ).
fof(f139004,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(backward_demodulation,[],[f21333,f138998]) ).
fof(f138998,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X0)),
inference(backward_demodulation,[],[f34987,f138991]) ).
fof(f138991,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X0),c_Complex_Oii)),
inference(backward_demodulation,[],[f27816,f138980]) ).
fof(f138980,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(forward_demodulation,[],[f138979,f3950]) ).
fof(f3950,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_NthRoot_Osqrt(c_Complex_ORe(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Ocnj(X0)))),
inference(cnf_transformation,[],[f1271]) ).
fof(f1271,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_NthRoot_Osqrt(c_Complex_ORe(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Ocnj(X0)))),
inference(rectify,[],[f521]) ).
fof(f521,axiom,
! [X16] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X16) = c_NthRoot_Osqrt(c_Complex_ORe(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X16,c_Complex_Ocnj(X16)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__sqrt__Re__mult__cnj) ).
fof(f138979,plain,
! [X0] : c_NthRoot_Osqrt(c_Complex_ORe(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Ocnj(X0)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(forward_demodulation,[],[f138953,f18236]) ).
fof(f18236,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii)) = X0,
inference(superposition,[],[f18230,f11222]) ).
fof(f138953,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii)) = c_NthRoot_Osqrt(c_Complex_ORe(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X0),c_Complex_Oii))))),
inference(backward_demodulation,[],[f27818,f138940]) ).
fof(f138940,plain,
! [X2,X0,X1] : c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,X1),X2) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X1,X2)),
inference(resolution,[],[f5137,f3770]) ).
fof(f3770,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1174]) ).
fof(f1174,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(f5137,plain,
! [X2,X3,X0,X1] :
( ~ class_Groups_Oab__semigroup__mult(X3)
| c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X2,X1),X0) = c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Otimes__class_Otimes(X3,X1,X0)) ),
inference(cnf_transformation,[],[f2946]) ).
fof(f2946,plain,
! [X0,X1,X2,X3] :
( c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X2,X1),X0) = c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Otimes__class_Otimes(X3,X1,X0))
| ~ class_Groups_Oab__semigroup__mult(X3) ),
inference(ennf_transformation,[],[f2021]) ).
fof(f2021,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oab__semigroup__mult(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X2,X1),X0) = c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Otimes__class_Otimes(X3,X1,X0)) ),
inference(rectify,[],[f197]) ).
fof(f197,axiom,
! [X4,X3,X5,X6] :
( class_Groups_Oab__semigroup__mult(X6)
=> c_Groups_Otimes__class_Otimes(X6,c_Groups_Otimes__class_Otimes(X6,X5,X3),X4) = c_Groups_Otimes__class_Otimes(X6,X5,c_Groups_Otimes__class_Otimes(X6,X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(f27818,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii)) = c_NthRoot_Osqrt(c_Complex_ORe(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X0),c_Complex_Oii)))),
inference(superposition,[],[f3950,f14068]) ).
fof(f27816,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X0,c_Complex_Oii)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X0),c_Complex_Oii)),
inference(superposition,[],[f3932,f14068]) ).
fof(f3932,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocnj(X0)),
inference(cnf_transformation,[],[f1253]) ).
fof(f1253,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocnj(X0)),
inference(rectify,[],[f482]) ).
fof(f482,axiom,
! [X16] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X16) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocnj(X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__cnj) ).
fof(f34987,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X0)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X0),c_Complex_Oii)),
inference(forward_demodulation,[],[f34986,f21333]) ).
fof(f34986,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Complex_Ocnj(X0),c_Complex_Oii)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(forward_demodulation,[],[f34909,f18330]) ).
fof(f34909,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Ocnj(X0)))),
inference(superposition,[],[f9747,f13170]) ).
fof(f9747,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Ocnj(X0))),
inference(backward_demodulation,[],[f6045,f9744]) ).
fof(f9744,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
inference(resolution,[],[f4192,f3689]) ).
fof(f3689,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1167]) ).
fof(f1167,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f4192,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) ),
inference(cnf_transformation,[],[f2213]) ).
fof(f2213,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1439]) ).
fof(f1439,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) ),
inference(rectify,[],[f590]) ).
fof(f590,axiom,
! [X1,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_RealVector_Onorm__class_Onorm(X6,X1) = c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ouminus__class_Ouminus(X6,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
fof(f6045,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Ocnj(X0))),
inference(superposition,[],[f3932,f3939]) ).
fof(f21333,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,X0)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Complex_Oii)),
inference(superposition,[],[f9744,f18330]) ).
fof(f9590,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(backward_demodulation,[],[f6292,f9585]) ).
fof(f6292,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(forward_demodulation,[],[f6291,f3923]) ).
fof(f6291,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(backward_demodulation,[],[f5799,f6286]) ).
fof(f6286,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0,
inference(resolution,[],[f4260,f3805]) ).
fof(f3805,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1128]) ).
fof(f1128,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(f4260,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(cnf_transformation,[],[f2275]) ).
fof(f2275,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(ennf_transformation,[],[f1493]) ).
