%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW197+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 01:29:49 PM UTC 2026
% Result : Theorem 33.92s 5.20s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 32
% Syntax : Number of formulae : 194 ( 150 unt; 11 def)
% Number of atoms : 238 ( 175 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 88 ( 44 ~; 40 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 21 con; 0-3 aty)
% Number of variables : 211 ( 211 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(f76,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(f100,axiom,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(f508,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,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,X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(f510,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(f581,axiom,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(f742,axiom,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = hAPP(c_Int_Onat,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__def) ).
fof(f857,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f882,axiom,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_m____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_m) ).
fof(f907,axiom,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_csqrt) ).
fof(f909,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(f916,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
fof(f918,axiom,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_Nat_Onat,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
fof(f922,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(f935,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/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f955,axiom,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f959,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/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).
fof(f992,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/sandbox/benchmark/theBenchmark.p',fact_succ__def) ).
fof(f1168,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1188,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1189,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(negated_conjecture,[status(cth)],[f1188]) ).
fof(f1197,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(flattening,[],[f1189]) ).
fof(f1245,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f42]) ).
fof(f1284,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f76]) ).
fof(f2102,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f909]) ).
fof(f2114,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f922]) ).
fof(f2561,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f4]) ).
fof(f2609,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f1245]) ).
fof(f2647,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f1284]) ).
fof(f2685,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
inference(cnf_transformation,[],[f100]) ).
fof(f3322,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,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,X2,X0)),
inference(cnf_transformation,[],[f508]) ).
fof(f3326,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
inference(cnf_transformation,[],[f510]) ).
fof(f3418,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0,
inference(cnf_transformation,[],[f581]) ).
fof(f3653,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = hAPP(c_Int_Onat,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)),
inference(cnf_transformation,[],[f742]) ).
fof(f3839,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f857]) ).
fof(f3879,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_m____),
inference(cnf_transformation,[],[f882]) ).
fof(f3918,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X0,
inference(cnf_transformation,[],[f907]) ).
fof(f3922,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2102]) ).
fof(f3932,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f916]) ).
fof(f3934,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f918]) ).
fof(f3938,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2114]) ).
fof(f3952,plain,
! [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) = c_Int_OBit1(X0),
inference(cnf_transformation,[],[f935]) ).
fof(f3983,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f955]) ).
fof(f3987,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,[],[f959]) ).
fof(f4034,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,[],[f992]) ).
fof(f4210,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1168]) ).
fof(f4230,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f1197]) ).
fof(f4231,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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)))),v_m____),
inference(definition_unfolding,[],[f3879,f3983,f3952]) ).
fof(f4269,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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,[],[f3918,f3983,f3952]) ).
fof(f4273,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(definition_unfolding,[],[f3922,f3983,f3952]) ).
fof(f4283,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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,[],[f3932,f3983,f3952]) ).
fof(f4285,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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,[],[f3934,f3983,f3952]) ).
fof(f4289,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(definition_unfolding,[],[f3938,f3983,f3952]) ).
fof(f4336,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,[],[f3987,f3952,f3952,f3983,f4034]) ).
fof(f4566,definition,
sF48 = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[sF48])],[function_definition]) ).
fof(f4567,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = sF48,
inference(reorient_equations,[],[f4566]) ).
fof(f4568,definition,
sF49 = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[sF49])],[function_definition]) ).
fof(f4569,plain,
c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = sF49,
inference(reorient_equations,[],[f4568]) ).
fof(f4570,definition,
sF50 = hAPP(sF49,v_b),
introduced(definition,[new_symbols(definition,[sF50])],[function_definition]) ).
fof(f4571,plain,
hAPP(sF49,v_b) = sF50,
inference(reorient_equations,[],[f4570]) ).
fof(f4572,definition,
sF51 = c_Power_Opower__class_Opower(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[sF51])],[function_definition]) ).
fof(f4573,plain,
c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = sF51,
inference(reorient_equations,[],[f4572]) ).
fof(f4574,definition,
sF52 = c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____),
introduced(definition,[new_symbols(definition,[sF52])],[function_definition]) ).
fof(f4575,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____) = sF52,
inference(reorient_equations,[],[f4574]) ).
fof(f4576,definition,
sF53 = hAPP(sF51,sF52),
introduced(definition,[new_symbols(definition,[sF53])],[function_definition]) ).
fof(f4577,plain,
hAPP(sF51,sF52) = sF53,
inference(reorient_equations,[],[f4576]) ).
fof(f4578,definition,
sF54 = hAPP(sF53,v_na____),
introduced(definition,[new_symbols(definition,[sF54])],[function_definition]) ).
fof(f4579,plain,
hAPP(sF53,v_na____) = sF54,
inference(reorient_equations,[],[f4578]) ).
fof(f4580,definition,
sF55 = hAPP(sF50,sF54),
introduced(definition,[new_symbols(definition,[sF55])],[function_definition]) ).
