%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW211+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 : n020.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 01:29:51 PM UTC 2026
% Result : Theorem 15.08s 3.44s
% Output : Refutation 18.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 31
% Syntax : Number of formulae : 170 ( 92 unt; 4 def)
% Number of atoms : 279 ( 98 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 194 ( 85 ~; 89 |; 5 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 11 con; 0-5 aty)
% Number of variables : 190 ( 0 sgn 190 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(f14,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_Fun_Ocomp(X6,X5,X4,X3,X2) = X1
=> hAPP(X3,hAPP(X2,X0)) = hAPP(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
fof(f44,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(f142,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(f143,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(f182,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( X1 != X0
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(f283,axiom,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(f299,axiom,
! [X0,X1] : c_Complex_OIm(c_Complex_Ocomplex_OComplex(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Im) ).
fof(f300,axiom,
! [X0,X1] : c_Complex_ORe(c_Complex_Ocomplex_OComplex(X1,X0)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Re) ).
fof(f301,axiom,
! [X0,X1] : 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,X1,X0)),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(X1),c_Complex_ORe(X0))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),c_Complex_OIm(X0))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_metric__bound__lemma) ).
fof(f315,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(f316,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(f324,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(f348,axiom,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096abs_A_IRe_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ax_J_A_L_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_A_L_Ae_A_P_A2_096) ).
fof(f358,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
fof(f363,axiom,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f406,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(f407,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f411,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X0)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).
fof(f491,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f564,axiom,
! [X0] : c_Int_Osucc(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__def) ).
fof(f569,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X0)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_Osucc(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).
fof(f1110,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f1129,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(f1130,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f1163,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1230,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1231,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____),
inference(negated_conjecture,[status(cth)],[f1230]) ).
fof(f1234,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____),
inference(flattening,[],[f1231]) ).
fof(f1236,plain,
! [X0,X1,X2] :
( c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f1240,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( hAPP(X3,hAPP(X2,X0)) = hAPP(X1,X0)
| c_Fun_Ocomp(X6,X5,X4,X3,X2) != X1 ),
inference(ennf_transformation,[],[f14]) ).
fof(f1422,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,[],[f142]) ).
fof(f1423,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,[],[f1422]) ).
fof(f1424,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(ennf_transformation,[],[f143]) ).
fof(f1425,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(flattening,[],[f1424]) ).
fof(f1468,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f182]) ).
fof(f1469,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f1468]) ).
fof(f1571,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,[],[f324]) ).
fof(f2227,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,[],[f44]) ).
fof(f2228,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,[],[f2227]) ).
fof(f2560,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
inference(cnf_transformation,[],[f1236]) ).
fof(f2570,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(X1,X0) = hAPP(X3,hAPP(X2,X0))
| c_Fun_Ocomp(X6,X5,X4,X3,X2) != X1 ),
inference(cnf_transformation,[],[f1240]) ).
fof(f2612,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2228]) ).
fof(f2613,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2228]) ).
fof(f2737,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,[],[f1423]) ).
fof(f2738,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ),
inference(cnf_transformation,[],[f1425]) ).
fof(f2805,plain,
! [X2,X0,X1] :
( ~ class_Rings_Olinordered__idom(X2)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1) ),
inference(cnf_transformation,[],[f1469]) ).
fof(f2945,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f283]) ).
fof(f2964,plain,
! [X0,X1] : c_Complex_OIm(c_Complex_Ocomplex_OComplex(X1,X0)) = X0,
inference(cnf_transformation,[],[f299]) ).
fof(f2965,plain,
! [X0,X1] : c_Complex_ORe(c_Complex_Ocomplex_OComplex(X1,X0)) = X1,
inference(cnf_transformation,[],[f300]) ).
fof(f2966,plain,
! [X0,X1] : 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,X1,X0)),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(X1),c_Complex_ORe(X0))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),c_Complex_OIm(X0))))),
inference(cnf_transformation,[],[f301]) ).
fof(f2982,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),c_Complex_OIm(X0)) = c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)),
inference(cnf_transformation,[],[f315]) ).
fof(f2983,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X1),c_Complex_ORe(X0)) = c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)),
inference(cnf_transformation,[],[f316]) ).
fof(f2991,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,[],[f1571]) ).
