%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW203+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:29:50 PM UTC 2026
% Result : Theorem 18.98s 3.08s
% Output : Refutation 19.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 49
% Syntax : Number of formulae : 277 ( 156 unt; 3 def)
% Number of atoms : 460 ( 262 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 309 ( 126 ~; 131 |; 28 &)
% ( 10 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 4 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-3 aty)
% Number of variables : 328 ( 0 sgn 328 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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) ).
fof(f7,axiom,
! [X0] : c_NthRoot_Osqrt(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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs) ).
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(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(f28,axiom,
c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__zero) ).
fof(f66,axiom,
! [X0] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X0
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2__iff) ).
fof(f79,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(f81,axiom,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).
fof(f86,axiom,
! [X0,X1] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,X0)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__power) ).
fof(f93,axiom,
! [X0,X1] :
( 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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__sum__zero__iff) ).
fof(f101,axiom,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).
fof(f134,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(f136,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(f144,axiom,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f173,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Groups_Oabs__class_Oabs(X2,c_Power_Opower__class_Opower(X2,X1,X0)) = c_Power_Opower__class_Opower(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).
fof(f174,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(f190,axiom,
! [X0,X1,X2] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),X0) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(f230,axiom,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(f231,axiom,
! [X0] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).
fof(f307,axiom,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) = c_Groups_Oplus__class_Oplus(X1,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).
fof(f313,axiom,
! [X0,X1] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),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_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_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__squared__expand) ).
fof(f359,axiom,
! [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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f362,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(f364,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X2),c_Groups_Oplus__class_Oplus(X4,X1,X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(f446,axiom,
! [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_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)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__norm) ).
fof(f504,axiom,
! [X0] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X0),c_Complex_OIm(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__surj) ).
fof(f506,axiom,
! [X0,X1] :
( c_Complex_Ocomplex_OComplex(X1,X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
<=> ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Complex__eq__0) ).
fof(f507,axiom,
! [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)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__add) ).
fof(f524,axiom,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = 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_semiring__norm_I115_J) ).
fof(f546,axiom,
! [X0] : c_RealVector_Oof__real(tc_Complex_Ocomplex,X0) = c_Complex_Ocomplex_OComplex(X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__def) ).
fof(f554,axiom,
! [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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__add__Complex) ).
fof(f555,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X2,X1),c_RealVector_Oof__real(tc_Complex_Ocomplex,X0)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Complex__add__complex__of__real) ).
fof(f596,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(f647,axiom,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(f650,axiom,
! [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)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(f651,axiom,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(f813,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(f814,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
& X1 != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(f946,axiom,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__abs__def) ).
fof(f1102,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(f1130,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(f1131,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f1145,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(f1149,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
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(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(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,[status(cth)],[f1202]) ).
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(f1285,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,[],[f79]) ).
fof(f1288,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f81]) ).
fof(f1306,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X0) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f101]) ).
fof(f1320,plain,
! [X0,X1] :
( X1 = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f136]) ).
fof(f1321,plain,
! [X0,X1] :
( X1 = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(flattening,[],[f1320]) ).
fof(f1333,plain,
! [X0,X1,X2] :
( c_Groups_Oabs__class_Oabs(X2,c_Power_Opower__class_Opower(X2,X1,X0)) = c_Power_Opower__class_Opower(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f173]) ).
fof(f1334,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(ennf_transformation,[],[f174]) ).
fof(f1439,plain,
! [X0,X1] :
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f307]) ).
fof(f1471,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,[],[f359]) ).
fof(f1474,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f362]) ).
fof(f1476,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X2),c_Groups_Oplus__class_Oplus(X4,X1,X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(ennf_transformation,[],[f364]) ).
fof(f1655,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f596]) ).
fof(f2122,plain,
! [X0] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(ennf_transformation,[],[f946]) ).
fof(f2215,plain,
! [X0] :
( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != X0 ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f2222,plain,
! [X0,X1] :
( ( 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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 )
& ( ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != 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))))) ) ),
inference(nnf_transformation,[],[f93]) ).
fof(f2223,plain,
! [X0,X1] :
( ( 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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 )
& ( ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != 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))))) ) ),
inference(flattening,[],[f2222]) ).
fof(f2261,plain,
! [X0,X1] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 )
& ( ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) ) ),
inference(nnf_transformation,[],[f230]) ).
fof(f2262,plain,
! [X0,X1] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 )
& ( ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) ) ),
inference(flattening,[],[f2261]) ).
fof(f2333,plain,
! [X0,X1] :
( ( c_Complex_Ocomplex_OComplex(X1,X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 )
& ( ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X1,X0) ) ),
inference(nnf_transformation,[],[f506]) ).
fof(f2334,plain,
! [X0,X1] :
( ( c_Complex_Ocomplex_OComplex(X1,X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 )
& ( ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X0 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X1,X0) ) ),
inference(flattening,[],[f2333]) ).
fof(f2368,plain,
! [X0,X1] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X0 != X1 )
& ( X1 = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ) ),
inference(nnf_transformation,[],[f647]) ).
fof(f2426,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
& X0 != X1 ) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X1 = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f813]) ).
