%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW276+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:30:00 PM UTC 2026
% Result : Theorem 17.04s 3.13s
% Output : Refutation 17.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 24
% Syntax : Number of formulae : 113 ( 36 unt; 5 def)
% Number of atoms : 232 ( 93 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 207 ( 88 ~; 100 |; 5 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_oa) ).
fof(f8,axiom,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pne) ).
fof(f9,axiom,
v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sne) ).
fof(f10,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dpn) ).
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(f15,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(f78,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(f170,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
& X1 != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(f245,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(f268,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(f530,axiom,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(f750,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(f757,axiom,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(f852,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(f871,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(f1123,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1144,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(f1175,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(f1210,conjecture,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(f1211,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
inference(negated_conjecture,[status(cth)],[f1210]) ).
fof(f1212,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
inference(flattening,[],[f1211]) ).
fof(f1234,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1175]) ).
fof(f1270,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,[],[f268]) ).
fof(f1284,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,[],[f245]) ).
fof(f1409,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,[],[f78]) ).
fof(f1414,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,[],[f15]) ).
fof(f1479,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,[],[f852]) ).
fof(f1480,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,[],[f1479]) ).
fof(f1658,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 = X1 )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
& X1 != X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f170]) ).
fof(f1659,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 = X1 )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
& X1 != X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(flattening,[],[f1658]) ).
fof(f1743,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____)),
inference(cnf_transformation,[],[f1212]) ).
fof(f1759,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1123]) ).
fof(f1761,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(f1762,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_s____,
inference(cnf_transformation,[],[f9]) ).
fof(f1773,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),
inference(cnf_transformation,[],[f7]) ).
fof(f1777,plain,
v_na____ = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____),
inference(cnf_transformation,[],[f10]) ).
fof(f1778,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_pa____,
inference(cnf_transformation,[],[f8]) ).
fof(f1787,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f1234]) ).
fof(f1818,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f1270]) ).
fof(f1831,plain,
! [X2,X0,X1] :
( 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(cnf_transformation,[],[f1284]) ).
fof(f2032,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(cnf_transformation,[],[f1409]) ).
fof(f2041,plain,
! [X2,X0,X1] :
( 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(cnf_transformation,[],[f1414]) ).
fof(f2060,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f1659]) ).
fof(f2203,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1144]) ).
fof(f2205,plain,
! [X2,X0,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))
| 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(cnf_transformation,[],[f1480]) ).
fof(f2251,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),
inference(cnf_transformation,[],[f871]) ).
fof(f2296,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f757]) ).
fof(f2331,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,[],[f750]) ).
fof(f2361,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f530]) ).
fof(f2691,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____),
inference(forward_demodulation,[],[f1743,f1777]) ).
fof(f2775,plain,
( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(superposition,[],[f1831,f1761]) ).
fof(f2784,definition,
( spl9_3
<=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f2785,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f2784]) ).
fof(f2786,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| spl9_3 ),
inference(avatar_component_clause,[],[f2784]) ).
fof(f2788,definition,
( spl9_4
<=> v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f2790,plain,
( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(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_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f2788]) ).
fof(f2794,plain,
( ~ spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f2775,f2788,f2784]) ).
fof(f2802,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)) = 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____))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(superposition,[],[f2205,f1761]) ).
fof(f2808,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____))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[],[f2802,f1762]) ).
fof(f2810,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,[],[f2808,f2203]) ).
fof(f2812,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,[],[f2810,f2251]) ).
fof(f2814,definition,
( spl9_5
<=> 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____)) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f2815,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_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____))
| spl9_5 ),
inference(avatar_component_clause,[],[f2814]) ).
fof(f2816,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_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____))
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f2814]) ).
fof(f2826,plain,
( v_na____ = 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,[],[f2812,f1777]) ).
fof(f2828,definition,
( spl9_8
<=> v_na____ = 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____)))) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
fof(f2830,plain,
( v_na____ = 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____))))
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f2828]) ).