fof(f4581,plain,
hAPP(sF50,sF54) = sF55,
inference(reorient_equations,[],[f4580]) ).
fof(f4582,definition,
sF56 = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF48,sF55),
introduced(definition,[new_symbols(definition,[sF56])],[function_definition]) ).
fof(f4583,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF48,sF55) = sF56,
inference(reorient_equations,[],[f4582]) ).
fof(f4584,definition,
sF57 = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF56),
introduced(definition,[new_symbols(definition,[sF57])],[function_definition]) ).
fof(f4585,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF56) = sF57,
inference(reorient_equations,[],[f4584]) ).
fof(f4586,definition,
sF58 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
introduced(definition,[new_symbols(definition,[sF58])],[function_definition]) ).
fof(f4587,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = sF58,
inference(reorient_equations,[],[f4586]) ).
fof(f4588,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF57,sF58),
inference(definition_folding,[],[f4230,f4587,f4585,f4583,f4581,f4579,f4577,f4575,f4573,f4571,f4569,f4567]) ).
fof(f4628,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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))))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f4289,f4336]) ).
fof(f4632,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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,[],[f4285,f4336]) ).
fof(f4634,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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,[],[f4283,f4336]) ).
fof(f4644,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f4273,f4336]) ).
fof(f4648,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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,[],[f4269,f4336]) ).
fof(f4665,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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)))))),v_m____),
inference(forward_demodulation,[],[f4231,f4336]) ).
fof(f4878,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = hAPP(c_Int_Onat,X0),
inference(backward_demodulation,[],[f3653,f3418]) ).
fof(f4983,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF48,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(backward_demodulation,[],[f2561,f4567]) ).
fof(f5041,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_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))))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f4628,f3322]) ).
fof(f5045,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_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,[],[f4632,f3322]) ).
fof(f5047,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_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,[],[f4634,f3322]) ).
fof(f5057,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_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))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f4644,f3322]) ).
fof(f5061,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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_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,[],[f4648,f3322]) ).
fof(f5077,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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,[],[f4665,f2685]) ).
fof(f5234,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF48,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),sF58),
inference(forward_demodulation,[],[f4983,f4587]) ).
fof(f5264,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),hAPP(c_Int_Onat,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_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))))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5041,f4878]) ).
fof(f5268,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Int_Onat,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_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,[],[f5045,f4878]) ).
fof(f5270,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,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_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,[],[f5047,f4878]) ).
fof(f5280,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,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_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))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5057,f4878]) ).
fof(f5284,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),hAPP(c_Int_Onat,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_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,[],[f5061,f4878]) ).
fof(f5300,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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,[],[f5077,f4878]) ).
fof(f5379,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF48,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(sF51,v_z____),v_m____)))),sF58),
inference(forward_demodulation,[],[f5234,f4573]) ).
fof(f5407,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint)))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5264,f3839]) ).
fof(f5411,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint))))),
inference(forward_demodulation,[],[f5268,f3839]) ).
fof(f5413,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f5270,f3839]) ).
fof(f5423,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint))))),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5280,f3839]) ).
fof(f5427,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint))))) = X0,
inference(forward_demodulation,[],[f5284,f3839]) ).
fof(f5443,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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_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,[],[f5300,f3322]) ).
fof(f5465,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF48,hAPP(hAPP(sF49,v_b),hAPP(hAPP(sF51,v_z____),v_m____)))),sF58),
inference(forward_demodulation,[],[f5379,f4569]) ).
fof(f5493,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),hAPP(c_Int_Onat,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))))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5407,f3326]) ).
fof(f5497,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Int_Onat,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,[],[f5411,f3326]) ).
fof(f5499,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,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,[],[f5413,f3326]) ).
fof(f5509,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,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))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5423,f3326]) ).
fof(f5513,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),hAPP(c_Int_Onat,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,[],[f5427,f3326]) ).
fof(f5528,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint))))),
inference(forward_demodulation,[],[f5443,f3839]) ).
fof(f5538,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF48,hAPP(sF50,hAPP(hAPP(sF51,v_z____),v_m____)))),sF58),
inference(forward_demodulation,[],[f5465,f4571]) ).
fof(f5562,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),hAPP(c_Int_Onat,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))))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5493,f3322]) ).
fof(f5566,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Int_Onat,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,[],[f5497,f3322]) ).
fof(f5568,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,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,[],[f5499,f3322]) ).
fof(f5578,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,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))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5509,f3322]) ).
fof(f5582,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),hAPP(c_Int_Onat,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,[],[f5513,f3322]) ).
fof(f5597,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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,[],[f5528,f3326]) ).
fof(f5624,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),hAPP(c_Int_Onat,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)))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5562,f3839]) ).
fof(f5628,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Int_Onat,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,[],[f5566,f3839]) ).
fof(f5630,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,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,[],[f5568,f3839]) ).
fof(f5640,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,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))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5578,f3839]) ).
fof(f5644,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),hAPP(c_Int_Onat,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,[],[f5582,f3839]) ).