fof(f3022,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(cnf_transformation,[],[f348]) ).
fof(f3039,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X0,
inference(cnf_transformation,[],[f358]) ).
fof(f3044,plain,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f363]) ).
fof(f3108,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f406]) ).
fof(f3109,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f407]) ).
fof(f3113,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X0)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
inference(cnf_transformation,[],[f411]) ).
fof(f3236,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
inference(cnf_transformation,[],[f491]) ).
fof(f3344,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_Osucc(X0),
inference(cnf_transformation,[],[f564]) ).
fof(f3351,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X0)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_Osucc(X0))),
inference(cnf_transformation,[],[f569]) ).
fof(f4101,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1110]) ).
fof(f4120,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1129]) ).
fof(f4121,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1130]) ).
fof(f4154,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1163]) ).
fof(f4221,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____),
inference(cnf_transformation,[],[f1234]) ).
fof(f4222,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(definition_unfolding,[],[f3022,f3108,f3044,f3108,f3044]) ).
fof(f4231,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = X0,
inference(definition_unfolding,[],[f3039,f3108,f3044,f3108,f3044]) ).
fof(f4279,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
inference(definition_unfolding,[],[f3113,f3108,f3108,f3108]) ).
fof(f4343,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(definition_unfolding,[],[f3351,f3044,f3044,f3108,f3344]) ).
fof(f4425,plain,
! [X2,X3,X0,X6,X4,X5] : hAPP(X3,hAPP(X2,X0)) = hAPP(c_Fun_Ocomp(X6,X5,X4,X3,X2),X0),
inference(equality_resolution,[],[f2570]) ).
fof(f4436,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_resolution,[],[f2612]) ).
fof(f4688,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))),
inference(forward_demodulation,[],[f4279,f3236]) ).
fof(f4717,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = X0,
inference(forward_demodulation,[],[f4231,f4343]) ).
fof(f4726,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f4222,f4343]) ).
fof(f4727,plain,
! [X0,X1] : 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,X1,X0)),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(X1),c_Complex_ORe(X0))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0))))),
inference(forward_demodulation,[],[f2966,f2982]) ).
fof(f4778,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0))),
inference(forward_demodulation,[],[f4688,f3236]) ).
fof(f4796,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) = X0,
inference(forward_demodulation,[],[f4717,f3236]) ).
fof(f4805,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f4726,f3236]) ).
fof(f4806,plain,
! [X0,X1] : 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,X1,X0)),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,X1,X0))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0))))),
inference(forward_demodulation,[],[f4727,f2983]) ).
fof(f4850,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) = X0,
inference(forward_demodulation,[],[f4796,f4778]) ).
fof(f4859,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f4805,f4778]) ).
fof(f4896,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = X0,
inference(forward_demodulation,[],[f4850,f3109]) ).
fof(f4905,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f4859,f3109]) ).
fof(f4926,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = X0,
inference(forward_demodulation,[],[f4896,f3109]) ).
fof(f4931,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f4905,f3109]) ).
fof(f4951,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = X0,
inference(forward_demodulation,[],[f4926,f3236]) ).
fof(f4956,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f4931,f3236]) ).
fof(f4975,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = X0,
inference(forward_demodulation,[],[f4951,f4778]) ).
fof(f4980,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f4956,f4778]) ).
fof(f4999,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = X0,
inference(forward_demodulation,[],[f4975,f3109]) ).
fof(f5004,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f4980,f3109]) ).
fof(f5023,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = X0,
inference(forward_demodulation,[],[f4999,f3109]) ).
fof(f5028,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),
inference(forward_demodulation,[],[f5004,f3109]) ).
fof(f5033,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),v_e____),
inference(forward_demodulation,[],[f5028,f5023]) ).
fof(f5064,plain,
! [X0,X1] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),
inference(resolution,[],[f4154,f2560]) ).
fof(f5075,plain,
! [X0,X1] : 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,X0,X1)),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,X1,X0))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0))))),
inference(superposition,[],[f4806,f5064]) ).
fof(f5082,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(resolution,[],[f2738,f2613]) ).
fof(f5096,plain,
! [X2,X0,X1] : c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X0,X1),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Complex_ORe(X2)),
inference(superposition,[],[f2983,f2965]) ).
