%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW282+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 : n019.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 01:30:01 PM UTC 2026
% Result : Theorem 38.43s 6.57s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 26
% Syntax : Number of formulae : 134 ( 37 unt; 3 def)
% Number of atoms : 253 ( 126 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 238 ( 119 ~; 103 |; 0 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-3 aty)
% Number of variables : 155 ( 0 sgn 154 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dpn) ).
fof(f5,axiom,
v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sne) ).
fof(f6,axiom,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pne) ).
fof(f7,axiom,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
fof(f11,axiom,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s) ).
fof(f16,axiom,
~ ! [X0] : v_pa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bs_O_Ap_A_061_A_091_058_N_Aa_M_A1_058_093_A_094_Aorder_Aa_Ap_A_K_As_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(f19,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__linear__power) ).
fof(f70,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(f395,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f396,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f397,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(f406,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f409,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(f617,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(f854,axiom,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(f855,axiom,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(f864,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(f916,axiom,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> ( X0 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__mult__eq) ).
fof(f926,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f1125,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1147,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(f1179,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(f1214,conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1215,negated_conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))),
inference(negated_conjecture,[status(cth)],[f1214]) ).
fof(f1216,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))),
inference(flattening,[],[f1215]) ).
fof(f1275,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f916]) ).
fof(f1276,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f1275]) ).
fof(f1314,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) = X0
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f1315,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1179]) ).
fof(f1321,plain,
? [X0] : v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),X0),
inference(ennf_transformation,[],[f16]) ).
fof(f1330,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,[],[f864]) ).
fof(f1336,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,[],[f409]) ).
fof(f1525,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f1663,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f406]) ).
fof(f1670,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f397]) ).
fof(f1671,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f396]) ).
fof(f1672,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f395]) ).
fof(f1756,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f617]) ).
fof(f2113,plain,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f1321]) ).
fof(f2316,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))))),
inference(cnf_transformation,[],[f1216]) ).
fof(f2325,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(cnf_transformation,[],[f926]) ).
fof(f2440,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1125]) ).
fof(f2442,plain,
! [X2,X0,X1] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ),
inference(cnf_transformation,[],[f1276]) ).
fof(f2469,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) = X0 ),
inference(cnf_transformation,[],[f1314]) ).
fof(f2470,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f1315]) ).
fof(f2489,plain,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),sK4),
inference(cnf_transformation,[],[f2113]) ).
fof(f2492,plain,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
inference(cnf_transformation,[],[f11]) ).
fof(f2494,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_pa____,
inference(cnf_transformation,[],[f6]) ).
fof(f2495,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____,
inference(cnf_transformation,[],[f4]) ).
fof(f2506,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_s____,
inference(cnf_transformation,[],[f5]) ).
fof(f2509,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = 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)) ),
inference(cnf_transformation,[],[f1330]) ).
fof(f2516,plain,
! [X2,X3,X0,X1] :
( ~ 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)) ),
inference(cnf_transformation,[],[f1336]) ).
fof(f2576,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____),
inference(cnf_transformation,[],[f7]) ).
fof(f2648,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
inference(cnf_transformation,[],[f855]) ).
fof(f2649,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
inference(cnf_transformation,[],[f854]) ).
fof(f2786,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f1525]) ).
fof(f2997,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f3004,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) ),
inference(cnf_transformation,[],[f1670]) ).
fof(f3005,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1671]) ).
fof(f3006,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) ),
inference(cnf_transformation,[],[f1672]) ).
fof(f3028,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1147]) ).
fof(f3113,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(cnf_transformation,[],[f1756]) ).
fof(f3870,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[],[f2786,f2440]) ).
fof(f3950,plain,
! [X0,X1] :
( c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ),
inference(resolution,[],[f2442,f3028]) ).
fof(f3951,plain,
! [X0,X1] : c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),X1)) = X1,
inference(resolution,[],[f2469,f2440]) ).
fof(f3953,plain,
! [X0,X1] : c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),X1)) = X1,
inference(forward_demodulation,[],[f3951,f3870]) ).
fof(f3979,definition,
( spl13_1
<=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f3980,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f3979]) ).
fof(f3981,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| spl13_1 ),
inference(avatar_component_clause,[],[f3979]) ).