fof(f5659,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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,[],[f5597,f3322]) ).
fof(f5685,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint)))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5624,f3322]) ).
fof(f5689,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint))))),
inference(forward_demodulation,[],[f5628,f3322]) ).
fof(f5691,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f5630,f3322]) ).
fof(f5701,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint))))),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5640,f3322]) ).
fof(f5705,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint))))) = X0,
inference(forward_demodulation,[],[f5644,f3322]) ).
fof(f5720,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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,[],[f5659,f3839]) ).
fof(f5743,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5685,f3839]) ).
fof(f5747,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f5689,f3839]) ).
fof(f5749,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f5691,f3839]) ).
fof(f5759,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint)))),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5701,f3839]) ).
fof(f5763,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint)))) = X0,
inference(forward_demodulation,[],[f5705,f3839]) ).
fof(f5778,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint))))),
inference(forward_demodulation,[],[f5720,f3322]) ).
fof(f5801,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),hAPP(c_Int_Onat,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)))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5743,f3326]) ).
fof(f5805,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Int_Onat,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,[],[f5747,f3326]) ).
fof(f5807,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,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,[],[f5749,f3326]) ).
fof(f5817,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,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))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5759,f3326]) ).
fof(f5821,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),hAPP(c_Int_Onat,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,[],[f5763,f3326]) ).
fof(f5836,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f5778,f3839]) ).
fof(f5859,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),hAPP(c_Int_Onat,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)))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5801,f3322]) ).
fof(f5863,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Int_Onat,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,[],[f5805,f3322]) ).
fof(f5865,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,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,[],[f5807,f3322]) ).
fof(f5875,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,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))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5817,f3322]) ).
fof(f5879,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),hAPP(c_Int_Onat,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,[],[f5821,f3322]) ).
fof(f5894,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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,[],[f5836,f3326]) ).
fof(f5913,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f5859,f3839]) ).
fof(f5917,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Int_Onat,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,[],[f5863,f3839]) ).
fof(f5919,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,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,[],[f5865,f3839]) ).
fof(f5929,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,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))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5875,f3839]) ).
fof(f5933,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),hAPP(c_Int_Onat,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,[],[f5879,f3839]) ).
fof(f5948,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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,[],[f5894,f3322]) ).
fof(f5966,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(backward_demodulation,[],[f5913,f5919]) ).
fof(f5970,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(backward_demodulation,[],[f5917,f5919]) ).
fof(f5981,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(forward_demodulation,[],[f5929,f5919]) ).
fof(f5985,plain,
! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0,
inference(forward_demodulation,[],[f5933,f5919]) ).
fof(f5999,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),hAPP(c_Int_Onat,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,[],[f5948,f3839]) ).
fof(f6008,plain,
! [X0] : hAPP(hAPP(sF51,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0,
inference(forward_demodulation,[],[f5985,f4573]) ).
fof(f6009,plain,
v_na____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),v_m____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f5999,f5919]) ).
fof(f6015,plain,
v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_m____,v_m____),
inference(forward_demodulation,[],[f6009,f5970]) ).
fof(f6127,plain,
v_z____ = hAPP(hAPP(sF51,sF52),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[],[f6008,f4575]) ).
fof(f6128,plain,
v_z____ = hAPP(sF53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f6127,f4577]) ).
fof(f6145,plain,
! [X0] :
( hAPP(hAPP(sF51,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X0)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[],[f5966,f4573]) ).
fof(f6153,plain,
! [X0] : hAPP(hAPP(sF51,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X0),
inference(forward_subsumption_resolution,[],[f6145,f4210]) ).
fof(f6155,plain,
! [X0] : hAPP(hAPP(sF51,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(sF49,X0),X0),
inference(forward_demodulation,[],[f6153,f4569]) ).
fof(f6158,plain,
hAPP(sF53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(sF49,sF52),sF52),
inference(superposition,[],[f6155,f4577]) ).
fof(f6161,plain,
v_z____ = hAPP(hAPP(sF49,sF52),sF52),
inference(forward_demodulation,[],[f6158,f6128]) ).
fof(f6396,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(sF51,X0),X1)),hAPP(hAPP(sF51,X0),X1)) = hAPP(hAPP(sF51,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[],[f5981,f4573]) ).
fof(f6412,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(sF51,X0),X1)),hAPP(hAPP(sF51,X0),X1)) = hAPP(hAPP(sF51,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)),
inference(forward_subsumption_resolution,[],[f6396,f4210]) ).
fof(f6416,plain,
! [X0,X1] : hAPP(hAPP(sF51,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)) = hAPP(hAPP(sF49,hAPP(hAPP(sF51,X0),X1)),hAPP(hAPP(sF51,X0),X1)),
inference(forward_demodulation,[],[f6412,f4569]) ).
fof(f7265,plain,
! [X0] : hAPP(sF53,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) = hAPP(hAPP(sF49,hAPP(sF53,X0)),hAPP(sF53,X0)),
inference(superposition,[],[f6416,f4577]) ).
