%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW275+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:30:00 PM UTC 2026
% Result : Theorem 7.22s 1.86s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 27
% Syntax : Number of formulae : 114 ( 46 unt; 2 def)
% Number of atoms : 205 ( 127 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 154 ( 63 ~; 70 |; 5 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 118 ( 0 sgn 118 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n0) ).
fof(f6,axiom,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pne) ).
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/sandbox2/benchmark/theBenchmark.p',fact_s) ).
fof(f14,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dpn) ).
fof(f16,axiom,
v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sne) ).
fof(f27,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ds0) ).
fof(f97,axiom,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(f141,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/sandbox2/benchmark/theBenchmark.p',fact_degree__linear__power) ).
fof(f274,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
fof(f321,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/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(f323,axiom,
! [X0] :
( class_Groups_Ozero(X0)
=> c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__0) ).
fof(f392,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f394,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(f402,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f802,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(f860,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(f912,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/sandbox2/benchmark/theBenchmark.p',fact_degree__mult__eq) ).
fof(f915,axiom,
! [X0,X1] :
( ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0 )
& ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(f922,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f1125,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1126,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f1145,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(f1147,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(f1214,conjecture,
( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) )
| 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_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____)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1215,negated_conjecture,
~ ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) )
| 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_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____)))) ),
inference(negated_conjecture,[status(cth)],[f1214]) ).
fof(f1350,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,[],[f141]) ).
fof(f1481,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f274]) ).
fof(f1557,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,[],[f321]) ).
fof(f1559,plain,
! [X0] :
( c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X0) ),
inference(ennf_transformation,[],[f323]) ).
fof(f1662,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,[],[f392]) ).
fof(f1664,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f394]) ).
fof(f1673,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,[],[f402]) ).
fof(f2203,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,[],[f860]) ).
fof(f2235,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,[],[f912]) ).
fof(f2236,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,[],[f2235]) ).
fof(f2239,plain,
! [X0,X1] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(ennf_transformation,[],[f915]) ).
fof(f2386,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1179]) ).
fof(f2419,plain,
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_r____
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) )
& 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_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____)))) ),
inference(ennf_transformation,[],[f1215]) ).
fof(f2774,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != v_na____,
inference(cnf_transformation,[],[f3]) ).
fof(f2777,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_pa____,
inference(cnf_transformation,[],[f6]) ).
fof(f2782,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(f2785,plain,
v_na____ = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____),
inference(cnf_transformation,[],[f14]) ).
fof(f2787,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_s____,
inference(cnf_transformation,[],[f16]) ).
fof(f2800,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_s____),
inference(cnf_transformation,[],[f27]) ).
fof(f2910,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f97]) ).
fof(f2966,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,[],[f1350]) ).
fof(f3147,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
inference(cnf_transformation,[],[f1481]) ).
fof(f3227,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,[],[f1557]) ).
fof(f3229,plain,
! [X0] :
( ~ class_Groups_Ozero(X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f1559]) ).
fof(f3329,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,[],[f1662]) ).
fof(f3331,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,[],[f1664]) ).
fof(f3340,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,[],[f1673]) ).
fof(f3890,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f802]) ).
fof(f3962,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,[],[f2203]) ).
fof(f4052,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,[],[f2236]) ).
fof(f4056,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f2239]) ).
fof(f4066,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,[],[f922]) ).
fof(f4312,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1125]) ).
fof(f4313,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1126]) ).
fof(f4332,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1145]) ).
fof(f4334,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1147]) ).
fof(f4366,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2386]) ).
fof(f4401,plain,
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_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____)))),
inference(cnf_transformation,[],[f2419]) ).
fof(f4764,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(equality_resolution,[],[f4056]) ).
fof(f4931,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,[],[f2966,f4312]) ).
fof(f5041,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,[],[f4052,f4334]) ).
fof(f5121,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,[],[f3227,f4312]) ).
fof(f5184,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)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0),
inference(resolution,[],[f3147,f4313]) ).
fof(f5632,plain,
class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[],[f4366,f4312]) ).
fof(f5637,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)),
inference(resolution,[],[f5632,f3329]) ).
fof(f5638,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)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)),X2),
inference(resolution,[],[f5632,f3331]) ).
fof(f5641,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))),
inference(resolution,[],[f5632,f3340]) ).
fof(f5650,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)),
inference(resolution,[],[f5632,f3962]) ).