fof(f5099,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1 ),
inference(resolution,[],[f4120,f2805]) ).
fof(f5101,plain,
! [X2,X0,X1] : c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X0),X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Complex_OIm(X2)),
inference(superposition,[],[f2982,f2964]) ).
fof(f5108,plain,
! [X0,X1] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)),
inference(resolution,[],[f4101,f2560]) ).
fof(f5109,plain,
! [X0,X1] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)),
inference(forward_demodulation,[],[f5108,f2945]) ).
fof(f5112,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)),
inference(forward_demodulation,[],[f5109,f2945]) ).
fof(f5117,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X1),c_Complex_ORe(X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1))),
inference(superposition,[],[f5112,f2983]) ).
fof(f5118,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),c_Complex_OIm(X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1))),
inference(superposition,[],[f5112,f2982]) ).
fof(f5122,plain,
c_Orderings_Oord__class_Oless(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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))),v_e____),
inference(superposition,[],[f5033,f5112]) ).
fof(f5123,plain,
c_Orderings_Oord__class_Oless(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,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))),v_e____),
inference(forward_demodulation,[],[f5122,f5112]) ).
fof(f5127,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1))),
inference(forward_demodulation,[],[f5118,f2982]) ).
fof(f5128,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1))),
inference(forward_demodulation,[],[f5117,f2983]) ).
fof(f5153,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))))
| v_e____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))) ),
inference(resolution,[],[f5099,f4221]) ).
fof(f5161,definition,
( spl27_3
<=> v_e____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))) ),
introduced(definition,[new_symbols(definition,[spl27_3])],[avatar_definition]) ).
fof(f5162,plain,
( v_e____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f5161]) ).
fof(f5164,definition,
( spl27_4
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))) ),
introduced(definition,[new_symbols(definition,[spl27_4])],[avatar_definition]) ).
fof(f5165,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))
| ~ spl27_4 ),
inference(avatar_component_clause,[],[f5164]) ).
fof(f5169,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)))))
| v_e____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))) ),
inference(forward_demodulation,[],[f5153,f5064]) ).
fof(f5171,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))
| v_e____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))) ),
inference(forward_demodulation,[],[f5169,f4425]) ).
fof(f5173,plain,
( v_e____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))) ),
inference(forward_demodulation,[],[f5171,f5064]) ).
fof(f5175,plain,
( v_e____ = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))) ),
inference(forward_demodulation,[],[f5173,f4425]) ).
fof(f5177,plain,
( spl27_4
| spl27_3 ),
inference(avatar_split_clause,[],[f5175,f5161,f5164]) ).
fof(f5197,definition,
( spl27_6
<=> v_e____ = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))) ),
introduced(definition,[new_symbols(definition,[spl27_6])],[avatar_definition]) ).
fof(f5198,plain,
( v_e____ = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))))
| ~ spl27_6 ),
inference(avatar_component_clause,[],[f5197]) ).
fof(f5245,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(resolution,[],[f2737,f2613]) ).
fof(f5284,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),
inference(resolution,[],[f2991,f4121]) ).
fof(f5537,plain,
( v_e____ = 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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____)))) ),
inference(resolution,[],[f5245,f5033]) ).
fof(f5546,plain,
( v_e____ = 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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____)))) ),
inference(forward_demodulation,[],[f5537,f5112]) ).
fof(f5558,plain,
( v_e____ = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____)))) ),
inference(forward_demodulation,[],[f5546,f5284]) ).
fof(f5559,plain,
( v_e____ = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____)))) ),
inference(forward_demodulation,[],[f5558,f5112]) ).
fof(f5560,plain,
( v_e____ = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____)))) ),
inference(forward_demodulation,[],[f5559,f5284]) ).
fof(f5561,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| v_e____ = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))) ),
inference(forward_demodulation,[],[f5560,f5112]) ).
fof(f5562,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____))))
| v_e____ = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))) ),
inference(forward_demodulation,[],[f5561,f5284]) ).
fof(f5563,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| v_e____ = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))) ),
inference(forward_demodulation,[],[f5562,f5112]) ).
fof(f5564,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| v_e____ = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))) ),
inference(forward_demodulation,[],[f5563,f5284]) ).
