%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW283+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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:30:01 PM UTC 2026
% Result : Theorem 12.60s 2.16s
% Output : Refutation 13.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 29
% Syntax : Number of formulae : 167 ( 28 unt; 8 def)
% Number of atoms : 469 ( 203 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 501 ( 199 ~; 239 |; 25 &)
% ( 15 <=>; 22 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 9 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 198 ( 0 sgn 192 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
=> X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).
fof(f4,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(f8,axiom,
! [X0,X1,X2] :
( class_Rings_Oring__1__no__zero__divisors(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ! [X3] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) = X0
=> ( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nullstellensatz__lemma) ).
fof(f11,axiom,
! [X0,X1,X2] :
( ( class_Int_Oring__char__0(X2)
& class_Rings_Oidom(X2) )
=> ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(f34,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(f192,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(f211,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(f313,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(f641,axiom,
! [X0,X1,X2] :
( class_Fields_Ofield(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X0,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X0,X1)),c_Polynomial_Odegree(X2,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mod__less) ).
fof(f644,axiom,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
<=> c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(f764,axiom,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Divides_Odiv__class_Odiv(X2,X0,X1)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).
fof(f1105,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(f1114,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1115,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f1129,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f1133,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(f1137,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(f1169,axiom,
! [X0] :
( class_Fields_Ofield(X0)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(f1199,conjecture,
( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1200,negated_conjecture,
~ ( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1199]) ).
fof(f1205,plain,
! [X0,X1] :
( X1 = X0
| ? [X2] : hAPP(X1,X2) != hAPP(X0,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1207,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f3]) ).
fof(f1208,plain,
! [X0,X1] :
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f1215,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f1216,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(flattening,[],[f1215]) ).
fof(f1219,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| ? [X3] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X3)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f1220,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| ? [X3] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X3)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(flattening,[],[f1219]) ).
fof(f1221,plain,
! [X0,X1,X2] :
( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X1 = X0 )
| ~ class_Int_Oring__char__0(X2)
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f1222,plain,
! [X0,X1,X2] :
( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X1 = X0 )
| ~ class_Int_Oring__char__0(X2)
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f1221]) ).
fof(f1254,plain,
! [X0,X1] :
( c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f1454,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f192]) ).
fof(f1462,plain,
! [X0,X1] :
( X0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f211]) ).
fof(f1602,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f313]) ).
fof(f1994,plain,
! [X0,X1,X2] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X0,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X0,X1)),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Fields_Ofield(X2) ),
inference(ennf_transformation,[],[f641]) ).
fof(f1995,plain,
! [X0,X1,X2] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X0,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X0,X1)),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Fields_Ofield(X2) ),
inference(flattening,[],[f1994]) ).
fof(f2000,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
<=> c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Groups_Ozero__class_Ozero(X2) )
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f644]) ).
fof(f2106,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Divides_Odiv__class_Odiv(X2,X0,X1)) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f764]) ).
fof(f2107,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Divides_Odiv__class_Odiv(X2,X0,X1)) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Divides_Osemiring__div(X2) ),
inference(flattening,[],[f2106]) ).
fof(f2383,plain,
! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(ennf_transformation,[],[f1169]) ).
fof(f2413,plain,
( ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) )
<~> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(ennf_transformation,[],[f1200]) ).
fof(f2416,plain,
! [X0,X1] :
( X1 = X0
| hAPP(X1,sK1(X0,X1)) != hAPP(X0,sK1(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f1205]) ).
fof(f2420,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK2(X1,X2))
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK2(X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X1,X2))],[f1220]) ).
fof(f2421,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
| X0 != X1 )
& ( X1 = X0
| c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0) ) )
| ~ class_Int_Oring__char__0(X2)
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f1222]) ).
fof(f2642,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X2,X0,X1) )
& ( c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ) )
| ~ class_Divides_Osemiring__div(X2) ),
inference(nnf_transformation,[],[f2000]) ).
fof(f2746,plain,
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
& ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) ) ),
inference(nnf_transformation,[],[f2413]) ).
fof(f2747,plain,
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
& ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) ) ),
inference(flattening,[],[f2746]) ).