fof(f2427,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
& X0 != X1 ) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X1 = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(flattening,[],[f2426]) ).
fof(f2428,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 = X1 )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
& X1 != X0 )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f814]) ).
fof(f2429,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 = X1 )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
& X1 != X0 )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(flattening,[],[f2428]) ).
fof(f2505,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(f2511,plain,
! [X0] : c_NthRoot_Osqrt(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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f2516,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(f2517,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(f2540,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f28]) ).
fof(f2596,plain,
! [X0] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f2215]) ).
fof(f2612,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,[],[f1285]) ).
fof(f2614,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0)) ),
inference(cnf_transformation,[],[f1288]) ).
fof(f2620,plain,
! [X0,X1] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,X0)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),X0),
inference(cnf_transformation,[],[f86]) ).
fof(f2631,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = 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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(cnf_transformation,[],[f2223]) ).
fof(f2644,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X0) = X0 ),
inference(cnf_transformation,[],[f1306]) ).
fof(f2685,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f2687,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1321]) ).
fof(f2698,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f144]) ).
fof(f2738,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| c_Power_Opower__class_Opower(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0) = c_Groups_Oabs__class_Oabs(X2,c_Power_Opower__class_Opower(X2,X1,X0)) ),
inference(cnf_transformation,[],[f1333]) ).
fof(f2739,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)) ),
inference(cnf_transformation,[],[f1334]) ).
fof(f2756,plain,
! [X2,X0,X1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),X0) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0)),
inference(cnf_transformation,[],[f190]) ).
fof(f2808,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(cnf_transformation,[],[f2262]) ).
fof(f2809,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)),
inference(cnf_transformation,[],[f231]) ).
fof(f2901,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2907,plain,
! [X0,X1] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),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_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_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),X0)),
inference(cnf_transformation,[],[f313]) ).
fof(f2957,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,[],[f1471]) ).
fof(f2960,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f2962,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X2),c_Groups_Oplus__class_Oplus(X4,X1,X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(cnf_transformation,[],[f1476]) ).
fof(f3079,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(f3164,plain,
! [X0] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X0),c_Complex_OIm(X0)) = X0,
inference(cnf_transformation,[],[f504]) ).
fof(f3168,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(cnf_transformation,[],[f2334]) ).
fof(f3169,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,[],[f507]) ).
fof(f3190,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,[],[f524]) ).
fof(f3216,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,[],[f546]) ).
fof(f3224,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,[],[f554]) ).
fof(f3225,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X2,X1),c_RealVector_Oof__real(tc_Complex_Ocomplex,X0)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0),X1),
inference(cnf_transformation,[],[f555]) ).
fof(f3273,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
inference(cnf_transformation,[],[f1655]) ).
fof(f3348,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f2368]) ).
fof(f3353,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,[],[f650]) ).
fof(f3354,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
inference(cnf_transformation,[],[f651]) ).
fof(f3602,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f2427]) ).
fof(f3605,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2429]) ).
fof(f3811,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ),
inference(cnf_transformation,[],[f2122]) ).
fof(f4099,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1102]) ).
fof(f4127,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1130]) ).
fof(f4128,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1131]) ).
fof(f4142,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1145]) ).
fof(f4146,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1149]) ).
fof(f4176,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1179]) ).
fof(f4199,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(f4200,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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))))),
inference(definition_unfolding,[],[f2505,f2698,f2698,f2698,f2698,f2698,f2698]) ).
fof(f4206,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))))),
inference(definition_unfolding,[],[f2511,f2698]) ).
fof(f4224,plain,
! [X0] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(definition_unfolding,[],[f2596,f2698]) ).
fof(f4229,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = 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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(definition_unfolding,[],[f2631,f2698,f2698]) ).
fof(f4273,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),X0) ),
inference(definition_unfolding,[],[f2901,f2698]) ).
fof(f4279,plain,
! [X0,X1] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),X1),X0)),
inference(definition_unfolding,[],[f2907,f2698,f2698,f2698,f2698]) ).
fof(f4285,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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),
inference(definition_unfolding,[],[f3079,f2698,f2698]) ).
fof(f4304,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),
inference(definition_unfolding,[],[f3190,f2698]) ).
fof(f4354,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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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(definition_unfolding,[],[f4199,f2698,f2698]) ).
fof(f4378,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = 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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(equality_resolution,[],[f4229]) ).
fof(f4379,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = 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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))))),
inference(equality_resolution,[],[f4378]) ).
fof(f4401,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(equality_resolution,[],[f2808]) ).
fof(f4402,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(equality_resolution,[],[f4401]) ).
fof(f4459,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(equality_resolution,[],[f3168]) ).
fof(f4460,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(equality_resolution,[],[f4459]) ).
fof(f4487,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
inference(equality_resolution,[],[f3348]) ).
fof(f4536,plain,
! [X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(equality_resolution,[],[f3602]) ).
fof(f4566,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1),
inference(forward_demodulation,[],[f4487,f3353]) ).
fof(f4572,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f4460,f3216]) ).
fof(f4578,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,[],[f4285,f4304]) ).
fof(f4586,plain,
! [X0,X1] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,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))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),X1),X0)),
inference(forward_demodulation,[],[f4279,f4304]) ).