fof(f1493,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X5,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Ozero__class_Ozero(X6)) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(f5799,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(forward_demodulation,[],[f5798,f4460]) ).
fof(f4460,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X2),c_Complex_Ocomplex_OComplex(X1,X0)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),X0),
inference(cnf_transformation,[],[f1601]) ).
fof(f1601,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X2),c_Complex_Ocomplex_OComplex(X1,X0)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),X0),
inference(rectify,[],[f554]) ).
fof(f554,axiom,
! [X0,X1,X43] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X43),c_Complex_Ocomplex_OComplex(X1,X0)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X43,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__add__Complex) ).
fof(f5798,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(forward_demodulation,[],[f5797,f3931]) ).
fof(f3931,plain,
! [X0] : c_RealVector_Oof__real(tc_Complex_Ocomplex,X0) = c_Complex_Ocomplex_OComplex(X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f1252]) ).
fof(f1252,plain,
! [X0] : c_RealVector_Oof__real(tc_Complex_Ocomplex,X0) = c_Complex_Ocomplex_OComplex(X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(rectify,[],[f546]) ).
fof(f546,axiom,
! [X43] : c_RealVector_Oof__real(tc_Complex_Ocomplex,X43) = c_Complex_Ocomplex_OComplex(X43,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__def) ).
fof(f5797,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(backward_demodulation,[],[f5713,f4916]) ).
fof(f4916,plain,
! [X2,X3,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X3,X2),c_Complex_Ocomplex_OComplex(X1,X0)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0)),
inference(cnf_transformation,[],[f1908]) ).
fof(f1908,plain,
! [X0,X1,X2,X3] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X3,X2),c_Complex_Ocomplex_OComplex(X1,X0)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0)),
inference(rectify,[],[f507]) ).
fof(f507,axiom,
! [X2,X4,X3,X5] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X5,X3),c_Complex_Ocomplex_OComplex(X4,X2)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X4),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__add) ).
fof(f5713,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(forward_demodulation,[],[f5712,f5704]) ).
fof(f5704,plain,
! [X0,X1] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X0)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
inference(forward_demodulation,[],[f4113,f3878]) ).
fof(f4113,plain,
! [X0,X1] : c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X0)),
inference(cnf_transformation,[],[f446]) ).
fof(f446,axiom,
! [X0,X1] : c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__norm) ).
fof(f5712,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(forward_demodulation,[],[f5711,f3931]) ).
fof(f5711,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(forward_demodulation,[],[f5710,f5704]) ).
fof(f5710,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
inference(backward_demodulation,[],[f5683,f5704]) ).
fof(f5683,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
inference(backward_demodulation,[],[f5682,f4075]) ).
fof(f5682,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
inference(backward_demodulation,[],[f5631,f4073]) ).
fof(f5631,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
inference(forward_demodulation,[],[f3883,f3878]) ).
fof(f3883,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096sqrt_A_I_IRe_Ax_A_N_ARe_Ay_A_L_A0_J_A_094_A2_A_L_A_I0_A_L_A_IIm_Ax_A_N_AIm_Ay_J_J_A_094_A2_J_060_061_Asqrt_A_I_IRe_Ax_A_N_ARe_Ay_J_A_094_A2_A_L_A0_A_094_A2_J_A_L_Asqrt_A_I0_A_094_A2_A_L_A_IIm_Ax_A_N_AIm_Ay_J_A_094_A2_J_096) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SWW203+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.29 % Computer : n027.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri May 3 19:43:38 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % (5961)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.34 % (5984)WARNING: value z3 for option sas not known
% 0.14/0.34 % (5986)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.34 % (5981)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.34 % (5984)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.34 % (5987)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.34 % (5985)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.35 % (5982)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.35 % (5988)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 1.58/0.56 TRYING [1]
% 1.73/0.58 TRYING [2]
% 4.94/1.02 TRYING [3]
% 5.34/1.15 TRYING [1]
% 6.45/1.24 TRYING [2]
% 8.54/1.59 TRYING [1]
% 8.54/1.61 TRYING [2]
% 11.15/1.95 TRYING [3]
% 17.73/2.89 TRYING [3]
% 22.65/3.57 TRYING [4]
% 26.72/4.13 TRYING [4]
% 84.37/12.42 TRYING [5]
% 85.63/12.52 TRYING [4]
% 91.95/13.41 TRYING [5]
% 93.67/13.72 % (5987)First to succeed.
% 93.67/13.73 % (5987)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5961"
% 93.67/13.74 % (5987)Refutation found. Thanks to Tanya!
% 93.67/13.74 % SZS status Theorem for theBenchmark
% 93.67/13.74 % SZS output start Proof for theBenchmark
% See solution above
% 93.67/13.74 % (5987)------------------------------
% 93.67/13.74 % (5987)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 93.67/13.74 % (5987)Termination reason: Refutation
% 93.67/13.74
% 93.67/13.74 % (5987)Memory used [KB]: 144137
% 93.67/13.74 % (5987)Time elapsed: 13.387 s
% 93.67/13.74 % (5987)Instructions burned: 35145 (million)
% 93.67/13.74 % (5961)Success in time 13.295 s
%------------------------------------------------------------------------------