fof(f9327,plain,
! [X2,X0,X1] :
( hAPP(hAPP(sF51,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(sF51,X0),X2)),hAPP(hAPP(sF51,X1),X2))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[],[f2647,f4573]) ).
fof(f9380,plain,
! [X2,X0,X1] : hAPP(hAPP(sF51,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(sF51,X0),X2)),hAPP(hAPP(sF51,X1),X2)),
inference(forward_subsumption_resolution,[],[f9327,f4210]) ).
fof(f9383,plain,
! [X2,X0,X1] : hAPP(hAPP(sF51,hAPP(hAPP(sF49,X0),X1)),X2) = hAPP(hAPP(sF49,hAPP(hAPP(sF51,X0),X2)),hAPP(hAPP(sF51,X1),X2)),
inference(forward_demodulation,[],[f9380,f4569]) ).
fof(f9387,plain,
! [X0,X1] : hAPP(hAPP(sF51,X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)) = hAPP(hAPP(sF51,hAPP(hAPP(sF49,X0),X0)),X1),
inference(backward_demodulation,[],[f6416,f9383]) ).
fof(f9401,plain,
! [X0] : hAPP(sF53,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) = hAPP(hAPP(sF51,hAPP(hAPP(sF49,sF52),sF52)),X0),
inference(superposition,[],[f9387,f4577]) ).
fof(f9431,plain,
! [X0] : hAPP(sF53,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) = hAPP(hAPP(sF51,v_z____),X0),
inference(forward_demodulation,[],[f9401,f6161]) ).
fof(f9436,plain,
! [X0] : hAPP(hAPP(sF49,hAPP(sF53,X0)),hAPP(sF53,X0)) = hAPP(hAPP(sF51,v_z____),X0),
inference(backward_demodulation,[],[f7265,f9431]) ).
fof(f9831,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(sF51,X0),X1)),hAPP(hAPP(sF51,X0),X2)) = hAPP(hAPP(sF51,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[],[f2609,f4573]) ).
fof(f9902,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(sF51,X0),X1)),hAPP(hAPP(sF51,X0),X2)) = hAPP(hAPP(sF51,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(forward_subsumption_resolution,[],[f9831,f4210]) ).
fof(f9908,plain,
! [X2,X0,X1] : hAPP(hAPP(sF51,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(sF49,hAPP(hAPP(sF51,X0),X1)),hAPP(hAPP(sF51,X0),X2)),
inference(forward_demodulation,[],[f9902,f4569]) ).
fof(f9917,plain,
! [X0,X1] : hAPP(sF53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) = hAPP(hAPP(sF49,hAPP(sF53,X0)),hAPP(sF53,X1)),
inference(superposition,[],[f9908,f4577]) ).
fof(f9969,plain,
! [X0] : hAPP(hAPP(sF51,v_z____),X0) = hAPP(sF53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0)),
inference(backward_demodulation,[],[f9436,f9917]) ).
fof(f10053,plain,
hAPP(sF53,v_na____) = hAPP(hAPP(sF51,v_z____),v_m____),
inference(superposition,[],[f9969,f6015]) ).
fof(f10055,plain,
sF54 = hAPP(hAPP(sF51,v_z____),v_m____),
inference(forward_demodulation,[],[f10053,f4579]) ).
fof(f10056,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF48,hAPP(sF50,sF54))),sF58),
inference(backward_demodulation,[],[f5538,f10055]) ).
fof(f10159,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF48,sF55)),sF58),
inference(forward_demodulation,[],[f10056,f4581]) ).
fof(f10211,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF56),sF58),
inference(forward_demodulation,[],[f10159,f4583]) ).
fof(f10264,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sF57,sF58),
inference(forward_demodulation,[],[f10211,f4585]) ).
fof(f10271,plain,
$false,
inference(forward_subsumption_resolution,[],[f10264,f4588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW197+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n009.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 13:17:15 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.00/2.15 % (3020703)Detected formulas, will run a generic FOF schedule.
% 12.00/2.15 % (3020714)dis-21_1_sil=8000:lcm=predicate:random_seed=1969223407: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)
% 12.00/2.15 % (3020714)Instruction limit reached!