fof(f4618,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = 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_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(forward_demodulation,[],[f4379,f4304]) ).
fof(f4623,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X0 ),
inference(forward_demodulation,[],[f4224,f4304]) ).
fof(f4640,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),
inference(forward_demodulation,[],[f4206,f2620]) ).
fof(f4646,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,[],[f4200,f4304]) ).
fof(f4649,plain,
! [X0,X1] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,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))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0))),
inference(forward_demodulation,[],[f4586,f2756]) ).
fof(f4664,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(forward_demodulation,[],[f4640,f4304]) ).
fof(f4670,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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(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)))))),
inference(forward_demodulation,[],[f4646,f4578]) ).
fof(f4675,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_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,[],[f4670,f2516]) ).
fof(f4680,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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(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_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,[],[f4675,f4578]) ).
fof(f4683,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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(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,[],[f4680,f3216]) ).
fof(f4684,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,[],[f4683,f2517]) ).
fof(f4685,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,[],[f4684,f4578]) ).
fof(f4686,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(forward_demodulation,[],[f4685,f3169]) ).
fof(f4687,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,[],[f4686,f3216]) ).
fof(f4688,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,[],[f4687,f3224]) ).
fof(f4692,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,[],[f2957,f4128]) ).
fof(f4693,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,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,X0,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(resolution,[],[f4688,f2739]) ).
fof(f4700,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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,X0,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,[],[f4693,f4692]) ).
fof(f4713,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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)))),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))))))),
inference(resolution,[],[f2685,f4354]) ).
fof(f4718,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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)))),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))))))),
inference(forward_demodulation,[],[f4713,f4304]) ).
fof(f4720,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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)))),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))))),
inference(forward_demodulation,[],[f4718,f4578]) ).
fof(f4722,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),
inference(forward_demodulation,[],[f4720,f3164]) ).
fof(f4724,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),
inference(forward_demodulation,[],[f4722,f2516]) ).
fof(f4726,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),
inference(forward_demodulation,[],[f4724,f4692]) ).
fof(f4728,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),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_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),
inference(forward_demodulation,[],[f4726,f2517]) ).
fof(f4730,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),
inference(forward_demodulation,[],[f4728,f4692]) ).
fof(f4733,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)))))
| 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(resolution,[],[f4730,f2687]) ).
fof(f4736,definition,
( spl5_3
<=> 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)))) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f4737,plain,
( 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))))
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f4736]) ).
fof(f4739,definition,
( spl5_4
<=> 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))))) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f4740,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)))))
| spl5_4 ),
inference(avatar_component_clause,[],[f4739]) ).
fof(f4741,plain,
( spl5_3
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f4733,f4739,f4736]) ).
fof(f4750,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0),
inference(superposition,[],[f4692,f3353]) ).
fof(f4754,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),
inference(resolution,[],[f4099,f2614]) ).
fof(f4854,plain,
! [X0,X1] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,X1)),
inference(resolution,[],[f2738,f4127]) ).
fof(f4864,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ),
inference(resolution,[],[f3811,f3605]) ).
fof(f4922,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(superposition,[],[f4854,f4664]) ).
fof(f4945,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X1) = X0,
inference(resolution,[],[f2612,f4142]) ).
fof(f4946,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) = X0,
inference(forward_demodulation,[],[f4945,f4692]) ).
fof(f4947,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0,
inference(superposition,[],[f4946,f4566]) ).
fof(f4956,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) = X0,
inference(superposition,[],[f4692,f4947]) ).
fof(f4958,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0),
inference(superposition,[],[f4750,f4947]) ).
fof(f4967,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0,
inference(superposition,[],[f4946,f4956]) ).
fof(f4969,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),
inference(superposition,[],[f3354,f4956]) ).
fof(f4971,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(forward_demodulation,[],[f4969,f3353]) ).
fof(f4973,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(forward_demodulation,[],[f4971,f4967]) ).
fof(f4983,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(resolution,[],[f4864,f2739]) ).
fof(f4987,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),X1)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ),
inference(forward_demodulation,[],[f4983,f4947]) ).
fof(f4992,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X1)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ),
inference(superposition,[],[f4987,f4692]) ).
fof(f5003,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(superposition,[],[f4664,f2809]) ).
fof(f5068,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1 ),
inference(superposition,[],[f4992,f4946]) ).
fof(f5117,plain,
! [X0,X1] : c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Complex_ORe(X0)),c_Complex_OIm(X0)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1),X0),
inference(superposition,[],[f3224,f3164]) ).
fof(f5148,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)) = X1,
inference(resolution,[],[f3273,f4142]) ).
fof(f5149,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X0) = X1,
inference(forward_demodulation,[],[f5148,f4750]) ).
fof(f5151,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X1) = X0,
inference(superposition,[],[f5149,f4692]) ).
fof(f5267,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| 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(resolution,[],[f4623,f4864]) ).
fof(f5269,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(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)))),
inference(resolution,[],[f4623,f4754]) ).
fof(f5270,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(forward_demodulation,[],[f5269,f4664]) ).
fof(f5272,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))
| 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(forward_demodulation,[],[f5267,f4664]) ).
fof(f5273,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(duplicate_literal_removal,[],[f5272]) ).