fof(f5566,definition,
( spl27_10
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))))) ),
introduced(definition,[new_symbols(definition,[spl27_10])],[avatar_definition]) ).
fof(f5567,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| spl27_10 ),
inference(avatar_component_clause,[],[f5566]) ).
fof(f5568,plain,
( spl27_6
| ~ spl27_10 ),
inference(avatar_split_clause,[],[f5564,f5566,f5197]) ).
fof(f5609,plain,
( ! [X0] :
( ~ 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,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,X0) )
| ~ spl27_4 ),
inference(resolution,[],[f5082,f5165]) ).
fof(f5621,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_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_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____))))))
| ~ spl27_4 ),
inference(resolution,[],[f5609,f5075]) ).
fof(f5629,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| ~ spl27_4 ),
inference(forward_demodulation,[],[f5621,f5127]) ).
fof(f5631,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| ~ spl27_4 ),
inference(forward_demodulation,[],[f5629,f5101]) ).
fof(f5633,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____))))))
| ~ spl27_4 ),
inference(forward_demodulation,[],[f5631,f5284]) ).
fof(f5635,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| ~ spl27_4 ),
inference(forward_demodulation,[],[f5633,f5128]) ).
fof(f5637,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| ~ spl27_4 ),
inference(forward_demodulation,[],[f5635,f5096]) ).
fof(f5640,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| ~ spl27_4 ),
inference(forward_demodulation,[],[f5637,f5284]) ).
fof(f5641,plain,
( $false
| ~ spl27_4
| spl27_10 ),
inference(forward_subsumption_resolution,[],[f5640,f5567]) ).
fof(f5642,plain,
( ~ spl27_4
| spl27_10 ),
inference(avatar_contradiction_clause,[],[f5641]) ).
fof(f5699,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e____,v_e____)
| ~ spl27_6 ),
inference(superposition,[],[f5123,f5198]) ).
fof(f5700,plain,
( $false
| ~ spl27_6 ),
inference(forward_subsumption_resolution,[],[f5699,f4436]) ).
fof(f5701,plain,
~ spl27_6,
inference(avatar_contradiction_clause,[],[f5700]) ).
fof(f5708,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_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_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____))))))
| ~ spl27_3 ),
inference(superposition,[],[f5075,f5162]) ).
fof(f5747,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| ~ spl27_3 ),
inference(forward_demodulation,[],[f5708,f5127]) ).
fof(f5752,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,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_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| ~ spl27_3 ),
inference(forward_demodulation,[],[f5747,f5101]) ).
fof(f5755,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____))))))
| ~ spl27_3 ),
inference(forward_demodulation,[],[f5752,f5284]) ).
fof(f5758,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(v_x____,v_y____),v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| ~ spl27_3 ),
inference(forward_demodulation,[],[f5755,f5128]) ).
fof(f5761,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| ~ spl27_3 ),
inference(forward_demodulation,[],[f5758,f5096]) ).
fof(f5764,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x____,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_y____,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))))))))
| ~ spl27_3 ),
inference(forward_demodulation,[],[f5761,f5284]) ).
fof(f5765,plain,
( $false
| ~ spl27_3
| spl27_10 ),
inference(forward_subsumption_resolution,[],[f5764,f5567]) ).
fof(f5766,plain,
( ~ spl27_3
| spl27_10 ),
inference(avatar_contradiction_clause,[],[f5765]) ).
cnf(s5,plain,
( spl27_3
| spl27_4 ),
inference(sat_conversion,[],[f5177]) ).
cnf(s9,plain,
( spl27_6
| ~ spl27_10 ),
inference(sat_conversion,[],[f5568]) ).
cnf(s11,plain,
( ~ spl27_4
| spl27_10 ),
inference(sat_conversion,[],[f5642]) ).
cnf(s13,plain,
~ spl27_6,
inference(sat_conversion,[],[f5701]) ).
cnf(s17,plain,
( ~ spl27_3
| spl27_10 ),
inference(sat_conversion,[],[f5766]) ).
cnf(s18,plain,
~ spl27_10,
inference(rat,[],[s9,s13]) ).
cnf(s19,plain,
~ spl27_3,
inference(rat,[],[s17,s18]) ).