fof(f2831,plain,
( spl9_5
| spl9_8 ),
inference(avatar_split_clause,[],[f2826,f2828,f2814]) ).
fof(f3024,definition,
( spl9_11
<=> v_na____ = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f3025,plain,
( v_na____ != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)
| spl9_11 ),
inference(avatar_component_clause,[],[f3024]) ).
fof(f3026,plain,
( v_na____ = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f3024]) ).
fof(f3306,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_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[],[f1761,f2032]) ).
fof(f3328,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_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
inference(forward_subsumption_resolution,[],[f3306,f1759]) ).
fof(f3419,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X0 ),
inference(resolution,[],[f2296,f2060]) ).
fof(f4258,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_Groups_Oone__class_Oone(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)) = 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_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(superposition,[],[f2205,f3328]) ).
fof(f4886,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_Groups_Oone__class_Oone(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_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[],[f4258,f1762]) ).
fof(f4893,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_Groups_Oone__class_Oone(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_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
inference(forward_subsumption_resolution,[],[f4886,f2203]) ).
fof(f4896,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_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)) ),
inference(forward_demodulation,[],[f4893,f2251]) ).
fof(f5978,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| spl9_3 ),
inference(resolution,[],[f1787,f2786]) ).
fof(f5979,plain,
( $false
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f5978,f1759]) ).
fof(f5980,plain,
spl9_3,
inference(avatar_contradiction_clause,[],[f5979]) ).
fof(f5981,plain,
( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
| ~ spl9_4
| ~ spl9_5 ),
inference(forward_demodulation,[],[f2790,f2816]) ).
fof(f6039,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl9_4
| ~ spl9_5 ),
inference(superposition,[],[f5981,f1818]) ).
fof(f6042,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl9_4
| ~ spl9_5 ),
inference(forward_subsumption_resolution,[],[f6039,f1778]) ).
fof(f6045,plain,
( $false
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(forward_subsumption_resolution,[],[f6042,f2785]) ).
fof(f6046,plain,
( ~ spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(avatar_contradiction_clause,[],[f6045]) ).
fof(f6066,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____))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| spl9_5 ),
inference(superposition,[],[f2815,f2032]) ).
fof(f6067,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____))
| spl9_5 ),
inference(forward_subsumption_resolution,[],[f6066,f1759]) ).
fof(f6166,plain,
( v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_na____,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____))))
| ~ spl9_8
| ~ spl9_11 ),
inference(forward_demodulation,[],[f2830,f3026]) ).
fof(f6243,plain,
( v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl9_8
| ~ spl9_11 ),
inference(superposition,[],[f6166,f2041]) ).
fof(f6272,plain,
( v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))
| ~ spl9_8
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f6243,f1759]) ).
fof(f6310,plain,
( c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____)
| ~ spl9_8
| ~ spl9_11 ),
inference(superposition,[],[f2331,f6272]) ).
fof(f6324,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)
| ~ spl9_8
| ~ spl9_11 ),
inference(forward_demodulation,[],[f6310,f2361]) ).
fof(f6327,plain,
( $false
| ~ spl9_8
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f6324,f1773]) ).
fof(f6328,plain,
( ~ spl9_8
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f6327]) ).
fof(f6329,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____))))
| spl9_5 ),
inference(forward_subsumption_resolution,[],[f4896,f6067]) ).
fof(f6331,plain,
( v_na____ = 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____))))
| spl9_5 ),
inference(forward_demodulation,[],[f6329,f1777]) ).
fof(f6365,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),v_na____)
| v_na____ = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)
| spl9_5 ),
inference(superposition,[],[f3419,f6331]) ).
fof(f6376,plain,
( v_na____ = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____)
| spl9_5 ),
inference(forward_subsumption_resolution,[],[f6365,f2691]) ).