fof(f5340,plain,
! [X0,X1] : c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(X0),X1),c_Complex_OIm(X0)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),
inference(superposition,[],[f3225,f3164]) ).
fof(f5415,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),
inference(resolution,[],[f2960,f4128]) ).
fof(f5434,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)),
inference(superposition,[],[f4692,f5415]) ).
fof(f5669,plain,
! [X2,X3,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3)),
inference(resolution,[],[f2962,f4128]) ).
fof(f5670,plain,
! [X2,X3,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3))),
inference(forward_demodulation,[],[f5669,f5415]) ).
fof(f5671,plain,
! [X2,X3,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3))),
inference(forward_demodulation,[],[f5670,f5415]) ).
fof(f6051,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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)))),
inference(superposition,[],[f4922,f2540]) ).
fof(f6063,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(forward_demodulation,[],[f6051,f5003]) ).
fof(f6069,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(forward_demodulation,[],[f6063,f5270]) ).
fof(f6072,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(forward_demodulation,[],[f6069,f5273]) ).
fof(f6684,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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),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_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(superposition,[],[f4354,f2517]) ).
fof(f6702,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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),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(forward_demodulation,[],[f6684,f2516]) ).
fof(f6705,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_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(forward_demodulation,[],[f6702,f4304]) ).
fof(f6706,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_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(forward_demodulation,[],[f6705,f4578]) ).
fof(f6707,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(forward_demodulation,[],[f6706,f3164]) ).
fof(f6858,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(superposition,[],[f5151,f4402]) ).
fof(f6877,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(forward_demodulation,[],[f6858,f4958]) ).
fof(f6888,definition,
( spl5_10
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f6889,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f6888]) ).
fof(f10307,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X0),
inference(resolution,[],[f4273,f4146]) ).
fof(f10350,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),X0))),
inference(superposition,[],[f5671,f10307]) ).
fof(f12631,plain,
! [X0] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0
| c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(resolution,[],[f5068,f4623]) ).
fof(f12663,plain,
! [X0] :
( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ),
inference(forward_demodulation,[],[f12631,f4664]) ).
fof(f12669,plain,
! [X0] :
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ),
inference(forward_demodulation,[],[f12663,f4958]) ).
fof(f12672,plain,
! [X0] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ),
inference(forward_demodulation,[],[f12669,f4973]) ).
fof(f12682,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(superposition,[],[f12672,f6072]) ).
fof(f12802,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(forward_demodulation,[],[f12682,f6877]) ).
fof(f12803,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(duplicate_literal_removal,[],[f12802]) ).
fof(f12851,plain,
spl5_10,
inference(avatar_split_clause,[],[f12803,f6888]) ).
fof(f14016,plain,
! [X0] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X0),c_Complex_OIm(X0)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(superposition,[],[f5340,f4947]) ).
fof(f14044,plain,
! [X0] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X0),c_Complex_OIm(X0)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(forward_demodulation,[],[f14016,f4572]) ).
fof(f14056,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0,
inference(forward_demodulation,[],[f14044,f3164]) ).
fof(f18787,plain,
! [X0,X1] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_NthRoot_Osqrt(X0),X1)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
inference(superposition,[],[f4578,f4664]) ).
fof(f18838,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
inference(superposition,[],[f18787,f5273]) ).
fof(f18913,plain,
! [X0] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)),
inference(forward_demodulation,[],[f18838,f4956]) ).
fof(f18934,plain,
! [X0] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)),
inference(forward_demodulation,[],[f18913,f2540]) ).
fof(f18941,plain,
! [X0] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)),
inference(forward_demodulation,[],[f18934,f2620]) ).
fof(f18943,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,[],[f18941,f4664]) ).
fof(f19354,plain,
( 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_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,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_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ spl5_10 ),
inference(superposition,[],[f4649,f6889]) ).
fof(f19468,plain,
( 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_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = 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_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_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f19354,f5415]) ).
fof(f19516,plain,
( 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_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = 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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f19468,f10350]) ).
fof(f19536,plain,
( 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_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,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_Groups_Ozero__class_Ozero(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))))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f19516,f5434]) ).
fof(f19544,plain,
( 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_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,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_Groups_Ozero__class_Ozero(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)))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f19536,f4956]) ).
fof(f19550,plain,
( 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_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = 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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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))))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f19544,f5415]) ).
fof(f19554,plain,
( 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_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f19550,f5434]) ).
fof(f19557,plain,
( 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_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_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f19554,f4956]) ).
fof(f19559,plain,
( 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_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_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f19557,f4956]) ).
fof(f19560,plain,
( c_Groups_Ozero__class_Ozero(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))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f19559,f4618]) ).
fof(f22145,plain,
( ! [X0] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X0,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,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ spl5_10 ),
inference(superposition,[],[f4578,f19560]) ).
fof(f22175,plain,
( ! [X0] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f22145,f4947]) ).
fof(f22188,plain,
( ! [X0] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X0))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f22175,f3216]) ).
fof(f22198,plain,
( ! [X0] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X0))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f22188,f2620]) ).
fof(f22205,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))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f22198,f4664]) ).
fof(f23288,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,[],[f4176,f2957]) ).