fof(f3997,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| spl13_1 ),
inference(resolution,[],[f3981,f2470]) ).
fof(f3998,plain,
( $false
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f3997,f2440]) ).
fof(f3999,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f3998]) ).
fof(f4001,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X2))
| ~ spl13_1 ),
inference(resolution,[],[f3980,f2516]) ).
fof(f4008,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
| ~ spl13_1 ),
inference(resolution,[],[f3980,f2997]) ).
fof(f4010,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X2))
| ~ spl13_1 ),
inference(resolution,[],[f3980,f3004]) ).
fof(f4011,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X2))
| ~ spl13_1 ),
inference(resolution,[],[f3980,f3005]) ).
fof(f4012,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)
| ~ spl13_1 ),
inference(resolution,[],[f3980,f3006]) ).
fof(f4026,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))))
| ~ spl13_1 ),
inference(superposition,[],[f2316,f4012]) ).
fof(f4029,plain,
( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),sK4),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))
| ~ spl13_1 ),
inference(superposition,[],[f2489,f4012]) ).
fof(f4030,plain,
( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),sK4),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f4029,f3870]) ).
fof(f4032,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f4026,f4011]) ).
fof(f4040,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f4032,f4010]) ).
fof(f4042,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f4040,f4011]) ).
fof(f4044,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_na____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),v_na____)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))))))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f4042,f3870]) ).
fof(f4046,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_r____)),v_na____)
| ~ spl13_1 ),
inference(forward_demodulation,[],[f4044,f4001]) ).
fof(f4048,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)
| ~ spl13_1 ),
inference(forward_demodulation,[],[f4046,f4012]) ).
fof(f4188,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X2))
| ~ spl13_1 ),
inference(resolution,[],[f2509,f3980]) ).
fof(f4199,plain,
( ! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),v_u____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),X0))
| ~ spl13_1 ),
inference(superposition,[],[f4188,f2576]) ).
fof(f4214,plain,
( ! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),X0)))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f4199,f4010]) ).
fof(f4236,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),X0))),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),X0))),X1)
| ~ spl13_1 ),
inference(superposition,[],[f4010,f4214]) ).
fof(f4239,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),X0))),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),X0)),X1)))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f4236,f4010]) ).
fof(f4251,plain,
( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),X1))
| ~ spl13_1 ),
inference(resolution,[],[f3113,f3980]) ).
fof(f4785,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____ ),
inference(superposition,[],[f3950,f2492]) ).
fof(f4814,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
inference(forward_subsumption_resolution,[],[f4785,f2506]) ).
fof(f4830,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
inference(forward_demodulation,[],[f4814,f2325]) ).
fof(f4833,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
inference(forward_demodulation,[],[f4830,f3870]) ).
fof(f4835,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
inference(forward_demodulation,[],[f4833,f3953]) ).
fof(f4837,plain,
( v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
inference(forward_demodulation,[],[f4835,f2495]) ).
fof(f4839,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
inference(forward_demodulation,[],[f4837,f3870]) ).
fof(f4849,definition,
( spl13_24
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
introduced(definition,[new_symbols(definition,[spl13_24])],[avatar_definition]) ).
fof(f4851,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ~ spl13_24 ),
inference(avatar_component_clause,[],[f4849]) ).
fof(f4854,definition,
( spl13_25
<=> v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
introduced(definition,[new_symbols(definition,[spl13_25])],[avatar_definition]) ).
fof(f4856,plain,
( v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ~ spl13_25 ),
inference(avatar_component_clause,[],[f4854]) ).
fof(f4857,plain,
( spl13_25
| spl13_24 ),
inference(avatar_split_clause,[],[f4839,f4849,f4854]) ).
fof(f7468,plain,
( c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))
| ~ spl13_25 ),
inference(superposition,[],[f2649,f4856]) ).
fof(f7469,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ~ spl13_25 ),
inference(superposition,[],[f2648,f4856]) ).
fof(f7839,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X2)),X1) = hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1),X1)),X2)
| ~ spl13_1 ),
inference(superposition,[],[f4001,f4251]) ).
fof(f7840,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1),X2)),X0)
| ~ spl13_1 ),
inference(superposition,[],[f4188,f4251]) ).