fof(f5682,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_pa____),X0) = 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)),v_s____),X0)),
inference(superposition,[],[f5638,f2782]) ).
fof(f5705,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_pa____),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)),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(forward_demodulation,[],[f5682,f5637]) ).
fof(f8069,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(resolution,[],[f3229,f4332]) ).
fof(f8085,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_pa____),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)),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____))),X0)),
inference(forward_demodulation,[],[f5705,f5121]) ).
fof(f8192,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,[],[f5041,f2782]) ).
fof(f8210,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,[],[f8192,f2787]) ).
fof(f8214,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,[],[f8210,f4066]) ).
fof(f8218,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,[],[f8214,f4931]) ).
fof(f8231,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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,[],[f8218,f2800]) ).
fof(f8237,plain,
( c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,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,[],[f8231,f4764]) ).
fof(f8245,definition,
( spl25_31
<=> 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,[spl25_31])],[avatar_definition]) ).
fof(f8246,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____))
| ~ spl25_31 ),
inference(avatar_component_clause,[],[f8245]) ).
fof(f8248,plain,
( v_na____ = 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,[],[f8237,f2785]) ).
fof(f8249,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_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ),
inference(forward_demodulation,[],[f8248,f5121]) ).
fof(f8251,definition,
( spl25_32
<=> v_na____ = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) ),
introduced(definition,[new_symbols(definition,[spl25_32])],[avatar_definition]) ).
fof(f8252,plain,
( v_na____ = c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)
| ~ spl25_32 ),
inference(avatar_component_clause,[],[f8251]) ).
fof(f8253,plain,
( spl25_32
| spl25_31 ),
inference(avatar_split_clause,[],[f8249,f8245,f8251]) ).
fof(f8854,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_pa____),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)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0))
| ~ spl25_31 ),
inference(superposition,[],[f8085,f8246]) ).
fof(f8879,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_pa____),X0) = 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)))
| ~ spl25_31 ),
inference(forward_demodulation,[],[f8854,f5184]) ).
fof(f8890,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)),v_pa____),X0)
| ~ spl25_31 ),
inference(forward_demodulation,[],[f8879,f5641]) ).
fof(f8922,plain,
( ! [X0] :
( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____),c_Polynomial_Odegree(tc_Complex_Ocomplex,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 )
| ~ spl25_31 ),
inference(superposition,[],[f5041,f8890]) ).
fof(f8943,plain,
( ! [X0] :
( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____),c_Polynomial_Odegree(tc_Complex_Ocomplex,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 )
| ~ spl25_31 ),
inference(forward_subsumption_resolution,[],[f8922,f2777]) ).
fof(f8948,plain,
( ! [X0] :
( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 )
| ~ spl25_31 ),
inference(forward_demodulation,[],[f8943,f2785]) ).
fof(f8949,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_na____,c_Polynomial_Odegree(tc_Complex_Ocomplex,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 )
| ~ spl25_31 ),
inference(forward_demodulation,[],[f8948,f8069]) ).
fof(f8953,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_na____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____
| ~ spl25_31 ),
inference(superposition,[],[f8949,f2800]) ).
fof(f8995,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_na____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl25_31 ),
inference(forward_subsumption_resolution,[],[f8953,f2787]) ).
fof(f9002,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v_na____
| ~ spl25_31 ),
inference(forward_demodulation,[],[f8995,f3890]) ).
fof(f9003,plain,
( $false
| ~ spl25_31 ),
inference(forward_subsumption_resolution,[],[f9002,f2774]) ).
fof(f9004,plain,
~ spl25_31,
inference(avatar_contradiction_clause,[],[f9003]) ).
fof(f9023,plain,
( 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_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)),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____,v_na____)))
| ~ spl25_32 ),
inference(superposition,[],[f4401,f8252]) ).
fof(f9035,plain,
( 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)),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_Oplus__class_Oplus(tc_Nat_Onat,v_na____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,v_na____)))
| ~ spl25_32 ),
inference(forward_demodulation,[],[f9023,f5650]) ).
fof(f9044,plain,
( 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)),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_Oplus__class_Oplus(tc_Nat_Onat,v_na____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl25_32 ),
inference(forward_demodulation,[],[f9035,f2910]) ).
fof(f9047,plain,
( 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)),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____)
| ~ spl25_32 ),
inference(forward_demodulation,[],[f9044,f3890]) ).
fof(f9048,plain,
( $false
| ~ spl25_32 ),
inference(trivial_inequality_removal,[],[f9047]) ).