fof(f44305,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),X0) = X0,
inference(resolution,[],[f2644,f4146]) ).
fof(f44440,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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(superposition,[],[f4700,f44305]) ).
fof(f44510,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))))),
inference(forward_demodulation,[],[f44440,f18943]) ).
fof(f44616,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),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)))))),
inference(forward_demodulation,[],[f44510,f4692]) ).
fof(f44655,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f44616,f22205]) ).
fof(f44667,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_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)))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f44655,f4692]) ).
fof(f44671,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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_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)))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f44667,f44305]) ).
fof(f44675,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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),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)))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f44671,f5117]) ).
fof(f44678,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_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),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)))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f44675,f23288]) ).
fof(f44679,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_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),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)))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f44678,f4572]) ).
fof(f44680,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)))))
| ~ spl5_10 ),
inference(forward_demodulation,[],[f44679,f14056]) ).
fof(f44681,plain,
( $false
| spl5_4
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f44680,f4740]) ).
fof(f44682,plain,
( spl5_4
| ~ spl5_10 ),
inference(avatar_contradiction_clause,[],[f44681]) ).
fof(f44684,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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))
| ~ spl5_3 ),
inference(forward_demodulation,[],[f6707,f4737]) ).
fof(f44689,plain,
( $false
| ~ spl5_3 ),
inference(forward_subsumption_resolution,[],[f44684,f4536]) ).
fof(f44690,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f44689]) ).
cnf(s2,plain,
( spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f4741]) ).
cnf(s13,plain,
spl5_10,
inference(sat_conversion,[],[f12851]) ).
cnf(s67,plain,
( spl5_4
| ~ spl5_10 ),
inference(sat_conversion,[],[f44682]) ).
cnf(s69,plain,
~ spl5_3,
inference(sat_conversion,[],[f44690]) ).
cnf(s70,plain,
spl5_4,
inference(rat,[],[s67,s13]) ).
cnf(s71,plain,
$false,
inference(rat,[],[s2,s70,s69]) ).
fof(f44692,plain,
$false,
inference(avatar_sat_refutation,[],[s71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW203+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 13:14:27 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 Running first-order theorem proving
% 0.09/0.13 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.90/1.51 % (3371424)Detected formulas, will run a generic FOF schedule.
% 7.90/1.51 % (3371430)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=788013448:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.90/1.51 % (3371433)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3976210196:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.90/1.51 % (3371432)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2528729190:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.90/1.51 % (3371429)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2470594650:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.90/1.51 % (3371431)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3014132594:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.90/1.51 % (3371434)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1186442733:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.90/1.51 % (3371435)dis-21_1_sil=8000:lcm=predicate:random_seed=2770234302:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 7.90/1.51 % (3371432)Instruction limit reached!
% 7.90/1.51 % (3371432)------------------------------
% 7.90/1.51 % (3371432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.90/1.51 % (3371432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.90/1.51 % (3371432)CaDiCaL version: 2.1.3
% 7.90/1.51 % (3371432)Termination reason: Instruction limit
% 7.90/1.51 % (3371432)Termination phase: Saturation
% 7.90/1.51 % (3371432)Time elapsed: 0.035 s
% 7.90/1.51 % (3371432)Peak memory usage: 90 MB
% 7.90/1.51 % (3371432)Instructions burned: 110 (million)
% 7.90/1.51 % (3371433)Instruction limit reached!
% 7.90/1.51 % (3371433)------------------------------
% 7.90/1.51 % (3371433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.90/1.51 % (3371433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.90/1.51 % (3371433)CaDiCaL version: 2.1.3
% 7.90/1.51 % (3371433)Termination reason: Instruction limit
% 7.90/1.51 % (3371433)Termination phase: Saturation
% 7.90/1.51 % (3371433)Time elapsed: 0.038 s
% 7.90/1.51 % (3371433)Peak memory usage: 89 MB
% 7.90/1.51 % (3371433)Instructions burned: 121 (million)
% 7.90/1.51 % (3371435)Instruction limit reached!
% 7.90/1.51 % (3371435)------------------------------
% 7.90/1.51 % (3371435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.90/1.51 % (3371435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.90/1.51 % (3371435)CaDiCaL version: 2.1.3
% 7.90/1.51 % (3371435)Termination reason: Instruction limit
% 7.90/1.51 % (3371435)Termination phase: Saturation
% 7.90/1.51 % (3371435)Time elapsed: 0.036 s
% 7.90/1.51 % (3371435)Peak memory usage: 90 MB
% 7.90/1.51 % (3371435)Instructions burned: 130 (million)
% 7.90/1.51 % (3371434)Instruction limit reached!