fof(f2748,plain,
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
& ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) ) ) ),
inference(rectify,[],[f2747]) ).
fof(f2749,plain,
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
& ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK26)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK26) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(X0,sK26)],[f2748]) ).
fof(f2750,plain,
! [X0,X1] :
( hAPP(X1,sK1(X0,X1)) != hAPP(X0,sK1(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f2416]) ).
fof(f2752,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),X1) ),
inference(cnf_transformation,[],[f1207]) ).
fof(f2753,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
inference(cnf_transformation,[],[f1208]) ).
fof(f2760,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(cnf_transformation,[],[f1216]) ).
fof(f2762,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK2(X1,X2)) ),
inference(cnf_transformation,[],[f2420]) ).
fof(f2763,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK2(X1,X2)) ),
inference(cnf_transformation,[],[f2420]) ).
fof(f2764,plain,
! [X2,X0,X1] :
( ~ class_Int_Oring__char__0(X2)
| c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0)
| X0 = X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2421]) ).
fof(f2800,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f3035,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(cnf_transformation,[],[f1454]) ).
fof(f3061,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1462]) ).
fof(f3206,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(cnf_transformation,[],[f1602]) ).
fof(f3663,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X0,X1)),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Fields_Ofield(X2) ),
inference(cnf_transformation,[],[f1995]) ).
fof(f3668,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X2,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f2642]) ).
fof(f3819,plain,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Divides_Odiv__class_Odiv(X2,X0,X1)) = X0 ),
inference(cnf_transformation,[],[f2107]) ).
fof(f4242,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1105]) ).
fof(f4251,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1114]) ).
fof(f4252,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1115]) ).
fof(f4266,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1129]) ).
fof(f4270,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1133]) ).
fof(f4274,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1137]) ).
fof(f4306,plain,
! [X0] :
( ~ class_Fields_Ofield(X0)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0)) ),
inference(cnf_transformation,[],[f2383]) ).
fof(f4336,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) ),
inference(cnf_transformation,[],[f2749]) ).
fof(f4337,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) ),
inference(cnf_transformation,[],[f2749]) ).
fof(f4339,plain,
( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK26) ),
inference(cnf_transformation,[],[f2749]) ).
fof(f4340,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK26) ),
inference(cnf_transformation,[],[f2749]) ).
fof(f4341,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK26) ),
inference(cnf_transformation,[],[f2749]) ).
fof(f4352,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK2(X1,X2))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)))) ),
inference(equality_resolution,[],[f2763]) ).
fof(f4353,plain,
! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK2(X1,X2)) ),
inference(equality_resolution,[],[f2762]) ).
fof(f4415,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f3061]) ).
fof(f4543,definition,
( spl27_1
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) ) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f4544,plain,
( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) )
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f4543]) ).
fof(f4546,definition,
( spl27_2
<=> v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f4547,plain,
( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f4546]) ).
fof(f4549,definition,
( spl27_3
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
introduced(definition,[new_symbols(definition,[spl27_3])],[avatar_definition]) ).
fof(f4550,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f4549]) ).
fof(f4551,plain,
( spl27_1
| spl27_2
| spl27_3 ),
inference(avatar_split_clause,[],[f4336,f4549,f4546,f4543]) ).
fof(f4553,definition,
( spl27_4
<=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl27_4])],[avatar_definition]) ).
fof(f4554,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl27_4 ),
inference(avatar_component_clause,[],[f4553]) ).
fof(f4555,plain,
( spl27_1
| spl27_4
| spl27_3 ),
inference(avatar_split_clause,[],[f4337,f4549,f4553,f4543]) ).
fof(f4557,definition,
( spl27_5
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK26) ),
introduced(definition,[new_symbols(definition,[spl27_5])],[avatar_definition]) ).
fof(f4558,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK26)
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f4557]) ).
fof(f4559,plain,
( v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| spl27_2 ),
inference(avatar_component_clause,[],[f4546]) ).
fof(f4560,plain,
( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| spl27_4 ),
inference(avatar_component_clause,[],[f4553]) ).