cnf(s20,plain,
~ spl27_4,
inference(rat,[],[s11,s18]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s5,s20,s19]) ).
fof(f5767,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW211+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.28 % Computer : n020.cluster.edu
% 0.23/0.28 % Model : x86_64 x86_64
% 0.23/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.28 % Memory : 8046.5625MB
% 0.23/0.28 % OS : Linux 6.8.0-71-generic
% 0.23/0.28 % CPULimit : 300
% 0.23/0.28 % WCLimit : 300
% 0.23/0.28 % DateTime : Mon Sep 28 13:18:20 UTC 2026
% 0.23/0.28 % CPUTime :
% 0.23/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.32 Running first-order theorem proving
% 0.23/0.32 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
% 15.08/3.41 % (154310)Detected formulas, will run a generic FOF schedule.
% 15.08/3.41 % (154329)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=435100663:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 15.08/3.41 % (154333)dis-21_1_sil=8000:lcm=predicate:random_seed=2117798326: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)
% 15.08/3.41 % (154327)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=1793949865:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 15.08/3.41 % (154328)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=939034193:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 15.08/3.41 % (154330)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2350524198:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 15.08/3.41 % (154331)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3164525002:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 15.08/3.41 % (154333)Instruction limit reached!
% 15.08/3.41 % (154333)------------------------------
% 15.08/3.41 % (154333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.41 % (154333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.41 % (154333)CaDiCaL version: 2.1.3
% 15.08/3.41 % (154333)Termination reason: Instruction limit
% 15.08/3.41 % (154333)Termination phase: Saturation
% 15.08/3.41 % (154333)Time elapsed: 0.077 s
% 15.08/3.41 % (154333)Peak memory usage: 91 MB
% 15.08/3.41 % (154333)Instructions burned: 130 (million)
% 15.08/3.41 % (154332)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1209781383:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 15.08/3.41 % (154330)Instruction limit reached!
% 15.08/3.41 % (154330)------------------------------
% 15.08/3.41 % (154330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.41 % (154330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.41 % (154330)CaDiCaL version: 2.1.3
% 15.08/3.41 % (154330)Termination reason: Instruction limit
% 15.08/3.41 % (154330)Termination phase: Saturation
% 15.08/3.41 % (154330)Time elapsed: 0.104 s
% 15.08/3.41 % (154330)Peak memory usage: 89 MB
% 15.08/3.41 % (154330)Instructions burned: 110 (million)
% 15.08/3.41 % (154331)Instruction limit reached!
% 15.08/3.41 % (154331)------------------------------
% 15.08/3.41 % (154331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.41 % (154331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.41 % (154331)CaDiCaL version: 2.1.3
% 15.08/3.41 % (154331)Termination reason: Instruction limit
% 15.08/3.41 % (154331)Termination phase: Saturation
% 15.08/3.41 % (154331)Time elapsed: 0.120 s
% 15.08/3.41 % (154331)Peak memory usage: 89 MB
% 15.08/3.41 % (154331)Instructions burned: 119 (million)
% 15.08/3.41 % (154342)lrs+10_1_sil=8000:sp=occurrence:random_seed=2614601461:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 15.08/3.41 % (154332)Instruction limit reached!
% 15.08/3.41 % (154332)------------------------------
% 15.08/3.41 % (154332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.41 % (154332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.41 % (154332)CaDiCaL version: 2.1.3
% 15.08/3.41 % (154332)Termination reason: Instruction limit
% 15.08/3.41 % (154332)Termination phase: Saturation
% 15.08/3.41 % (154332)Time elapsed: 0.133 s
% 15.08/3.41 % (154332)Peak memory usage: 91 MB
% 15.08/3.41 % (154332)Instructions burned: 139 (million)
% 15.08/3.41 % (154344)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2488217485:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 15.08/3.41 % (154345)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3722158625:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 15.08/3.41 % (154347)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=1687099226:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 15.08/3.41 % (154342)Instruction limit reached!
% 15.08/3.41 % (154342)------------------------------
% 15.08/3.41 % (154342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154342)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154342)Termination reason: Instruction limit
% 15.08/3.44 % (154342)Termination phase: Saturation
% 15.08/3.44 % (154342)Time elapsed: 0.289 s
% 15.08/3.44 % (154342)Peak memory usage: 92 MB
% 15.08/3.44 % (154342)Instructions burned: 285 (million)
% 15.08/3.44 % (154344)Instruction limit reached!