% 7.90/1.51 % (3371434)------------------------------
% 7.90/1.51 % (3371434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.90/1.51 % (3371434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.90/1.51 % (3371434)CaDiCaL version: 2.1.3
% 7.90/1.51 % (3371434)Termination reason: Instruction limit
% 7.90/1.51 % (3371434)Termination phase: Saturation
% 7.90/1.51 % (3371434)Time elapsed: 0.042 s
% 7.90/1.51 % (3371434)Peak memory usage: 90 MB
% 7.90/1.51 % (3371434)Instructions burned: 141 (million)
% 7.90/1.51 % (3371444)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2931232519:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 7.90/1.51 % (3371443)lrs+10_1_sil=8000:sp=occurrence:random_seed=857287832:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 7.90/1.51 % (3371445)lrs+1011_1_sil=32000:sp=occurrence:random_seed=365945961:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 7.90/1.51 % (3371446)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=926225039:s2a=on:i=248:s2at=1.23:gtg=position_2998 on theBenchmark for (2998ds/248Mi)
% 7.90/1.51 % (3371444)Instruction limit reached!
% 11.94/2.03 % (3371444)------------------------------
% 11.94/2.03 % (3371444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.94/2.03 % (3371444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.94/2.03 % (3371444)CaDiCaL version: 2.1.3
% 11.94/2.03 % (3371444)Termination reason: Instruction limit
% 11.94/2.03 % (3371444)Termination phase: Saturation
% 11.94/2.03 % (3371444)Time elapsed: 0.048 s
% 11.94/2.03 % (3371444)Peak memory usage: 90 MB
% 11.94/2.03 % (3371444)Instructions burned: 158 (million)
% 11.94/2.03 % (3371443)Instruction limit reached!
% 11.94/2.03 % (3371443)------------------------------
% 11.94/2.03 % (3371443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.94/2.03 % (3371443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.94/2.03 % (3371443)CaDiCaL version: 2.1.3
% 11.94/2.03 % (3371443)Termination reason: Instruction limit
% 11.94/2.03 % (3371443)Termination phase: Saturation
% 11.94/2.03 % (3371443)Time elapsed: 0.098 s
% 11.94/2.03 % (3371443)Peak memory usage: 92 MB
% 11.94/2.03 % (3371443)Instructions burned: 288 (million)
% 11.94/2.03 % (3371446)Instruction limit reached!
% 11.94/2.03 % (3371446)------------------------------
% 11.94/2.03 % (3371446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.94/2.03 % (3371446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.94/2.03 % (3371446)CaDiCaL version: 2.1.3
% 11.94/2.03 % (3371446)Termination reason: Instruction limit
% 11.94/2.03 % (3371446)Termination phase: Saturation
% 11.94/2.03 % (3371446)Time elapsed: 0.075 s
% 11.94/2.03 % (3371446)Peak memory usage: 92 MB
% 11.94/2.03 % (3371446)Instructions burned: 248 (million)
% 11.94/2.03 % (3371445)Instruction limit reached!
% 11.94/2.03 % (3371445)------------------------------
% 11.94/2.03 % (3371445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.94/2.03 % (3371445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.94/2.03 % (3371445)CaDiCaL version: 2.1.3
% 11.94/2.03 % (3371445)Termination reason: Instruction limit
% 11.94/2.03 % (3371445)Termination phase: Saturation
% 11.94/2.03 % (3371445)Time elapsed: 0.112 s
% 11.94/2.03 % (3371445)Peak memory usage: 93 MB
% 11.94/2.03 % (3371445)Instructions burned: 328 (million)
% 11.94/2.03 % (3371451)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1871090865:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2997 on theBenchmark for (2997ds/294Mi)
% 11.94/2.03 % (3371452)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=984646173:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 11.94/2.03 % (3371453)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3128066334:cts=off:i=113:fsr=off:ss=included:sgt=4_2996 on theBenchmark for (2996ds/113Mi)
% 11.94/2.03 % (3371451)Instruction limit reached!
% 11.94/2.03 % (3371451)------------------------------
% 11.94/2.03 % (3371451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.94/2.03 % (3371451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.94/2.03 % (3371451)CaDiCaL version: 2.1.3
% 11.94/2.03 % (3371451)Termination reason: Instruction limit
% 11.94/2.03 % (3371451)Termination phase: Saturation
% 11.94/2.03 % (3371451)Time elapsed: 0.093 s
% 11.94/2.03 % (3371451)Peak memory usage: 91 MB
% 11.94/2.03 % (3371451)Instructions burned: 297 (million)
% 11.94/2.03 % (3371453)Instruction limit reached!
% 11.94/2.03 % (3371453)------------------------------
% 11.94/2.03 % (3371453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.94/2.03 % (3371453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.94/2.03 % (3371454)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3124835348:i=127:av=off:fsr=off:sup=off_2996 on theBenchmark for (2996ds/127Mi)
% 11.94/2.03 % (3371453)CaDiCaL version: 2.1.3
% 11.94/2.03 % (3371453)Termination reason: Instruction limit
% 11.94/2.03 % (3371453)Termination phase: Saturation
% 11.94/2.03 % (3371453)Time elapsed: 0.033 s
% 11.94/2.03 % (3371453)Peak memory usage: 90 MB
% 11.94/2.03 % (3371453)Instructions burned: 113 (million)
% 11.94/2.03 % (3371454)Instruction limit reached!