fof(f7842,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_u____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)))),hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))))
| ~ spl13_1 ),
inference(superposition,[],[f4048,f4251]) ).
fof(f7856,plain,
( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),X1)),X0)
| ~ spl13_1 ),
inference(superposition,[],[f4012,f4251]) ).
fof(f7880,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))),hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f7842,f4239]) ).
fof(f7892,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))))),v_r____)
| ~ spl13_1 ),
inference(forward_demodulation,[],[f7880,f7856]) ).
fof(f7898,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),v_r____)
| ~ spl13_1
| ~ spl13_25 ),
inference(forward_demodulation,[],[f7892,f7468]) ).
fof(f7903,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_na____)),v_r____)
| ~ spl13_1
| ~ spl13_25 ),
inference(forward_demodulation,[],[f7898,f4856]) ).
fof(f7905,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),v_na____)),v_r____)
| ~ spl13_1
| ~ spl13_25 ),
inference(forward_demodulation,[],[f7903,f7840]) ).
fof(f7907,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____))),v_na____)),v_r____)
| ~ spl13_1
| ~ spl13_25 ),
inference(forward_demodulation,[],[f7905,f7469]) ).
fof(f7909,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_na____)),v_r____)
| ~ spl13_1
| ~ spl13_25 ),
inference(forward_demodulation,[],[f7907,f2325]) ).
fof(f7911,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(c_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_na____),v_na____)),v_r____)
| ~ spl13_1
| ~ spl13_25 ),
inference(forward_demodulation,[],[f7909,f4856]) ).
fof(f7912,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),v_r____)),v_na____) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)
| ~ spl13_1
| ~ spl13_25 ),
inference(forward_demodulation,[],[f7911,f7839]) ).
fof(f7920,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_r____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____)
| ~ spl13_1
| ~ spl13_25 ),
inference(forward_demodulation,[],[f7912,f4012]) ).
fof(f7921,plain,
( $false
| ~ spl13_1
| ~ spl13_25 ),
inference(trivial_inequality_removal,[],[f7920]) ).
fof(f7922,plain,
( ~ spl13_1
| ~ spl13_25 ),
inference(avatar_contradiction_clause,[],[f7921]) ).
fof(f8111,plain,
( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),sK4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
| ~ spl13_1
| ~ spl13_24 ),
inference(superposition,[],[f4030,f4851]) ).
fof(f8128,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____
| ~ spl13_1
| ~ spl13_24 ),
inference(forward_demodulation,[],[f8111,f4008]) ).
fof(f8133,plain,
( $false
| ~ spl13_1
| ~ spl13_24 ),
inference(forward_subsumption_resolution,[],[f8128,f2494]) ).
fof(f8134,plain,
( ~ spl13_1
| ~ spl13_24 ),
inference(avatar_contradiction_clause,[],[f8133]) ).
cnf(s4,plain,
spl13_1,
inference(sat_conversion,[],[f3999]) ).
cnf(s18,plain,
( spl13_24
| spl13_25 ),
inference(sat_conversion,[],[f4857]) ).
cnf(s144,plain,
( ~ spl13_1
| ~ spl13_25 ),
inference(sat_conversion,[],[f7922]) ).
cnf(s148,plain,
( ~ spl13_1
| ~ spl13_24 ),
inference(sat_conversion,[],[f8134]) ).
cnf(s151,plain,
~ spl13_24,
inference(rat,[],[s148,s4]) ).
cnf(s152,plain,
~ spl13_25,
inference(rat,[],[s144,s4]) ).
cnf(s156,plain,
$false,
inference(rat,[],[s18,s152,s151]) ).
fof(f8140,plain,
$false,
inference(avatar_sat_refutation,[],[s156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW282+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n019.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Mon Sep 28 13:29:48 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.33 Running first-order theorem proving
% 0.26/0.33 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
% 21.24/4.12 % (4001070)Detected formulas, will run a generic FOF schedule.
% 21.24/4.12 % (4001076)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=810019726:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 21.24/4.12 % (4001080)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3047368047:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 21.24/4.12 % (4001080)Instruction limit reached!