% 15.08/3.44 % (154344)------------------------------
% 15.08/3.44 % (154344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154344)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154344)Termination reason: Instruction limit
% 15.08/3.44 % (154344)Termination phase: Saturation
% 15.08/3.44 % (154344)Time elapsed: 0.154 s
% 15.08/3.44 % (154344)Peak memory usage: 91 MB
% 15.08/3.44 % (154344)Instructions burned: 158 (million)
% 15.08/3.44 % (154353)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4249240169:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 15.08/3.44 % (154353)Refutation not found, incomplete strategy
% 15.08/3.44 % (154353)------------------------------
% 15.08/3.44 % (154353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154353)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154353)Termination reason: Refutation not found, incomplete strategy
% 15.08/3.44 % (154353)Time elapsed: 0.020 s
% 15.08/3.44 % (154353)Peak memory usage: 90 MB
% 15.08/3.44 % (154353)Instructions burned: 66 (million)
% 15.08/3.44 % (154347)Instruction limit reached!
% 15.08/3.44 % (154347)------------------------------
% 15.08/3.44 % (154347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154347)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154347)Termination reason: Instruction limit
% 15.08/3.44 % (154347)Termination phase: Saturation
% 15.08/3.44 % (154347)Time elapsed: 0.222 s
% 15.08/3.44 % (154347)Peak memory usage: 92 MB
% 15.08/3.44 % (154347)Instructions burned: 249 (million)
% 15.08/3.44 % (154345)Instruction limit reached!
% 15.08/3.44 % (154345)------------------------------
% 15.08/3.44 % (154345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154345)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154345)Termination reason: Instruction limit
% 15.08/3.44 % (154345)Termination phase: Saturation
% 15.08/3.44 % (154345)Time elapsed: 0.349 s
% 15.08/3.44 % (154345)Peak memory usage: 92 MB
% 15.08/3.44 % (154345)Instructions burned: 325 (million)
% 15.08/3.44 % (154354)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3589759589:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 15.08/3.44 % (154353)------------------------------
% 15.08/3.44 % (154353)------------------------------
% 15.08/3.44 % (154356)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2115078856:cts=off:i=113:fsr=off:ss=included:sgt=4_2990 on theBenchmark for (2990ds/113Mi)
% 15.08/3.44 % (154359)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3584854690:i=127:av=off:fsr=off:sup=off_2990 on theBenchmark for (2990ds/127Mi)
% 15.08/3.44 % (154356)Instruction limit reached!
% 15.08/3.44 % (154356)------------------------------
% 15.08/3.44 % (154356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154356)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154356)Termination reason: Instruction limit
% 15.08/3.44 % (154356)Termination phase: Saturation
% 15.08/3.44 % (154356)Time elapsed: 0.101 s
% 15.08/3.44 % (154356)Peak memory usage: 90 MB
% 15.08/3.44 % (154356)Instructions burned: 113 (million)
% 15.08/3.44 % (154359)Instruction limit reached!
% 15.08/3.44 % (154359)------------------------------
% 15.08/3.44 % (154359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154359)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154359)Termination reason: Instruction limit
% 15.08/3.44 % (154359)Termination phase: Saturation
% 15.08/3.44 % (154359)Time elapsed: 0.109 s
% 15.08/3.44 % (154359)Peak memory usage: 90 MB
% 15.08/3.44 % (154359)Instructions burned: 127 (million)
% 15.08/3.44 % (154361)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3234997296:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2989 on theBenchmark for (2989ds/114Mi)
% 15.08/3.44 % (154361)Instruction limit reached!
% 15.08/3.44 % (154361)------------------------------
% 15.08/3.44 % (154361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154361)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154361)Termination reason: Instruction limit
% 15.08/3.44 % (154361)Termination phase: Saturation
% 15.08/3.44 % (154361)Time elapsed: 0.104 s
% 15.08/3.44 % (154361)Peak memory usage: 89 MB
% 15.08/3.44 % (154361)Instructions burned: 114 (million)
% 15.08/3.44 % (154364)lrs+10_1_sil=8000:sp=occurrence:random_seed=3221051105:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2987 on theBenchmark for (2987ds/907Mi)
% 15.08/3.44 % (154366)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=798792884:i=437:sd=1:aac=none:ss=included_2987 on theBenchmark for (2987ds/437Mi)
% 15.08/3.44 % (154367)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1321293934:i=5202:ss=axioms:sgt=16_2986 on theBenchmark for (2986ds/5202Mi)
% 15.08/3.44 % (154366)Instruction limit reached!