fof(f6400,plain,
( $false
| spl9_5
| spl9_11 ),
inference(forward_subsumption_resolution,[],[f6376,f3025]) ).
fof(f6401,plain,
( spl9_5
| spl9_11 ),
inference(avatar_contradiction_clause,[],[f6400]) ).
cnf(s6,plain,
( ~ spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f2794]) ).
cnf(s8,plain,
( spl9_5
| spl9_8 ),
inference(sat_conversion,[],[f2831]) ).
cnf(s99,plain,
spl9_3,
inference(sat_conversion,[],[f5980]) ).
cnf(s101,plain,
( ~ spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(sat_conversion,[],[f6046]) ).
cnf(s115,plain,
( ~ spl9_8
| ~ spl9_11 ),
inference(sat_conversion,[],[f6328]) ).
cnf(s121,plain,
( spl9_5
| spl9_11 ),
inference(sat_conversion,[],[f6401]) ).
cnf(s129,plain,
spl9_4,
inference(rat,[],[s6,s99]) ).
cnf(s130,plain,
~ spl9_5,
inference(rat,[],[s101,s99,s129]) ).
cnf(s132,plain,
spl9_11,
inference(rat,[],[s121,s130]) ).
cnf(s133,plain,
spl9_8,
inference(rat,[],[s8,s130]) ).
cnf(s135,plain,
$false,
inference(rat,[],[s115,s132,s133]) ).
fof(f6404,plain,
$false,
inference(avatar_sat_refutation,[],[s135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW276+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n009.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 13:29:30 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 13.14/2.63 % (3024898)Detected formulas, will run a generic FOF schedule.
% 13.14/2.63 % (3024903)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=3483661014:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 13.14/2.63 % (3024909)dis-21_1_sil=8000:lcm=predicate:random_seed=2202233327: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)
% 13.14/2.63 % (3024906)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2767848952:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 13.14/2.63 % (3024908)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4239041283:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 13.14/2.63 % (3024907)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1951967192:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 13.14/2.63 % (3024904)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=3824732273:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 13.14/2.63 % (3024905)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=3369247245:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 13.14/2.63 % (3024906)Refutation not found, incomplete strategy
% 13.14/2.63 % (3024906)------------------------------
% 13.14/2.63 % (3024906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.14/2.63 % (3024906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.63 % (3024906)CaDiCaL version: 2.1.3
% 13.14/2.63 % (3024906)Termination reason: Refutation not found, incomplete strategy
% 13.14/2.63 % (3024906)Time elapsed: 0.006 s
% 13.14/2.63 % (3024906)Peak memory usage: 89 MB
% 13.14/2.63 % (3024906)Instructions burned: 6 (million)
% 13.14/2.63 % (3024909)Instruction limit reached!
% 13.14/2.63 % (3024909)------------------------------
% 13.14/2.63 % (3024909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.14/2.63 % (3024909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.63 % (3024909)CaDiCaL version: 2.1.3
% 13.14/2.63 % (3024909)Termination reason: Instruction limit
% 13.14/2.63 % (3024909)Termination phase: Saturation
% 13.14/2.63 % (3024909)Time elapsed: 0.067 s
% 13.14/2.63 % (3024909)Peak memory usage: 91 MB
% 13.14/2.63 % (3024909)Instructions burned: 129 (million)
% 13.14/2.63 % (3024907)Instruction limit reached!
% 13.14/2.63 % (3024907)------------------------------
% 13.14/2.63 % (3024907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.14/2.63 % (3024907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.63 % (3024907)CaDiCaL version: 2.1.3
% 13.14/2.63 % (3024907)Termination reason: Instruction limit
% 13.14/2.63 % (3024907)Termination phase: Saturation
% 13.14/2.63 % (3024907)Time elapsed: 0.070 s
% 13.14/2.63 % (3024907)Peak memory usage: 89 MB
% 13.14/2.63 % (3024907)Instructions burned: 120 (million)
% 13.14/2.63 % (3024908)Instruction limit reached!