% 11.94/2.03 % (3371454)------------------------------
% 11.94/2.03 % (3371454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.94/2.03 % (3371454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.94/2.03 % (3371454)CaDiCaL version: 2.1.3
% 11.94/2.03 % (3371454)Termination reason: Instruction limit
% 11.94/2.03 % (3371454)Termination phase: Saturation
% 18.98/3.08 % (3371454)Time elapsed: 0.036 s
% 18.98/3.08 % (3371454)Peak memory usage: 90 MB
% 18.98/3.08 % (3371454)Instructions burned: 130 (million)
% 18.98/3.08 % (3371459)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2764970665:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2995 on theBenchmark for (2995ds/114Mi)
% 18.98/3.08 % (3371460)lrs+10_1_sil=8000:sp=occurrence:random_seed=116617928:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2995 on theBenchmark for (2995ds/907Mi)
% 18.98/3.08 % (3371459)Instruction limit reached!
% 18.98/3.08 % (3371459)------------------------------
% 18.98/3.08 % (3371459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371459)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371459)Termination reason: Instruction limit
% 18.98/3.08 % (3371459)Termination phase: Saturation
% 18.98/3.08 % (3371459)Time elapsed: 0.031 s
% 18.98/3.08 % (3371459)Peak memory usage: 90 MB
% 18.98/3.08 % (3371459)Instructions burned: 116 (million)
% 18.98/3.08 % (3371461)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2162720032:i=437:sd=1:aac=none:ss=included_2995 on theBenchmark for (2995ds/437Mi)
% 18.98/3.08 % (3371464)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=403838568:i=5202:ss=axioms:sgt=16_2994 on theBenchmark for (2994ds/5202Mi)
% 18.98/3.08 % (3371461)Instruction limit reached!
% 18.98/3.08 % (3371461)------------------------------
% 18.98/3.08 % (3371461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371461)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371461)Termination reason: Instruction limit
% 18.98/3.08 % (3371461)Termination phase: Saturation
% 18.98/3.08 % (3371461)Time elapsed: 0.127 s
% 18.98/3.08 % (3371461)Peak memory usage: 93 MB
% 18.98/3.08 % (3371461)Instructions burned: 440 (million)
% 18.98/3.08 % (3371467)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3569199853:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2992 on theBenchmark for (2992ds/134Mi)
% 18.98/3.08 % (3371467)Instruction limit reached!
% 18.98/3.08 % (3371467)------------------------------
% 18.98/3.08 % (3371467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371467)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371467)Termination reason: Instruction limit
% 18.98/3.08 % (3371467)Termination phase: Saturation
% 18.98/3.08 % (3371467)Time elapsed: 0.040 s
% 18.98/3.08 % (3371467)Peak memory usage: 92 MB
% 18.98/3.08 % (3371467)Instructions burned: 137 (million)
% 18.98/3.08 % (3371460)Instruction limit reached!
% 18.98/3.08 % (3371460)------------------------------
% 18.98/3.08 % (3371460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371460)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371460)Termination reason: Instruction limit
% 18.98/3.08 % (3371460)Termination phase: Saturation
% 18.98/3.08 % (3371460)Time elapsed: 0.302 s
% 18.98/3.08 % (3371460)Peak memory usage: 99 MB
% 18.98/3.08 % (3371460)Instructions burned: 910 (million)
% 18.98/3.08 % (3371469)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3398010821:st=8:i=592:sd=3:ep=RST:ss=axioms_2991 on theBenchmark for (2991ds/592Mi)
% 18.98/3.08 % (3371470)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3545814881:st=3:i=13193:sd=3:ss=axioms_2991 on theBenchmark for (2991ds/13193Mi)
% 18.98/3.08 % (3371469)Instruction limit reached!
% 18.98/3.08 % (3371469)------------------------------
% 18.98/3.08 % (3371469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371469)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371469)Termination reason: Instruction limit
% 18.98/3.08 % (3371469)Termination phase: Saturation
% 18.98/3.08 % (3371469)Time elapsed: 0.175 s
% 18.98/3.08 % (3371469)Peak memory usage: 95 MB
% 18.98/3.08 % (3371469)Instructions burned: 593 (million)
% 18.98/3.08 % (3371473)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=3886423517:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2988 on theBenchmark for (2988ds/125Mi)
% 18.98/3.08 % (3371452)Instruction limit reached!
% 18.98/3.08 % (3371452)------------------------------
% 18.98/3.08 % (3371452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371452)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371452)Termination reason: Instruction limit
% 18.98/3.08 % (3371452)Termination phase: Saturation
% 18.98/3.08 % (3371452)Time elapsed: 0.806 s
% 18.98/3.08 % (3371452)Peak memory usage: 145 MB
% 18.98/3.08 % (3371452)Instructions burned: 2350 (million)
% 18.98/3.08 % (3371473)Instruction limit reached!
% 18.98/3.08 % (3371473)------------------------------
% 18.98/3.08 % (3371473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371473)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371473)Termination reason: Instruction limit
% 18.98/3.08 % (3371473)Termination phase: Saturation
% 18.98/3.08 % (3371473)Time elapsed: 0.039 s
% 18.98/3.08 % (3371473)Peak memory usage: 91 MB
% 18.98/3.08 % (3371473)Instructions burned: 125 (million)
% 18.98/3.08 % (3371476)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3270645065:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2987 on theBenchmark for (2987ds/141Mi)
% 18.98/3.08 % (3371475)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=1249959872:i=134:gtgl=5:slsql=off:gtg=exists_sym_2987 on theBenchmark for (2987ds/134Mi)
% 18.98/3.08 % (3371475)Instruction limit reached!