% 12.00/2.15 % (3020714)------------------------------
% 12.00/2.15 % (3020714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.00/2.15 % (3020714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.00/2.15 % (3020714)CaDiCaL version: 2.1.3
% 12.00/2.15 % (3020714)Termination reason: Instruction limit
% 12.00/2.15 % (3020714)Termination phase: Saturation
% 12.00/2.15 % (3020714)Time elapsed: 0.036 s
% 12.00/2.15 % (3020714)Peak memory usage: 90 MB
% 12.00/2.15 % (3020714)Instructions burned: 130 (million)
% 12.00/2.15 % (3020708)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=63237335:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.00/2.15 % (3020710)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=3053776940:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.00/2.15 % (3020709)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=1961984550:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.00/2.15 % (3020711)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=517936695:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.00/2.15 % (3020713)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4174915837:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.00/2.15 % (3020712)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1420511168:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.00/2.15 % (3020711)Refutation not found, incomplete strategy
% 12.00/2.15 % (3020711)------------------------------
% 12.00/2.15 % (3020711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.00/2.15 % (3020711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.00/2.15 % (3020711)CaDiCaL version: 2.1.3
% 12.00/2.15 % (3020711)Termination reason: Refutation not found, incomplete strategy
% 12.00/2.15 % (3020711)Time elapsed: 0.020 s
% 12.00/2.15 % (3020711)Peak memory usage: 89 MB
% 12.00/2.15 % (3020711)Instructions burned: 35 (million)
% 12.00/2.15 % (3020712)Instruction limit reached!
% 12.00/2.15 % (3020712)------------------------------
% 12.00/2.15 % (3020712)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.00/2.15 % (3020712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.00/2.15 % (3020712)CaDiCaL version: 2.1.3
% 12.00/2.15 % (3020712)Termination reason: Instruction limit
% 12.00/2.15 % (3020712)Termination phase: Saturation
% 12.00/2.15 % (3020712)Time elapsed: 0.073 s
% 12.00/2.15 % (3020712)Peak memory usage: 90 MB
% 12.00/2.15 % (3020712)Instructions burned: 120 (million)
% 12.00/2.15 % (3020713)Instruction limit reached!
% 12.00/2.15 % (3020713)------------------------------
% 12.00/2.15 % (3020713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.00/2.15 % (3020713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.00/2.15 % (3020713)CaDiCaL version: 2.1.3
% 12.00/2.15 % (3020713)Termination reason: Instruction limit
% 12.00/2.15 % (3020713)Termination phase: Saturation
% 12.00/2.15 % (3020713)Time elapsed: 0.075 s
% 12.00/2.15 % (3020713)Peak memory usage: 90 MB
% 12.00/2.15 % (3020713)Instructions burned: 140 (million)
% 12.00/2.15 % (3020722)lrs+10_1_sil=8000:sp=occurrence:random_seed=412267370:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 12.00/2.15 % (3020722)Instruction limit reached!
% 12.00/2.15 % (3020722)------------------------------
% 12.00/2.15 % (3020722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.00/2.15 % (3020722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.00/2.15 % (3020722)CaDiCaL version: 2.1.3
% 12.00/2.15 % (3020722)Termination reason: Instruction limit
% 12.00/2.15 % (3020722)Termination phase: Saturation
% 12.00/2.15 % (3020722)Time elapsed: 0.096 s
% 12.00/2.15 % (3020722)Peak memory usage: 92 MB
% 12.00/2.15 % (3020722)Instructions burned: 286 (million)
% 12.00/2.15 % (3020723)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3187163056:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 19.33/3.16 % (3020724)lrs+1011_1_sil=32000:sp=occurrence:random_seed=501827327:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 19.33/3.16 % (3020711)------------------------------
% 19.33/3.16 % (3020711)------------------------------
% 19.33/3.16 % (3020723)Instruction limit reached!
% 19.33/3.16 % (3020723)------------------------------
% 19.33/3.16 % (3020723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.33/3.16 % (3020723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.33/3.16 % (3020723)CaDiCaL version: 2.1.3
% 19.33/3.16 % (3020723)Termination reason: Instruction limit
% 19.33/3.16 % (3020723)Termination phase: Saturation
% 19.33/3.16 % (3020723)Time elapsed: 0.090 s
% 19.33/3.16 % (3020723)Peak memory usage: 90 MB
% 19.33/3.16 % (3020723)Instructions burned: 158 (million)
% 19.33/3.16 % (3020726)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=3405301137:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 19.33/3.17 % (3020726)Instruction limit reached!
% 19.33/3.17 % (3020726)------------------------------
% 19.33/3.17 % (3020726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.33/3.17 % (3020726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.33/3.17 % (3020726)CaDiCaL version: 2.1.3
% 19.33/3.17 % (3020726)Termination reason: Instruction limit
% 19.33/3.17 % (3020726)Termination phase: Saturation
% 19.33/3.17 % (3020726)Time elapsed: 0.075 s
% 19.33/3.17 % (3020726)Peak memory usage: 92 MB
% 19.33/3.17 % (3020726)Instructions burned: 250 (million)
% 19.33/3.17 % (3020729)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2355443583:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 19.33/3.17 % (3020724)Instruction limit reached!