% 13.14/2.63 % (3024908)------------------------------
% 13.14/2.63 % (3024908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.14/2.63 % (3024908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.63 % (3024908)CaDiCaL version: 2.1.3
% 13.14/2.63 % (3024908)Termination reason: Instruction limit
% 13.14/2.63 % (3024908)Termination phase: Saturation
% 13.14/2.63 % (3024908)Time elapsed: 0.077 s
% 13.14/2.63 % (3024908)Peak memory usage: 91 MB
% 13.14/2.63 % (3024908)Instructions burned: 140 (million)
% 13.14/2.63 % (3024917)lrs+10_1_sil=8000:sp=occurrence:random_seed=2808448764:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 13.14/2.63 % (3024918)lrs+10_1_sil=32000:urr=on:br=off:random_seed=61451476:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 13.14/2.63 % (3024918)Refutation not found, incomplete strategy
% 13.14/2.63 % (3024918)------------------------------
% 13.14/2.63 % (3024918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.14/2.63 % (3024918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.14/2.63 % (3024918)CaDiCaL version: 2.1.3
% 13.14/2.63 % (3024918)Termination reason: Refutation not found, incomplete strategy
% 17.04/3.13 % (3024918)Time elapsed: 0.011 s
% 17.04/3.13 % (3024918)Peak memory usage: 89 MB
% 17.04/3.13 % (3024918)Instructions burned: 18 (million)
% 17.04/3.13 % (3024919)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2563469:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 17.04/3.13 % (3024919)Refutation not found, incomplete strategy
% 17.04/3.13 % (3024919)------------------------------
% 17.04/3.13 % (3024919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024919)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024919)Termination reason: Refutation not found, incomplete strategy
% 17.04/3.13 % (3024919)Time elapsed: 0.007 s
% 17.04/3.13 % (3024919)Peak memory usage: 89 MB
% 17.04/3.13 % (3024919)Instructions burned: 8 (million)
% 17.04/3.13 % (3024906)------------------------------
% 17.04/3.13 % (3024906)------------------------------
% 17.04/3.13 % (3024917)Instruction limit reached!
% 17.04/3.13 % (3024917)------------------------------
% 17.04/3.13 % (3024917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024917)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024917)Termination reason: Instruction limit
% 17.04/3.13 % (3024917)Termination phase: Saturation
% 17.04/3.13 % (3024917)Time elapsed: 0.184 s
% 17.04/3.13 % (3024917)Peak memory usage: 92 MB
% 17.04/3.13 % (3024917)Instructions burned: 286 (million)
% 17.04/3.13 % (3024923)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=4182087158:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 17.04/3.13 % (3024918)------------------------------
% 17.04/3.13 % (3024918)------------------------------
% 17.04/3.13 % (3024919)------------------------------
% 17.04/3.13 % (3024919)------------------------------
% 17.04/3.13 % (3024924)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1839249676:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 17.04/3.13 % (3024923)Instruction limit reached!
% 17.04/3.13 % (3024923)------------------------------
% 17.04/3.13 % (3024923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024923)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024923)Termination reason: Instruction limit
% 17.04/3.13 % (3024923)Termination phase: Saturation
% 17.04/3.13 % (3024923)Time elapsed: 0.146 s
% 17.04/3.13 % (3024923)Peak memory usage: 92 MB
% 17.04/3.13 % (3024923)Instructions burned: 248 (million)
% 17.04/3.13 % (3024926)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1464136356:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 17.04/3.13 % (3024927)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1809446483:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 17.04/3.13 % (3024927)Instruction limit reached!
% 17.04/3.13 % (3024927)------------------------------
% 17.04/3.13 % (3024927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024927)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024927)Termination reason: Instruction limit
% 17.04/3.13 % (3024927)Termination phase: Saturation
% 17.04/3.13 % (3024927)Time elapsed: 0.059 s
% 17.04/3.13 % (3024927)Peak memory usage: 90 MB
% 17.04/3.13 % (3024927)Instructions burned: 114 (million)
% 17.04/3.13 % (3024924)Instruction limit reached!