% 21.24/4.12 % (4001080)------------------------------
% 21.24/4.12 % (4001080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.24/4.12 % (4001080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.24/4.12 % (4001080)CaDiCaL version: 2.1.3
% 21.24/4.12 % (4001080)Termination reason: Instruction limit
% 21.24/4.12 % (4001080)Termination phase: Saturation
% 21.24/4.12 % (4001080)Time elapsed: 0.088 s
% 21.24/4.12 % (4001080)Peak memory usage: 91 MB
% 21.24/4.12 % (4001080)Instructions burned: 140 (million)
% 21.24/4.12 % (4001081)dis-21_1_sil=8000:lcm=predicate:random_seed=965354879: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)
% 21.24/4.12 % (4001078)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2628303109:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 21.24/4.12 % (4001077)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=1402869826:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 21.24/4.12 % (4001079)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=296826305:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 21.24/4.12 % (4001075)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=2881825743:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 21.24/4.12 % (4001078)Refutation not found, incomplete strategy
% 21.24/4.12 % (4001078)------------------------------
% 21.24/4.12 % (4001078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.24/4.12 % (4001078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.24/4.12 % (4001078)CaDiCaL version: 2.1.3
% 21.24/4.12 % (4001078)Termination reason: Refutation not found, incomplete strategy
% 21.24/4.12 % (4001078)Time elapsed: 0.030 s
% 21.24/4.12 % (4001078)Peak memory usage: 90 MB
% 21.24/4.12 % (4001078)Instructions burned: 30 (million)
% 21.24/4.12 % (4001081)Instruction limit reached!
% 21.24/4.12 % (4001081)------------------------------
% 21.24/4.12 % (4001081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.24/4.12 % (4001081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.24/4.12 % (4001081)CaDiCaL version: 2.1.3
% 21.24/4.12 % (4001081)Termination reason: Instruction limit
% 21.24/4.12 % (4001081)Termination phase: Saturation
% 21.24/4.12 % (4001081)Time elapsed: 0.112 s
% 21.24/4.12 % (4001081)Peak memory usage: 91 MB
% 21.24/4.12 % (4001081)Instructions burned: 129 (million)
% 21.24/4.12 % (4001079)Instruction limit reached!
% 21.24/4.12 % (4001079)------------------------------
% 21.24/4.12 % (4001079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.24/4.12 % (4001079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.24/4.12 % (4001079)CaDiCaL version: 2.1.3
% 21.24/4.12 % (4001079)Termination reason: Instruction limit
% 21.24/4.12 % (4001079)Termination phase: Saturation
% 21.24/4.12 % (4001079)Time elapsed: 0.118 s
% 21.24/4.12 % (4001079)Peak memory usage: 89 MB
% 21.24/4.12 % (4001079)Instructions burned: 119 (million)
% 21.24/4.12 % (4001089)lrs+10_1_sil=8000:sp=occurrence:random_seed=4170254180:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 21.24/4.12 % (4001091)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1964504036:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 21.24/4.12 % (4001090)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3124082056:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 21.24/4.12 % (4001078)------------------------------
% 21.24/4.12 % (4001078)------------------------------
% 21.24/4.12 % (4001090)Instruction limit reached!
% 21.24/4.12 % (4001090)------------------------------
% 21.24/4.12 % (4001090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.05/5.93 % (4001090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.05/5.93 % (4001090)CaDiCaL version: 2.1.3
% 33.05/5.93 % (4001090)Termination reason: Instruction limit
% 33.05/5.93 % (4001090)Termination phase: Saturation
% 33.05/5.93 % (4001090)Time elapsed: 0.150 s
% 33.05/5.93 % (4001090)Peak memory usage: 91 MB
% 33.05/5.93 % (4001090)Instructions burned: 157 (million)
% 33.05/5.93 % (4001089)Instruction limit reached!
% 33.05/5.93 % (4001089)------------------------------
% 33.05/5.93 % (4001089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.05/5.93 % (4001089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.05/5.93 % (4001089)CaDiCaL version: 2.1.3
% 33.05/5.93 % (4001089)Termination reason: Instruction limit
% 33.05/5.93 % (4001089)Termination phase: Saturation
% 33.05/5.93 % (4001089)Time elapsed: 0.295 s
% 33.05/5.93 % (4001089)Peak memory usage: 92 MB
% 33.05/5.93 % (4001089)Instructions burned: 285 (million)
% 33.05/5.93 % (4001091)Instruction limit reached!