fof(f4563,definition,
( spl27_6
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK26) ),
introduced(definition,[new_symbols(definition,[spl27_6])],[avatar_definition]) ).
fof(f4564,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK26)
| spl27_6 ),
inference(avatar_component_clause,[],[f4563]) ).
fof(f4565,plain,
( ~ spl27_6
| ~ spl27_2
| ~ spl27_4 ),
inference(avatar_split_clause,[],[f4339,f4553,f4546,f4563]) ).
fof(f4566,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| spl27_3 ),
inference(avatar_component_clause,[],[f4549]) ).
fof(f4567,plain,
( spl27_5
| ~ spl27_3 ),
inference(avatar_split_clause,[],[f4340,f4549,f4557]) ).
fof(f4568,plain,
( ~ spl27_6
| ~ spl27_3 ),
inference(avatar_split_clause,[],[f4341,f4549,f4563]) ).
fof(f4661,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X2)),
inference(resolution,[],[f3206,f4252]) ).
fof(f4665,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0),
inference(resolution,[],[f2753,f4252]) ).
fof(f4666,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| ~ spl27_2 ),
inference(forward_demodulation,[],[f4665,f4547]) ).
fof(f4667,plain,
( $false
| ~ spl27_2
| spl27_6 ),
inference(unit_resulting_resolution,[],[f4666,f4564]) ).
fof(f4672,plain,
( ~ spl27_2
| spl27_6 ),
inference(avatar_contradiction_clause,[],[f4667]) ).
fof(f4684,plain,
class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolution,[],[f4306,f4270]) ).
fof(f4686,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X0)) = X1 ),
inference(resolution,[],[f4684,f3819]) ).
fof(f4690,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2(v_q,v_p))
| spl27_3 ),
inference(resolution,[],[f4353,f4566]) ).
fof(f4705,definition,
( spl27_10
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2(v_q,v_p)) ),
introduced(definition,[new_symbols(definition,[spl27_10])],[avatar_definition]) ).
fof(f4706,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2(v_q,v_p))
| ~ spl27_10 ),
inference(avatar_component_clause,[],[f4705]) ).
fof(f4708,definition,
( spl27_11
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ),
introduced(definition,[new_symbols(definition,[spl27_11])],[avatar_definition]) ).
fof(f4709,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
| ~ spl27_11 ),
inference(avatar_component_clause,[],[f4708]) ).
fof(f4710,plain,
( spl27_10
| spl27_11
| spl27_3 ),
inference(avatar_split_clause,[],[f4690,f4549,f4708,f4705]) ).
fof(f4727,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0),
inference(resolution,[],[f2800,f4252]) ).
fof(f4733,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X2)),X1),
inference(resolution,[],[f2752,f4251]) ).
fof(f4765,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X2)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X2)),
inference(resolution,[],[f3035,f4252]) ).
fof(f4766,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X2),X1)),X2),
inference(forward_demodulation,[],[f4765,f4661]) ).
fof(f4770,plain,
( ! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),X0)),sK26) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)),sK26)
| ~ spl27_5 ),
inference(superposition,[],[f4766,f4558]) ).
fof(f6991,plain,
( ! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),X0)),sK26) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),sK26)
| ~ spl27_5 ),
inference(forward_demodulation,[],[f4770,f4727]) ).
fof(f7003,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),X0)),sK26)
| ~ spl27_5 ),
inference(forward_demodulation,[],[f6991,f4665]) ).
fof(f7026,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2(v_q,v_p))
| ~ spl27_1
| ~ spl27_10 ),
inference(superposition,[],[f4544,f4706]) ).
fof(f7032,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2(v_q,v_p))
| ~ spl27_1
| ~ spl27_10 ),
inference(trivial_inequality_removal,[],[f7026]) ).
fof(f7037,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ spl27_1
| ~ spl27_10 ),
inference(superposition,[],[f4352,f7032]) ).
fof(f7043,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ spl27_1
| ~ spl27_10 ),
inference(trivial_inequality_removal,[],[f7037]) ).
