TSTP Solution File: SWW222+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW222+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 : n003.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 : Tue Apr 30 17:29:00 EDT 2024
% Result : Theorem 154.23s 22.46s
% Output : Refutation 154.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 27
% Syntax : Number of formulae : 128 ( 66 unt; 0 def)
% Number of atoms : 222 ( 80 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 167 ( 73 ~; 54 |; 10 &)
% ( 8 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 148 ( 148 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f502910,plain,
$false,
inference(resolution,[],[f502740,f5801]) ).
fof(f5801,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_resolution,[],[f4759]) ).
fof(f4759,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3467]) ).
fof(f3467,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(flattening,[],[f3466]) ).
fof(f3466,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f1760]) ).
fof(f1760,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(rectify,[],[f471]) ).
fof(f471,axiom,
! [X23,X14] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,X23)
<=> ( X14 != X23
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(f502740,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f502642,f6295]) ).
fof(f6295,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(superposition,[],[f4175,f4074]) ).
fof(f4074,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f500]) ).
fof(f500,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
fof(f4175,plain,
! [X0] : c_RealDef_Oreal(tc_Nat_Onat,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(cnf_transformation,[],[f1320]) ).
fof(f1320,plain,
! [X0] : c_RealDef_Oreal(tc_Nat_Onat,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(rectify,[],[f462]) ).
fof(f462,axiom,
! [X8] : c_RealDef_Oreal(tc_Nat_Onat,X8) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
fof(f502642,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(backward_demodulation,[],[f119759,f502641]) ).
fof(f502641,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),
inference(resolution,[],[f502586,f3866]) ).
fof(f3866,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1106]) ).
fof(f1106,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f502586,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))) ),
inference(resolution,[],[f502585,f34489]) ).
fof(f34489,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| ~ class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
inference(superposition,[],[f4485,f4149]) ).
fof(f4149,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f1294]) ).
fof(f1294,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X21] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X21) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(f4485,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,[],[f3371]) ).
fof(f3371,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,[],[f2388]) ).
fof(f2388,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,[],[f1565]) ).
fof(f1565,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,[],[f35]) ).
fof(f35,axiom,
! [X14,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X14))
<=> c_Groups_Ozero__class_Ozero(X6) != X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(f502585,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))))),
inference(resolution,[],[f502547,f3882]) ).
fof(f3882,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1102]) ).
fof(f1102,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(f502547,plain,
( ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))))) ),
inference(forward_demodulation,[],[f502511,f4197]) ).
fof(f4197,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X0,
inference(cnf_transformation,[],[f1342]) ).
fof(f1342,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X0,
inference(rectify,[],[f333]) ).
fof(f333,axiom,
! [X8] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X8,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X8,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
fof(f502511,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[],[f502364,f4514]) ).
fof(f4514,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3395]) ).
fof(f3395,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0)) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2403]) ).
fof(f2403,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1580]) ).
fof(f1580,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f262]) ).
fof(f262,axiom,
! [X11,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X11,X11))
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(f502364,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(forward_demodulation,[],[f502363,f6322]) ).
fof(f6322,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(resolution,[],[f4212,f3865]) ).
fof(f3865,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1162]) ).
fof(f1162,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f4212,plain,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f2252]) ).
fof(f2252,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(ennf_transformation,[],[f1351]) ).
fof(f1351,plain,
! [X0] :
( class_RealVector_Oreal__normed__vector(X0)
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(f502363,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(forward_demodulation,[],[f502362,f6542]) ).
fof(f6542,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0),
inference(resolution,[],[f4568,f3954]) ).
fof(f3954,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1183]) ).
fof(f1183,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(f4568,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) ),
inference(cnf_transformation,[],[f2444]) ).
fof(f2444,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1617]) ).
fof(f1617,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X7,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ozero__class_Ozero(X6) = c_Groups_Ominus__class_Ominus(X6,X7,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
fof(f502362,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(forward_demodulation,[],[f502337,f16221]) ).
fof(f16221,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),
inference(resolution,[],[f5160,f4043]) ).
fof(f4043,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1127]) ).
fof(f1127,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f5160,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(cnf_transformation,[],[f2804]) ).
fof(f2804,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1977]) ).
fof(f1977,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(rectify,[],[f545]) ).
fof(f545,axiom,
! [X30,X7,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X7,X30) = c_Groups_Oplus__class_Oplus(X6,X30,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f502337,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),v_s____)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(backward_demodulation,[],[f10527,f502335]) ).
fof(f502335,plain,
v_wa____ = v_z____,
inference(forward_demodulation,[],[f502304,f6561]) ).
fof(f6561,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0,
inference(resolution,[],[f4570,f3954]) ).
fof(f4570,plain,
! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(cnf_transformation,[],[f2446]) ).
fof(f2446,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1619]) ).
fof(f1619,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f119]) ).
fof(f119,axiom,
! [X7,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,X7,c_Groups_Ozero__class_Ozero(X6)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(f502304,plain,
v_wa____ = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z____,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(superposition,[],[f16320,f501908]) ).
fof(f501908,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z____,v_wa____),
inference(resolution,[],[f501524,f393955]) ).
fof(f393955,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z____,v_wa____)),v_d____)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z____,v_wa____) ),
inference(resolution,[],[f380295,f3865]) ).
fof(f380295,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z____,v_wa____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z____,v_wa____)),v_d____) ),
inference(resolution,[],[f379433,f4485]) ).
fof(f379433,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,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z____,v_wa____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z____,v_wa____)),v_d____) ),
inference(forward_demodulation,[],[f379432,f93761]) ).