% 33.05/5.93 % (4001091)------------------------------
% 33.05/5.93 % (4001091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.05/5.93 % (4001091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.05/5.93 % (4001091)CaDiCaL version: 2.1.3
% 33.05/5.93 % (4001091)Termination reason: Instruction limit
% 33.05/5.93 % (4001091)Termination phase: Saturation
% 33.05/5.93 % (4001091)Time elapsed: 0.303 s
% 33.05/5.93 % (4001091)Peak memory usage: 93 MB
% 33.05/5.93 % (4001091)Instructions burned: 325 (million)
% 33.05/5.93 % (4001095)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=2695100821:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 33.05/5.93 % (4001095)Instruction limit reached!
% 33.05/5.93 % (4001095)------------------------------
% 33.05/5.93 % (4001095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.05/5.93 % (4001095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.05/5.93 % (4001095)CaDiCaL version: 2.1.3
% 33.05/5.93 % (4001095)Termination reason: Instruction limit
% 33.05/5.93 % (4001095)Termination phase: Saturation
% 33.05/5.93 % (4001095)Time elapsed: 0.100 s
% 33.05/5.93 % (4001095)Peak memory usage: 94 MB
% 33.05/5.93 % (4001095)Instructions burned: 250 (million)
% 33.05/5.93 % (4001097)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2680542805:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 33.05/5.93 % (4001096)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3051301963:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2990 on theBenchmark for (2990ds/294Mi)
% 33.05/5.93 % (4001099)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3449261926:cts=off:i=113:fsr=off:ss=included:sgt=4_2990 on theBenchmark for (2990ds/113Mi)
% 33.05/5.93 % (4001099)Instruction limit reached!
% 33.05/5.93 % (4001099)------------------------------
% 33.05/5.93 % (4001099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.05/5.93 % (4001099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.05/5.93 % (4001099)CaDiCaL version: 2.1.3
% 33.05/5.93 % (4001099)Termination reason: Instruction limit
% 33.05/5.93 % (4001099)Termination phase: Saturation
% 33.05/5.93 % (4001099)Time elapsed: 0.104 s
% 33.05/5.93 % (4001099)Peak memory usage: 90 MB
% 33.05/5.93 % (4001099)Instructions burned: 114 (million)
% 33.05/5.93 % (4001101)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4261821874:i=127:av=off:fsr=off:sup=off_2988 on theBenchmark for (2988ds/127Mi)
% 33.05/5.93 % (4001101)Refutation not found, incomplete strategy
% 33.05/5.93 % (4001101)------------------------------
% 33.05/5.93 % (4001101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.05/5.93 % (4001101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.05/5.93 % (4001101)CaDiCaL version: 2.1.3
% 33.05/5.93 % (4001101)Termination reason: Refutation not found, incomplete strategy
% 33.05/5.93 % (4001101)Time elapsed: 0.055 s
% 33.05/5.93 % (4001101)Peak memory usage: 90 MB
% 33.05/5.93 % (4001101)Instructions burned: 118 (million)
% 33.05/5.93 % (4001096)Instruction limit reached!
% 33.05/5.93 % (4001096)------------------------------
% 33.05/5.93 % (4001096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.05/5.93 % (4001096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.05/5.93 % (4001096)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001096)Termination reason: Instruction limit
% 38.43/6.57 % (4001096)Termination phase: Saturation
% 38.43/6.57 % (4001096)Time elapsed: 0.281 s
% 38.43/6.57 % (4001096)Peak memory usage: 92 MB
% 38.43/6.57 % (4001096)Instructions burned: 295 (million)
% 38.43/6.57 % (4001106)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3497419502:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2987 on theBenchmark for (2987ds/114Mi)
% 38.43/6.57 % (4001101)------------------------------
% 38.43/6.57 % (4001101)------------------------------
% 38.43/6.57 % (4001106)Instruction limit reached!