% 19.33/3.17 % (3020724)------------------------------
% 19.33/3.17 % (3020724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.33/3.17 % (3020724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.33/3.17 % (3020724)CaDiCaL version: 2.1.3
% 19.33/3.17 % (3020724)Termination reason: Instruction limit
% 19.33/3.17 % (3020724)Termination phase: Saturation
% 19.33/3.17 % (3020724)Time elapsed: 0.208 s
% 19.33/3.17 % (3020724)Peak memory usage: 92 MB
% 19.33/3.17 % (3020724)Instructions burned: 326 (million)
% 19.33/3.17 % (3020730)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2431379787:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 19.33/3.17 % (3020729)Refutation not found, incomplete strategy
% 19.33/3.17 % (3020729)------------------------------
% 19.33/3.17 % (3020729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.33/3.17 % (3020729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.33/3.17 % (3020729)CaDiCaL version: 2.1.3
% 19.33/3.17 % (3020729)Termination reason: Refutation not found, incomplete strategy
% 19.33/3.17 % (3020729)Time elapsed: 0.056 s
% 19.33/3.17 % (3020729)Peak memory usage: 91 MB
% 19.33/3.17 % (3020729)Instructions burned: 102 (million)
% 19.33/3.17 % (3020732)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2057027980:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 19.33/3.17 % (3020732)Instruction limit reached!
% 19.33/3.17 % (3020732)------------------------------
% 19.33/3.17 % (3020732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.33/3.17 % (3020732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.33/3.17 % (3020732)CaDiCaL version: 2.1.3
% 19.33/3.17 % (3020732)Termination reason: Instruction limit
% 19.33/3.17 % (3020732)Termination phase: Saturation
% 19.33/3.17 % (3020732)Time elapsed: 0.031 s
% 19.33/3.17 % (3020732)Peak memory usage: 90 MB
% 19.33/3.17 % (3020732)Instructions burned: 117 (million)
% 19.33/3.17 % (3020734)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=31483132:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 19.33/3.17 % (3020734)Instruction limit reached!
% 19.33/3.17 % (3020734)------------------------------
% 19.33/3.17 % (3020734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.33/3.17 % (3020734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.33/3.17 % (3020734)CaDiCaL version: 2.1.3
% 33.40/5.20 % (3020734)Termination reason: Instruction limit
% 33.40/5.20 % (3020734)Termination phase: Saturation
% 33.40/5.20 % (3020734)Time elapsed: 0.061 s
% 33.40/5.20 % (3020734)Peak memory usage: 90 MB
% 33.40/5.20 % (3020734)Instructions burned: 127 (million)
% 33.40/5.20 % (3020737)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=577080857:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 33.40/5.20 % (3020729)------------------------------
% 33.40/5.20 % (3020729)------------------------------
% 33.40/5.20 % (3020737)Instruction limit reached!
% 33.40/5.20 % (3020737)------------------------------
% 33.40/5.20 % (3020737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.40/5.20 % (3020737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.40/5.20 % (3020737)CaDiCaL version: 2.1.3
% 33.40/5.20 % (3020737)Termination reason: Instruction limit
% 33.40/5.20 % (3020737)Termination phase: Saturation
% 33.40/5.20 % (3020737)Time elapsed: 0.031 s
% 33.40/5.20 % (3020737)Peak memory usage: 90 MB
% 33.40/5.20 % (3020737)Instructions burned: 116 (million)
% 33.40/5.20 % (3020739)lrs+10_1_sil=8000:sp=occurrence:random_seed=92972218:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 33.40/5.20 % (3020741)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2317127502:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 33.40/5.20 % (3020742)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4254800803:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 33.40/5.20 % (3020741)Instruction limit reached!
% 33.40/5.20 % (3020741)------------------------------
% 33.40/5.20 % (3020741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.40/5.20 % (3020741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.40/5.20 % (3020741)CaDiCaL version: 2.1.3
% 33.40/5.20 % (3020741)Termination reason: Instruction limit
% 33.40/5.20 % (3020741)Termination phase: Saturation
% 33.40/5.20 % (3020741)Time elapsed: 0.125 s
% 33.40/5.20 % (3020741)Peak memory usage: 93 MB
% 33.40/5.20 % (3020741)Instructions burned: 440 (million)
% 33.40/5.20 % (3020746)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=850339049:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 33.40/5.20 % (3020746)Instruction limit reached!
% 33.40/5.20 % (3020746)------------------------------
% 33.40/5.20 % (3020746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.40/5.20 % (3020746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.40/5.20 % (3020746)CaDiCaL version: 2.1.3
% 33.40/5.20 % (3020746)Termination reason: Instruction limit
% 33.40/5.20 % (3020746)Termination phase: Saturation
% 33.40/5.20 % (3020746)Time elapsed: 0.038 s
% 33.40/5.20 % (3020746)Peak memory usage: 91 MB
% 33.40/5.20 % (3020746)Instructions burned: 136 (million)
% 33.40/5.20 % (3020748)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=438064938:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 33.40/5.20 % (3020739)Instruction limit reached!
% 33.40/5.20 % (3020739)------------------------------
% 33.40/5.20 % (3020739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.40/5.20 % (3020739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.40/5.20 % (3020739)CaDiCaL version: 2.1.3
% 33.40/5.20 % (3020739)Termination reason: Instruction limit
% 33.40/5.20 % (3020739)Termination phase: Saturation
% 33.40/5.20 % (3020739)Time elapsed: 0.565 s
% 33.40/5.20 % (3020739)Peak memory usage: 97 MB
% 33.40/5.20 % (3020739)Instructions burned: 908 (million)
% 33.40/5.20 % (3020748)Instruction limit reached!