fof(f93761,plain,
! [X0,X1] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)),
inference(resolution,[],[f4998,f3865]) ).
fof(f4998,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
inference(cnf_transformation,[],[f2663]) ).
fof(f2663,plain,
! [X0,X1,X2] :
( c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(ennf_transformation,[],[f1872]) ).
fof(f1872,plain,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
inference(rectify,[],[f75]) ).
fof(f75,axiom,
! [X9,X7,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X7,X9)) = c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X9,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(f379432,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z____,v_wa____)),v_d____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____))) ),
inference(forward_demodulation,[],[f379425,f93761]) ).
fof(f379425,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____))) ),
inference(resolution,[],[f10523,f10527]) ).
fof(f10523,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),v_s____)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z____))) ),
inference(backward_demodulation,[],[f4319,f10515]) ).
fof(f10515,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(superposition,[],[f4419,f6546]) ).
fof(f6546,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = X0,
inference(resolution,[],[f4569,f3956]) ).
fof(f3956,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1140]) ).
fof(f1140,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(f4569,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,[],[f2445]) ).
fof(f2445,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,[],[f1618]) ).
fof(f1618,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
inference(rectify,[],[f113]) ).
fof(f113,axiom,
! [X7,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Ouminus__class_Ouminus(X6,X7)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(f4419,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(cnf_transformation,[],[f1508]) ).
fof(f1508,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(rectify,[],[f308]) ).
fof(f308,axiom,
! [X42,X21] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X21,X42) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(f4319,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z____))) ),
inference(cnf_transformation,[],[f2361]) ).
fof(f2361,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z____))) ),
inference(flattening,[],[f2360]) ).
fof(f2360,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z____))) ),
inference(ennf_transformation,[],[f1451]) ).
fof(f1451,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z____)),v_d____)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z____))) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X3] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3,v_z____)),v_d____)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3,v_z____))) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d_I2_J) ).
fof(f501524,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z____,v_wa____)),v_d____),
inference(superposition,[],[f4085,f93761]) ).
fof(f4085,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_w) ).
fof(f16320,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)) = X0,
inference(superposition,[],[f16075,f16270]) ).
fof(f16270,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = X0,
inference(superposition,[],[f16222,f16131]) ).
fof(f16131,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X1) = X0,
inference(resolution,[],[f5126,f3954]) ).
fof(f5126,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f2776]) ).
fof(f2776,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1952]) ).
fof(f1952,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
inference(rectify,[],[f231]) ).
fof(f231,axiom,
! [X9,X7,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ominus__class_Ominus(X6,X7,X9),X9) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(f16222,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),
inference(resolution,[],[f5160,f4040]) ).
fof(f4040,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1172]) ).
fof(f1172,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f16075,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X1) = X0,
inference(resolution,[],[f5125,f3954]) ).
fof(f5125,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f2775]) ).
fof(f2775,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1951]) ).
fof(f1951,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
inference(rectify,[],[f230]) ).
fof(f230,axiom,
! [X9,X7,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,c_Groups_Oplus__class_Oplus(X6,X7,X9),X9) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(f10527,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),v_s____)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(backward_demodulation,[],[f3843,f10515]) ).
fof(f3843,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f1253]) ).
fof(f1253,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(flattening,[],[f1252]) ).
fof(f1252,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(negated_conjecture,[],[f1251]) ).
fof(f1251,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f119759,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))))),
inference(superposition,[],[f10526,f16221]) ).
fof(f10526,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),v_s____))),
inference(backward_demodulation,[],[f4100,f10515]) ).
fof(f4100,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_e) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW222+1 : TPTP v8.1.2. Released v5.2.0.
% 0.08/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 03:05:33 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (11241)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (11257)WARNING: value z3 for option sas not known
% 0.22/0.44 % (11255)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.44 % (11256)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.44 % (11257)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)
% 0.22/0.44 % (11258)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.44 % (11259)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)
% 0.22/0.44 % (11260)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)
% 0.22/0.44 % (11261)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)
% 1.64/0.67 TRYING [1]
% 1.64/0.70 TRYING [2]
% 3.35/0.89 TRYING [1]
% 3.56/0.91 TRYING [2]
% 5.53/1.21 TRYING [1]
% 6.34/1.33 TRYING [3]
% 6.34/1.35 TRYING [3]
% 6.34/1.37 TRYING [2]
% 24.63/3.98 TRYING [4]
% 25.24/4.07 TRYING [3]
% 25.75/4.11 TRYING [4]
% 74.19/11.06 TRYING [5]
% 77.33/11.47 TRYING [4]
% 84.85/12.52 TRYING [5]
% 154.23/22.42 % (11260)First to succeed.
% 154.23/22.46 % (11260)Refutation found. Thanks to Tanya!
% 154.23/22.46 % SZS status Theorem for theBenchmark
% 154.23/22.46 % SZS output start Proof for theBenchmark
% See solution above
% 154.23/22.46 % (11260)------------------------------
% 154.23/22.46 % (11260)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 154.23/22.46 % (11260)Termination reason: Refutation
% 154.23/22.46
% 154.23/22.46 % (11260)Memory used [KB]: 173641
% 154.23/22.46 % (11260)Time elapsed: 21.985 s
% 154.23/22.46 % (11260)Instructions burned: 46396 (million)
% 154.23/22.46 % (11260)------------------------------
% 154.23/22.46 % (11260)------------------------------
% 154.23/22.46 % (11241)Success in time 21.869 s
%------------------------------------------------------------------------------