fof(f9049,plain,
~ spl25_32,
inference(avatar_contradiction_clause,[],[f9048]) ).
cnf(s21,plain,
( spl25_31
| spl25_32 ),
inference(sat_conversion,[],[f8253]) ).
cnf(s53,plain,
~ spl25_31,
inference(sat_conversion,[],[f9004]) ).
cnf(s55,plain,
~ spl25_32,
inference(sat_conversion,[],[f9049]) ).
cnf(s63,plain,
$false,
inference(rat,[],[s21,s55,s53]) ).
fof(f9052,plain,
$false,
inference(avatar_sat_refutation,[],[s63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW275+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n020.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 13:27:50 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.22/1.86 % (160271)Detected formulas, will run a generic FOF schedule.
% 7.22/1.86 % (160277)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=2763800670:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.22/1.86 % (160276)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=1760774674:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.22/1.86 % (160278)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=3004506845:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.22/1.86 % (160279)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3035064479:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.22/1.86 % (160280)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3812884920:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.22/1.86 % (160282)dis-21_1_sil=8000:lcm=predicate:random_seed=3531011614:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 7.22/1.86 % (160281)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1155813388:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.22/1.86 % (160279)Refutation not found, incomplete strategy
% 7.22/1.86 % (160279)------------------------------
% 7.22/1.86 % (160279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160279)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160279)Termination reason: Refutation not found, incomplete strategy
% 7.22/1.86 % (160279)Time elapsed: 0.017 s
% 7.22/1.86 % (160279)Peak memory usage: 89 MB
% 7.22/1.86 % (160279)Instructions burned: 29 (million)
% 7.22/1.86 % (160282)Instruction limit reached!
% 7.22/1.86 % (160282)------------------------------
% 7.22/1.86 % (160282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160282)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160282)Termination reason: Instruction limit
% 7.22/1.86 % (160282)Termination phase: Saturation
% 7.22/1.86 % (160282)Time elapsed: 0.067 s
% 7.22/1.86 % (160282)Peak memory usage: 90 MB
% 7.22/1.86 % (160282)Instructions burned: 129 (million)
% 7.22/1.86 % (160280)Instruction limit reached!
% 7.22/1.86 % (160280)------------------------------
% 7.22/1.86 % (160280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160280)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160280)Termination reason: Instruction limit
% 7.22/1.86 % (160280)Termination phase: Saturation
% 7.22/1.86 % (160280)Time elapsed: 0.071 s
% 7.22/1.86 % (160280)Peak memory usage: 90 MB
% 7.22/1.86 % (160280)Instructions burned: 120 (million)
% 7.22/1.86 % (160281)Instruction limit reached!
% 7.22/1.86 % (160281)------------------------------
% 7.22/1.86 % (160281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160281)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160281)Termination reason: Instruction limit
% 7.22/1.86 % (160281)Termination phase: Saturation
% 7.22/1.86 % (160281)Time elapsed: 0.076 s
% 7.22/1.86 % (160281)Peak memory usage: 91 MB
% 7.22/1.86 % (160281)Instructions burned: 139 (million)
% 7.22/1.86 % (160290)lrs+10_1_sil=8000:sp=occurrence:random_seed=1282366927:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.22/1.86 % (160291)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2928105924:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.22/1.86 % (160292)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3559242198:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.22/1.86 % (160279)------------------------------
% 7.22/1.86 % (160279)------------------------------
% 7.22/1.86 % (160291)Instruction limit reached!
% 7.22/1.86 % (160291)------------------------------
% 7.22/1.86 % (160291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160291)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160291)Termination reason: Instruction limit
% 7.22/1.86 % (160291)Termination phase: Saturation
% 7.22/1.86 % (160291)Time elapsed: 0.081 s
% 7.22/1.86 % (160291)Peak memory usage: 90 MB
% 7.22/1.86 % (160291)Instructions burned: 157 (million)
% 7.22/1.86 % (160290)Instruction limit reached!
% 7.22/1.86 % (160290)------------------------------
% 7.22/1.86 % (160290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160290)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160290)Termination reason: Instruction limit
% 7.22/1.86 % (160290)Termination phase: Saturation
% 7.22/1.86 % (160290)Time elapsed: 0.184 s
% 7.22/1.86 % (160290)Peak memory usage: 92 MB
% 7.22/1.86 % (160290)Instructions burned: 285 (million)
% 7.22/1.86 % (160296)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=728472040:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 7.22/1.86 % (160292)Instruction limit reached!