% 33.40/5.20 % (3020748)------------------------------
% 33.40/5.20 % (3020748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.40/5.20 % (3020748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.40/5.20 % (3020748)CaDiCaL version: 2.1.3
% 33.40/5.20 % (3020748)Termination reason: Instruction limit
% 33.40/5.20 % (3020748)Termination phase: Saturation
% 33.40/5.20 % (3020748)Time elapsed: 0.166 s
% 33.40/5.20 % (3020748)Peak memory usage: 94 MB
% 33.40/5.20 % (3020748)Instructions burned: 594 (million)
% 33.40/5.20 % (3020751)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=823678050:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/125Mi)
% 33.92/5.20 % (3020750)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1674067647:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 33.92/5.20 % (3020751)Instruction limit reached!
% 33.92/5.20 % (3020751)------------------------------
% 33.92/5.20 % (3020751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.92/5.20 % (3020751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.92/5.20 % (3020751)CaDiCaL version: 2.1.3
% 33.92/5.20 % (3020751)Termination reason: Instruction limit
% 33.92/5.20 % (3020751)Termination phase: Saturation
% 33.92/5.20 % (3020751)Time elapsed: 0.037 s
% 33.92/5.20 % (3020751)Peak memory usage: 91 MB
% 33.92/5.20 % (3020751)Instructions burned: 126 (million)
% 33.92/5.20 % (3020754)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=50974903:i=134:gtgl=5:slsql=off:gtg=exists_sym_2982 on theBenchmark for (2982ds/134Mi)
% 33.92/5.20 % (3020754)Instruction limit reached!
% 33.92/5.20 % (3020754)------------------------------
% 33.92/5.20 % (3020754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.92/5.20 % (3020754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.92/5.20 % (3020754)CaDiCaL version: 2.1.3
% 33.92/5.20 % (3020754)Termination reason: Instruction limit
% 33.92/5.20 % (3020754)Termination phase: Saturation
% 33.92/5.20 % (3020754)Time elapsed: 0.034 s
% 33.92/5.20 % (3020754)Peak memory usage: 90 MB
% 33.92/5.20 % (3020754)Instructions burned: 138 (million)
% 33.92/5.20 % (3020756)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3463352477:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2980 on theBenchmark for (2980ds/141Mi)
% 33.92/5.20 % (3020756)Refutation not found, incomplete strategy
% 33.92/5.20 % (3020756)------------------------------
% 33.92/5.20 % (3020756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.92/5.20 % (3020756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.92/5.20 % (3020756)CaDiCaL version: 2.1.3
% 33.92/5.20 % (3020756)Termination reason: Refutation not found, incomplete strategy
% 33.92/5.20 % (3020756)Time elapsed: 0.006 s
% 33.92/5.20 % (3020756)Peak memory usage: 89 MB
% 33.92/5.20 % (3020756)Instructions burned: 18 (million)
% 33.92/5.20 % (3020730)Instruction limit reached!
% 33.92/5.20 % (3020730)------------------------------
% 33.92/5.20 % (3020730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.92/5.20 % (3020730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.92/5.20 % (3020730)CaDiCaL version: 2.1.3
% 33.92/5.20 % (3020730)Termination reason: Instruction limit
% 33.92/5.20 % (3020730)Termination phase: Saturation
% 33.92/5.20 % (3020730)Time elapsed: 1.481 s
% 33.92/5.20 % (3020730)Peak memory usage: 149 MB
% 33.92/5.20 % (3020730)Instructions burned: 2351 (million)
% 33.92/5.20 % (3020756)------------------------------
% 33.92/5.20 % (3020756)------------------------------
% 33.92/5.20 % (3020758)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=166140404:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2978 on theBenchmark for (2978ds/431Mi)
% 33.92/5.20 % (3020759)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=2831640064:i=6060:aac=none:ins=25_2977 on theBenchmark for (2977ds/6060Mi)
% 33.92/5.20 % (3020758)Instruction limit reached!
% 33.92/5.20 % (3020758)------------------------------
% 33.92/5.20 % (3020758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.92/5.20 % (3020758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.92/5.20 % (3020758)CaDiCaL version: 2.1.3
% 33.92/5.20 % (3020758)Termination reason: Instruction limit
% 33.92/5.20 % (3020758)Termination phase: Saturation
% 33.92/5.20 % (3020758)Time elapsed: 0.210 s
% 33.92/5.20 % (3020758)Peak memory usage: 92 MB
% 33.92/5.20 % (3020758)Instructions burned: 431 (million)
% 33.92/5.20 % (3020762)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=2254612979:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2974 on theBenchmark for (2974ds/150Mi)
% 33.92/5.20 % (3020762)Instruction limit reached!