% 17.04/3.13 % (3024924)------------------------------
% 17.04/3.13 % (3024924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024924)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024924)Termination reason: Instruction limit
% 17.04/3.13 % (3024924)Termination phase: Saturation
% 17.04/3.13 % (3024924)Time elapsed: 0.160 s
% 17.04/3.13 % (3024924)Peak memory usage: 91 MB
% 17.04/3.13 % (3024924)Instructions burned: 296 (million)
% 17.04/3.13 % (3024929)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=933147441:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 17.04/3.13 % (3024929)Instruction limit reached!
% 17.04/3.13 % (3024929)------------------------------
% 17.04/3.13 % (3024929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024929)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024929)Termination reason: Instruction limit
% 17.04/3.13 % (3024929)Termination phase: Saturation
% 17.04/3.13 % (3024929)Time elapsed: 0.062 s
% 17.04/3.13 % (3024929)Peak memory usage: 90 MB
% 17.04/3.13 % (3024929)Instructions burned: 128 (million)
% 17.04/3.13 % (3024932)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2133454428:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 17.04/3.13 % (3024933)lrs+10_1_sil=8000:sp=occurrence:random_seed=2196945754:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 17.04/3.13 % (3024932)Instruction limit reached!
% 17.04/3.13 % (3024932)------------------------------
% 17.04/3.13 % (3024932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024932)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024932)Termination reason: Instruction limit
% 17.04/3.13 % (3024932)Termination phase: Saturation
% 17.04/3.13 % (3024932)Time elapsed: 0.057 s
% 17.04/3.13 % (3024932)Peak memory usage: 90 MB
% 17.04/3.13 % (3024932)Instructions burned: 114 (million)
% 17.04/3.13 % (3024935)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=525343648:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 17.04/3.13 % (3024938)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2659560382:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 17.04/3.13 % (3024935)Instruction limit reached!
% 17.04/3.13 % (3024935)------------------------------
% 17.04/3.13 % (3024935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024935)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024935)Termination reason: Instruction limit
% 17.04/3.13 % (3024935)Termination phase: Saturation
% 17.04/3.13 % (3024935)Time elapsed: 0.237 s
% 17.04/3.13 % (3024935)Peak memory usage: 93 MB
% 17.04/3.13 % (3024935)Instructions burned: 438 (million)
% 17.04/3.13 % (3024941)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3333645425:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 17.04/3.13 % (3024941)Instruction limit reached!
% 17.04/3.13 % (3024941)------------------------------
% 17.04/3.13 % (3024941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024941)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024941)Termination reason: Instruction limit
% 17.04/3.13 % (3024941)Termination phase: Saturation
% 17.04/3.13 % (3024941)Time elapsed: 0.073 s
% 17.04/3.13 % (3024941)Peak memory usage: 92 MB
% 17.04/3.13 % (3024941)Instructions burned: 135 (million)
% 17.04/3.13 % (3024933)Instruction limit reached!
% 17.04/3.13 % (3024933)------------------------------
% 17.04/3.13 % (3024933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024933)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024933)Termination reason: Instruction limit
% 17.04/3.13 % (3024933)Termination phase: Saturation
% 17.04/3.13 % (3024933)Time elapsed: 0.581 s
% 17.04/3.13 % (3024933)Peak memory usage: 97 MB
% 17.04/3.13 % (3024933)Instructions burned: 907 (million)
% 17.04/3.13 % (3024943)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2911832442:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 17.04/3.13 % (3024944)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=401147384:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 17.04/3.13 % (3024943)Instruction limit reached!