% 15.08/3.44 % (154366)------------------------------
% 15.08/3.44 % (154366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154366)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154366)Termination reason: Instruction limit
% 15.08/3.44 % (154366)Termination phase: Saturation
% 15.08/3.44 % (154366)Time elapsed: 0.383 s
% 15.08/3.44 % (154366)Peak memory usage: 93 MB
% 15.08/3.44 % (154366)Instructions burned: 437 (million)
% 15.08/3.44 % (154375)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1245508700:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2981 on theBenchmark for (2981ds/134Mi)
% 15.08/3.44 % (154328)First to succeed.
% 15.08/3.44 % (154328)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-154310"
% 15.08/3.44 % (154375)Instruction limit reached!
% 15.08/3.44 % (154375)------------------------------
% 15.08/3.44 % (154375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154375)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154375)Termination reason: Instruction limit
% 15.08/3.44 % (154375)Termination phase: Saturation
% 15.08/3.44 % (154375)Time elapsed: 0.121 s
% 15.08/3.44 % (154375)Peak memory usage: 92 MB
% 15.08/3.44 % (154375)Instructions burned: 134 (million)
% 15.08/3.44 % (154364)Instruction limit reached!
% 15.08/3.44 % (154364)------------------------------
% 15.08/3.44 % (154364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154364)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154364)Termination reason: Instruction limit
% 15.08/3.44 % (154364)Termination phase: Saturation
% 15.08/3.44 % (154364)Time elapsed: 0.843 s
% 15.08/3.44 % (154364)Peak memory usage: 97 MB
% 15.08/3.44 % (154364)Instructions burned: 907 (million)
% 15.08/3.44 % (154327)Also succeeded, but the first one will report.
% 15.08/3.44 % (154354)Instruction limit reached!
% 15.08/3.44 % (154354)------------------------------
% 15.08/3.44 % (154354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.08/3.44 % (154354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.08/3.44 % (154354)CaDiCaL version: 2.1.3
% 15.08/3.44 % (154354)Termination reason: Instruction limit
% 15.08/3.44 % (154354)Termination phase: Saturation
% 15.08/3.44 % (154354)Time elapsed: 1.379 s
% 15.08/3.44 % (154354)Peak memory usage: 144 MB
% 15.08/3.44 % (154354)Instructions burned: 2350 (million)
% 15.08/3.44 % (154377)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1368910903:st=8:i=592:sd=3:ep=RST:ss=axioms_2978 on theBenchmark for (2978ds/592Mi)
% 15.08/3.44 % (154378)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=91664325:st=3:i=13193:sd=3:ss=axioms_2977 on theBenchmark for (2977ds/13193Mi)
% 15.08/3.44 % (154379)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=3398680343:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2976 on theBenchmark for (2976ds/125Mi)
% 15.08/3.44 % (154328)Refutation found. Thanks to Tanya!
% 15.08/3.44 % SZS status Theorem for theBenchmark
% 15.08/3.44 % SZS output start Proof for theBenchmark
% See solution above
% 18.28/3.67 % (154328)------------------------------
% 18.28/3.67 % (154328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.28/3.67 % (154328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.28/3.67 % (154328)CaDiCaL version: 2.1.3
% 18.28/3.67 % (154328)Termination reason: Refutation
% 18.28/3.67 % (154328)Time elapsed: 1.823 s
% 18.28/3.67 % (154328)Peak memory usage: 143 MB
% 18.28/3.67 % (154328)Instructions burned: 1738 (million)
% 18.28/3.67 % (154328)------------------------------
% 18.28/3.67 % (154328)------------------------------
% 18.28/3.67 % (154310)Success in time 2.527 s
% 18.28/3.67 % Vampire exiting
%------------------------------------------------------------------------------