% 33.92/5.20 % (3020762)------------------------------
% 33.92/5.20 % (3020762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.92/5.20 % (3020762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.92/5.20 % (3020762)CaDiCaL version: 2.1.3
% 33.92/5.20 % (3020762)Termination reason: Instruction limit
% 33.92/5.20 % (3020762)Termination phase: Saturation
% 33.92/5.20 % (3020762)Time elapsed: 0.077 s
% 33.92/5.20 % (3020762)Peak memory usage: 91 MB
% 33.92/5.20 % (3020762)Instructions burned: 151 (million)
% 33.92/5.20 % (3020764)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=2648598677:i=14155:bd=all_2972 on theBenchmark for (2972ds/14155Mi)
% 33.92/5.20 % (3020759)Instruction limit reached!
% 33.92/5.20 % (3020759)------------------------------
% 33.92/5.20 % (3020759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.92/5.20 % (3020759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.92/5.20 % (3020759)CaDiCaL version: 2.1.3
% 33.92/5.20 % (3020759)Termination reason: Instruction limit
% 33.92/5.20 % (3020759)Termination phase: Saturation
% 33.92/5.20 % (3020759)Time elapsed: 2.043 s
% 33.92/5.20 % (3020759)Peak memory usage: 179 MB
% 33.92/5.20 % (3020759)Instructions burned: 6062 (million)
% 33.92/5.20 % (3020742)Instruction limit reached!
% 33.92/5.20 % (3020742)------------------------------
% 33.92/5.20 % (3020742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.92/5.20 % (3020742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.92/5.20 % (3020742)CaDiCaL version: 2.1.3
% 33.92/5.20 % (3020742)Termination reason: Instruction limit
% 33.92/5.20 % (3020742)Termination phase: Saturation
% 33.92/5.20 % (3020742)Time elapsed: 3.291 s
% 33.92/5.20 % (3020742)Peak memory usage: 160 MB
% 33.92/5.20 % (3020742)Instructions burned: 5202 (million)
% 33.92/5.20 % (3020764)First to succeed.
% 33.92/5.20 % (3020766)lrs+10_1024_sil=16000:plsq=on:plsqr=32,1:sos=all:fs=off:gs=on:newcnf=on:random_seed=1250114951:i=667:av=off:fsr=off_2956 on theBenchmark for (2956ds/667Mi)
% 33.92/5.20 % (3020764)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3020703"
% 33.92/5.20 % (3020767)ott-1011_3:1_anc=all_dependent:to=lpo:sil=8000:drc=ordering:sas=cadical:fdtod=off:sp=reverse_frequency:spb=goal_then_units:urr=full:lftc=20:newcnf=on:random_seed=576875643:s2a=on:i=185:s2at=1.8:fdi=4_2956 on theBenchmark for (2956ds/185Mi)
% 33.92/5.20 % (3020767)Instruction limit reached!
% 33.92/5.20 % (3020767)------------------------------
% 33.92/5.20 % (3020767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.92/5.20 % (3020767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.92/5.20 % (3020767)CaDiCaL version: 2.1.3
% 33.92/5.20 % (3020767)Termination reason: Instruction limit
% 33.92/5.20 % (3020767)Termination phase: Saturation
% 33.92/5.20 % (3020767)Time elapsed: 0.091 s
% 33.92/5.20 % (3020767)Peak memory usage: 92 MB
% 33.92/5.20 % (3020767)Instructions burned: 185 (million)
% 33.92/5.20 % (3020766)Instruction limit reached!
% 33.92/5.20 % (3020766)------------------------------
% 33.92/5.20 % (3020766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.92/5.20 % (3020766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.92/5.20 % (3020766)CaDiCaL version: 2.1.3
% 33.92/5.20 % (3020766)Termination reason: Instruction limit
% 33.92/5.20 % (3020766)Termination phase: Saturation
% 33.92/5.20 % (3020766)Time elapsed: 0.158 s
% 33.92/5.20 % (3020766)Peak memory usage: 93 MB
% 33.92/5.20 % (3020766)Instructions burned: 669 (million)
% 33.92/5.20 % (3020764)Refutation found. Thanks to Tanya!
% 33.92/5.20 % SZS status Theorem for theBenchmark
% 33.92/5.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/5.40 % (3020764)------------------------------
% 0.19/5.40 % (3020764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/5.40 % (3020764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/5.40 % (3020764)CaDiCaL version: 2.1.3
% 0.19/5.40 % (3020764)Termination reason: Refutation
% 0.19/5.40 % (3020764)Time elapsed: 1.588 s
% 0.19/5.40 % (3020764)Peak memory usage: 148 MB
% 0.19/5.40 % (3020764)Instructions burned: 2546 (million)
% 0.19/5.40 % (3020764)------------------------------
% 0.19/5.40 % (3020764)------------------------------
% 0.19/5.40 % (3020703)Success in time 4.779 s
% 0.19/5.40 % Vampire exiting
%------------------------------------------------------------------------------