% 7.22/1.86 % (160292)------------------------------
% 7.22/1.86 % (160292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160292)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160292)Termination reason: Instruction limit
% 7.22/1.86 % (160292)Termination phase: Saturation
% 7.22/1.86 % (160292)Time elapsed: 0.202 s
% 7.22/1.86 % (160292)Peak memory usage: 93 MB
% 7.22/1.86 % (160292)Instructions burned: 326 (million)
% 7.22/1.86 % (160297)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1834406116:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 7.22/1.86 % (160296)Instruction limit reached!
% 7.22/1.86 % (160296)------------------------------
% 7.22/1.86 % (160296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160296)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160296)Termination reason: Instruction limit
% 7.22/1.86 % (160296)Termination phase: Saturation
% 7.22/1.86 % (160296)Time elapsed: 0.139 s
% 7.22/1.86 % (160296)Peak memory usage: 93 MB
% 7.22/1.86 % (160296)Instructions burned: 248 (million)
% 7.22/1.86 % (160298)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1722980618:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 7.22/1.86 % (160301)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3529699491:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 7.22/1.86 % (160297)Instruction limit reached!
% 7.22/1.86 % (160297)------------------------------
% 7.22/1.86 % (160297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160297)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160297)Termination reason: Instruction limit
% 7.22/1.86 % (160297)Termination phase: Saturation
% 7.22/1.86 % (160297)Time elapsed: 0.161 s
% 7.22/1.86 % (160297)Peak memory usage: 91 MB
% 7.22/1.86 % (160297)Instructions burned: 295 (million)
% 7.22/1.86 % (160301)Instruction limit reached!
% 7.22/1.86 % (160301)------------------------------
% 7.22/1.86 % (160301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160301)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160301)Termination reason: Instruction limit
% 7.22/1.86 % (160301)Termination phase: Saturation
% 7.22/1.86 % (160301)Time elapsed: 0.059 s
% 7.22/1.86 % (160301)Peak memory usage: 90 MB
% 7.22/1.86 % (160301)Instructions burned: 115 (million)
% 7.22/1.86 % (160303)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3624594608:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 7.22/1.86 % (160305)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1293777696:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 7.22/1.86 % (160277)First to succeed.
% 7.22/1.86 % (160277)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-160271"
% 7.22/1.86 % (160303)Instruction limit reached!
% 7.22/1.86 % (160303)------------------------------
% 7.22/1.86 % (160303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160303)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160303)Termination reason: Instruction limit
% 7.22/1.86 % (160303)Termination phase: Saturation
% 7.22/1.86 % (160303)Time elapsed: 0.062 s
% 7.22/1.86 % (160303)Peak memory usage: 90 MB
% 7.22/1.86 % (160303)Instructions burned: 128 (million)
% 7.22/1.86 % (160305)Instruction limit reached!
% 7.22/1.86 % (160305)------------------------------
% 7.22/1.86 % (160305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.22/1.86 % (160305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.22/1.86 % (160305)CaDiCaL version: 2.1.3
% 7.22/1.86 % (160305)Termination reason: Instruction limit
% 7.22/1.86 % (160305)Termination phase: Saturation
% 7.22/1.86 % (160305)Time elapsed: 0.058 s
% 7.22/1.86 % (160305)Peak memory usage: 90 MB
% 7.22/1.86 % (160305)Instructions burned: 116 (million)
% 7.22/1.86 % (160306)lrs+10_1_sil=8000:sp=occurrence:random_seed=3873820175:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 7.22/1.86 % (160277)Refutation found. Thanks to Tanya!
% 7.22/1.86 % SZS status Theorem for theBenchmark
% 7.22/1.86 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/2.03 % (160277)------------------------------
% 0.22/2.03 % (160277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/2.03 % (160277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/2.03 % (160277)CaDiCaL version: 2.1.3
% 0.22/2.03 % (160277)Termination reason: Refutation
% 0.22/2.03 % (160277)Time elapsed: 0.840 s
% 0.22/2.03 % (160277)Peak memory usage: 149 MB
% 0.22/2.03 % (160277)Instructions burned: 2371 (million)
% 0.22/2.03 % (160277)------------------------------
% 0.22/2.03 % (160277)------------------------------
% 0.22/2.03 % (160271)Success in time 1.182 s
% 0.22/2.03 % Vampire exiting
%------------------------------------------------------------------------------