% 38.43/6.57 % (4001106)------------------------------
% 38.43/6.57 % (4001106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001106)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001106)Termination reason: Instruction limit
% 38.43/6.57 % (4001106)Termination phase: Saturation
% 38.43/6.57 % (4001106)Time elapsed: 0.103 s
% 38.43/6.57 % (4001106)Peak memory usage: 90 MB
% 38.43/6.57 % (4001106)Instructions burned: 114 (million)
% 38.43/6.57 % (4001108)lrs+10_1_sil=8000:sp=occurrence:random_seed=244715380:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2985 on theBenchmark for (2985ds/907Mi)
% 38.43/6.57 % (4001110)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1464378628:i=437:sd=1:aac=none:ss=included_2983 on theBenchmark for (2983ds/437Mi)
% 38.43/6.57 % (4001111)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1649261430:i=5202:ss=axioms:sgt=16_2982 on theBenchmark for (2982ds/5202Mi)
% 38.43/6.57 % (4001110)Instruction limit reached!
% 38.43/6.57 % (4001110)------------------------------
% 38.43/6.57 % (4001110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001110)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001110)Termination reason: Instruction limit
% 38.43/6.57 % (4001110)Termination phase: Saturation
% 38.43/6.57 % (4001110)Time elapsed: 0.201 s
% 38.43/6.57 % (4001110)Peak memory usage: 93 MB
% 38.43/6.57 % (4001110)Instructions burned: 438 (million)
% 38.43/6.57 % (4001116)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3599664686:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2980 on theBenchmark for (2980ds/134Mi)
% 38.43/6.57 % (4001116)Instruction limit reached!
% 38.43/6.57 % (4001116)------------------------------
% 38.43/6.57 % (4001116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001116)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001116)Termination reason: Instruction limit
% 38.43/6.57 % (4001116)Termination phase: Saturation
% 38.43/6.57 % (4001116)Time elapsed: 0.067 s
% 38.43/6.57 % (4001116)Peak memory usage: 92 MB
% 38.43/6.57 % (4001116)Instructions burned: 135 (million)
% 38.43/6.57 % (4001119)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=347737423:st=8:i=592:sd=3:ep=RST:ss=axioms_2977 on theBenchmark for (2977ds/592Mi)
% 38.43/6.57 % (4001108)Instruction limit reached!
% 38.43/6.57 % (4001108)------------------------------
% 38.43/6.57 % (4001108)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001108)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001108)Termination reason: Instruction limit
% 38.43/6.57 % (4001108)Termination phase: Saturation
% 38.43/6.57 % (4001108)Time elapsed: 0.930 s
% 38.43/6.57 % (4001108)Peak memory usage: 97 MB
% 38.43/6.57 % (4001108)Instructions burned: 908 (million)
% 38.43/6.57 % (4001119)Instruction limit reached!
% 38.43/6.57 % (4001119)------------------------------
% 38.43/6.57 % (4001119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001119)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001119)Termination reason: Instruction limit
% 38.43/6.57 % (4001119)Termination phase: Saturation
% 38.43/6.57 % (4001119)Time elapsed: 0.289 s
% 38.43/6.57 % (4001119)Peak memory usage: 94 MB
% 38.43/6.57 % (4001119)Instructions burned: 592 (million)
% 38.43/6.57 % (4001122)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3072316424:st=3:i=13193:sd=3:ss=axioms_2973 on theBenchmark for (2973ds/13193Mi)
% 38.43/6.57 % (4001123)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=1833441714:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2971 on theBenchmark for (2971ds/125Mi)
% 38.43/6.57 % (4001123)Instruction limit reached!
% 38.43/6.57 % (4001123)------------------------------
% 38.43/6.57 % (4001123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001123)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001123)Termination reason: Instruction limit
% 38.43/6.57 % (4001123)Termination phase: Saturation
% 38.43/6.57 % (4001123)Time elapsed: 0.059 s
% 38.43/6.57 % (4001123)Peak memory usage: 90 MB
% 38.43/6.57 % (4001123)Instructions burned: 125 (million)
% 38.43/6.57 % (4001127)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=1032071656:i=134:gtgl=5:slsql=off:gtg=exists_sym_2968 on theBenchmark for (2968ds/134Mi)
% 38.43/6.57 % (4001127)Instruction limit reached!