% 18.98/3.08 % (3371475)------------------------------
% 18.98/3.08 % (3371475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371475)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371475)Termination reason: Instruction limit
% 18.98/3.08 % (3371475)Termination phase: Saturation
% 18.98/3.08 % (3371475)Time elapsed: 0.035 s
% 18.98/3.08 % (3371475)Peak memory usage: 90 MB
% 18.98/3.08 % (3371475)Instructions burned: 135 (million)
% 18.98/3.08 % (3371476)Instruction limit reached!
% 18.98/3.08 % (3371476)------------------------------
% 18.98/3.08 % (3371476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371476)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371476)Termination reason: Instruction limit
% 18.98/3.08 % (3371476)Termination phase: Saturation
% 18.98/3.08 % (3371476)Time elapsed: 0.043 s
% 18.98/3.08 % (3371476)Peak memory usage: 91 MB
% 18.98/3.08 % (3371476)Instructions burned: 145 (million)
% 18.98/3.08 % (3371479)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1412247980:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/431Mi)
% 18.98/3.08 % (3371480)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=3732045672:i=6060:aac=none:ins=25_2986 on theBenchmark for (2986ds/6060Mi)
% 18.98/3.08 % (3371479)Instruction limit reached!
% 18.98/3.08 % (3371479)------------------------------
% 18.98/3.08 % (3371479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371479)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371479)Termination reason: Instruction limit
% 18.98/3.08 % (3371479)Termination phase: Saturation
% 18.98/3.08 % (3371479)Time elapsed: 0.121 s
% 18.98/3.08 % (3371479)Peak memory usage: 92 MB
% 18.98/3.08 % (3371479)Instructions burned: 431 (million)
% 18.98/3.08 % (3371483)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=1290375021:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2984 on theBenchmark for (2984ds/150Mi)
% 18.98/3.08 % (3371483)Instruction limit reached!
% 18.98/3.08 % (3371483)------------------------------
% 18.98/3.08 % (3371483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371483)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371483)Termination reason: Instruction limit
% 18.98/3.08 % (3371483)Termination phase: Saturation
% 18.98/3.08 % (3371483)Time elapsed: 0.043 s
% 18.98/3.08 % (3371483)Peak memory usage: 92 MB
% 18.98/3.08 % (3371483)Instructions burned: 150 (million)
% 18.98/3.08 % (3371485)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=2073808443:i=14155:bd=all_2982 on theBenchmark for (2982ds/14155Mi)
% 18.98/3.08 % (3371464)Instruction limit reached!
% 18.98/3.08 % (3371464)------------------------------
% 18.98/3.08 % (3371464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371464)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371464)Termination reason: Instruction limit
% 18.98/3.08 % (3371464)Termination phase: Saturation
% 18.98/3.08 % (3371464)Time elapsed: 1.754 s
% 18.98/3.08 % (3371464)Peak memory usage: 170 MB
% 18.98/3.08 % (3371464)Instructions burned: 5202 (million)
% 18.98/3.08 % (3371487)lrs+10_1024_sil=16000:plsq=on:plsqr=32,1:sos=all:fs=off:gs=on:newcnf=on:random_seed=1840571964:i=667:av=off:fsr=off_2975 on theBenchmark for (2975ds/667Mi)
% 18.98/3.08 % (3371430)First to succeed.
% 18.98/3.08 % (3371430)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3371424"
% 18.98/3.08 % (3371487)Instruction limit reached!
% 18.98/3.08 % (3371487)------------------------------
% 18.98/3.08 % (3371487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.98/3.08 % (3371487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.98/3.08 % (3371487)CaDiCaL version: 2.1.3
% 18.98/3.08 % (3371487)Termination reason: Instruction limit
% 18.98/3.08 % (3371487)Termination phase: Saturation
% 18.98/3.08 % (3371487)Time elapsed: 0.162 s
% 18.98/3.08 % (3371487)Peak memory usage: 93 MB
% 18.98/3.08 % (3371487)Instructions burned: 669 (million)
% 18.98/3.08 % (3371430)Refutation found. Thanks to Tanya!
% 18.98/3.08 % SZS status Theorem for theBenchmark
% 18.98/3.08 % SZS output start Proof for theBenchmark
% See solution above
% 19.54/3.18 % (3371430)------------------------------
% 19.54/3.18 % (3371430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.54/3.18 % (3371430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.54/3.18 % (3371430)CaDiCaL version: 2.1.3
% 19.54/3.18 % (3371430)Termination reason: Refutation
% 19.54/3.18 % (3371430)Time elapsed: 2.489 s
% 19.54/3.18 % (3371430)Peak memory usage: 187 MB
% 19.54/3.18 % (3371430)Instructions burned: 7396 (million)
% 19.54/3.18 % (3371430)------------------------------
% 19.54/3.18 % (3371430)------------------------------
% 19.54/3.18 % (3371424)Success in time 2.766 s
% 19.54/3.18 % Vampire exiting
%------------------------------------------------------------------------------