% 17.04/3.13 % (3024943)------------------------------
% 17.04/3.13 % (3024943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024943)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024943)Termination reason: Instruction limit
% 17.04/3.13 % (3024943)Termination phase: Saturation
% 17.04/3.13 % (3024943)Time elapsed: 0.335 s
% 17.04/3.13 % (3024943)Peak memory usage: 94 MB
% 17.04/3.13 % (3024943)Instructions burned: 593 (million)
% 17.04/3.13 % (3024947)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=701412922:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2980 on theBenchmark for (2980ds/125Mi)
% 17.04/3.13 % (3024926)Instruction limit reached!
% 17.04/3.13 % (3024926)------------------------------
% 17.04/3.13 % (3024926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024926)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024926)Termination reason: Instruction limit
% 17.04/3.13 % (3024926)Termination phase: Saturation
% 17.04/3.13 % (3024926)Time elapsed: 1.423 s
% 17.04/3.13 % (3024926)Peak memory usage: 148 MB
% 17.04/3.13 % (3024926)Instructions burned: 2351 (million)
% 17.04/3.13 % (3024947)Instruction limit reached!
% 17.04/3.13 % (3024947)------------------------------
% 17.04/3.13 % (3024947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024947)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024947)Termination reason: Instruction limit
% 17.04/3.13 % (3024947)Termination phase: Saturation
% 17.04/3.13 % (3024947)Time elapsed: 0.067 s
% 17.04/3.13 % (3024947)Peak memory usage: 91 MB
% 17.04/3.13 % (3024947)Instructions burned: 125 (million)
% 17.04/3.13 % (3024938)First to succeed.
% 17.04/3.13 % (3024938)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3024898"
% 17.04/3.13 % (3024949)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=2261826904:i=134:gtgl=5:slsql=off:gtg=exists_sym_2978 on theBenchmark for (2978ds/134Mi)
% 17.04/3.13 % (3024950)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3613347043:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2977 on theBenchmark for (2977ds/141Mi)
% 17.04/3.13 % (3024950)Refutation not found, incomplete strategy
% 17.04/3.13 % (3024950)------------------------------
% 17.04/3.13 % (3024950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024950)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024950)Termination reason: Refutation not found, incomplete strategy
% 17.04/3.13 % (3024950)Time elapsed: 0.005 s
% 17.04/3.13 % (3024950)Peak memory usage: 89 MB
% 17.04/3.13 % (3024950)Instructions burned: 5 (million)
% 17.04/3.13 % (3024949)Instruction limit reached!
% 17.04/3.13 % (3024949)------------------------------
% 17.04/3.13 % (3024949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.13 % (3024949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.13 % (3024949)CaDiCaL version: 2.1.3
% 17.04/3.13 % (3024949)Termination reason: Instruction limit
% 17.04/3.13 % (3024949)Termination phase: Saturation
% 17.04/3.13 % (3024949)Time elapsed: 0.066 s
% 17.04/3.13 % (3024949)Peak memory usage: 90 MB
% 17.04/3.13 % (3024949)Instructions burned: 135 (million)
% 17.04/3.13 % (3024938)Refutation found. Thanks to Tanya!
% 17.04/3.13 % SZS status Theorem for theBenchmark
% 17.04/3.13 % SZS output start Proof for theBenchmark
% See solution above
% 17.90/3.32 % (3024938)------------------------------
% 17.90/3.32 % (3024938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.90/3.32 % (3024938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.90/3.32 % (3024938)CaDiCaL version: 2.1.3
% 17.90/3.32 % (3024938)Termination reason: Refutation
% 17.90/3.32 % (3024938)Time elapsed: 1.055 s
% 17.90/3.32 % (3024938)Peak memory usage: 138 MB
% 17.90/3.32 % (3024938)Instructions burned: 1630 (million)
% 17.90/3.32 % (3024938)------------------------------
% 17.90/3.32 % (3024938)------------------------------
% 17.90/3.32 % (3024898)Success in time 2.486 s
% 17.90/3.32 % Vampire exiting
%------------------------------------------------------------------------------