% 38.43/6.57 % (4001127)------------------------------
% 38.43/6.57 % (4001127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001127)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001127)Termination reason: Instruction limit
% 38.43/6.57 % (4001127)Termination phase: Saturation
% 38.43/6.57 % (4001127)Time elapsed: 0.079 s
% 38.43/6.57 % (4001127)Peak memory usage: 91 MB
% 38.43/6.57 % (4001127)Instructions burned: 134 (million)
% 38.43/6.57 % (4001097)Instruction limit reached!
% 38.43/6.57 % (4001097)------------------------------
% 38.43/6.57 % (4001097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001097)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001097)Termination reason: Instruction limit
% 38.43/6.57 % (4001097)Termination phase: Saturation
% 38.43/6.57 % (4001097)Time elapsed: 2.461 s
% 38.43/6.57 % (4001097)Peak memory usage: 144 MB
% 38.43/6.57 % (4001097)Instructions burned: 2350 (million)
% 38.43/6.57 % (4001129)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=65448520:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2965 on theBenchmark for (2965ds/141Mi)
% 38.43/6.57 % (4001129)Refutation not found, incomplete strategy
% 38.43/6.57 % (4001129)------------------------------
% 38.43/6.57 % (4001129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001129)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001129)Termination reason: Refutation not found, incomplete strategy
% 38.43/6.57 % (4001129)Time elapsed: 0.022 s
% 38.43/6.57 % (4001129)Peak memory usage: 89 MB
% 38.43/6.57 % (4001129)Instructions burned: 16 (million)
% 38.43/6.57 % (4001130)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1612565593:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2963 on theBenchmark for (2963ds/431Mi)
% 38.43/6.57 % (4001129)------------------------------
% 38.43/6.57 % (4001129)------------------------------
% 38.43/6.57 % (4001133)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=1257033723:i=6060:aac=none:ins=25_2958 on theBenchmark for (2958ds/6060Mi)
% 38.43/6.57 % (4001130)Instruction limit reached!
% 38.43/6.57 % (4001130)------------------------------
% 38.43/6.57 % (4001130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001130)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001130)Termination reason: Instruction limit
% 38.43/6.57 % (4001130)Termination phase: Saturation
% 38.43/6.57 % (4001130)Time elapsed: 0.444 s
% 38.43/6.57 % (4001130)Peak memory usage: 92 MB
% 38.43/6.57 % (4001130)Instructions burned: 431 (million)
% 38.43/6.57 % (4001135)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=643022878:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2955 on theBenchmark for (2955ds/150Mi)
% 38.43/6.57 % (4001135)Instruction limit reached!
% 38.43/6.57 % (4001135)------------------------------
% 38.43/6.57 % (4001135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 38.43/6.57 % (4001135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.43/6.57 % (4001135)CaDiCaL version: 2.1.3
% 38.43/6.57 % (4001135)Termination reason: Instruction limit
% 38.43/6.57 % (4001135)Termination phase: Saturation
% 38.43/6.57 % (4001135)Time elapsed: 0.142 s
% 38.43/6.57 % (4001135)Peak memory usage: 91 MB
% 38.43/6.57 % (4001135)Instructions burned: 150 (million)
% 38.43/6.57 % (4001122)First to succeed.
% 38.43/6.57 % (4001122)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4001070"
% 38.43/6.57 % (4001137)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=3356523084:i=14155:bd=all_2951 on theBenchmark for (2951ds/14155Mi)
% 38.43/6.57 % (4001122)Refutation found. Thanks to Tanya!
% 38.43/6.57 % SZS status Theorem for theBenchmark
% 38.43/6.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/6.90 % (4001122)------------------------------
% 0.30/6.90 % (4001122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/6.90 % (4001122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/6.90 % (4001122)CaDiCaL version: 2.1.3
% 0.30/6.90 % (4001122)Termination reason: Refutation
% 0.30/6.90 % (4001122)Time elapsed: 2.091 s
% 0.30/6.90 % (4001122)Peak memory usage: 141 MB
% 0.30/6.90 % (4001122)Instructions burned: 1987 (million)
% 0.30/6.90 % (4001122)------------------------------
% 0.30/6.90 % (4001122)------------------------------
% 0.30/6.90 % (4001070)Success in time 5.5 s
% 0.30/6.91 % Vampire exiting
%------------------------------------------------------------------------------