fof(f7048,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
| ~ spl27_1
| spl27_3
| ~ spl27_10 ),
inference(forward_subsumption_resolution,[],[f7043,f4566]) ).
fof(f7051,plain,
( spl27_11
| ~ spl27_1
| spl27_3
| ~ spl27_10 ),
inference(avatar_split_clause,[],[f7048,f4705,f4549,f4543,f4708]) ).
fof(f7057,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,v_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,v_p)
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Fields_Ofield(tc_Complex_Ocomplex) )
| ~ spl27_11 ),
inference(superposition,[],[f3663,f4709]) ).
fof(f7058,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,v_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,v_p)
| ~ class_Fields_Ofield(tc_Complex_Ocomplex) )
| spl27_4
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f7057,f4560]) ).
fof(f7060,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,v_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,v_p) )
| spl27_4
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f7058,f4270]) ).
fof(f7061,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,v_p)
| spl27_4
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f7060,f4415]) ).
fof(f7077,plain,
( $false
| spl27_3
| spl27_4
| ~ spl27_11 ),
inference(unit_resulting_resolution,[],[f3668,f4684,f4566,f7061]) ).
fof(f7080,plain,
( spl27_3
| spl27_4
| ~ spl27_11 ),
inference(avatar_contradiction_clause,[],[f7077]) ).
fof(f7082,plain,
( v_p != v_q
| spl27_2
| ~ spl27_4 ),
inference(superposition,[],[f4559,f4554]) ).
fof(f7188,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)
| ~ spl27_4 ),
inference(superposition,[],[f4665,f4554]) ).
fof(f7228,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) )
| ~ spl27_1
| ~ spl27_4 ),
inference(superposition,[],[f4544,f7188]) ).
fof(f7243,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| ~ spl27_1
| ~ spl27_4 ),
inference(trivial_inequality_removal,[],[f7228]) ).
fof(f7260,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(X0,sK1(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0))
| c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q) = X0 )
| ~ spl27_1
| ~ spl27_4 ),
inference(superposition,[],[f2750,f7243]) ).
fof(f7759,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p) = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q)
| ~ spl27_1
| ~ spl27_4 ),
inference(superposition,[],[f7260,f7188]) ).
fof(f7776,plain,
( c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p) = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q)
| ~ spl27_1
| ~ spl27_4 ),
inference(trivial_inequality_removal,[],[f7759]) ).
fof(f7879,plain,
( $false
| ~ spl27_1
| spl27_2
| ~ spl27_4 ),
inference(unit_resulting_resolution,[],[f2764,f4274,f4266,f7082,f7776]) ).
fof(f7901,plain,
( ~ spl27_1
| spl27_2
| ~ spl27_4 ),
inference(avatar_contradiction_clause,[],[f7879]) ).
fof(f21541,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)),v_p))
| ~ spl27_3 ),
inference(resolution,[],[f4686,f4550]) ).
fof(f21852,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))),sK26)
| ~ spl27_3
| ~ spl27_5 ),
inference(superposition,[],[f7003,f21541]) ).
fof(f21974,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK26)),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))
| ~ spl27_3
| ~ spl27_5 ),
inference(forward_demodulation,[],[f21852,f4733]) ).
fof(f21992,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK26)
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
| ~ spl27_3
| ~ spl27_5 ),
inference(superposition,[],[f2760,f21974]) ).
fof(f21993,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK26)
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
| ~ spl27_3
| ~ spl27_5 ),
inference(trivial_inequality_removal,[],[f21992]) ).
fof(f21995,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
| ~ spl27_3
| ~ spl27_5
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f21993,f4564]) ).
fof(f21998,plain,
( $false
| ~ spl27_3
| ~ spl27_5
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f21995,f4242]) ).
fof(f21999,plain,
( ~ spl27_3
| ~ spl27_5
| spl27_6 ),
inference(avatar_contradiction_clause,[],[f21998]) ).
cnf(s1,plain,
( spl27_1
| spl27_2
| spl27_3 ),
inference(sat_conversion,[],[f4551]) ).
cnf(s2,plain,
( spl27_1
| spl27_3
| spl27_4 ),
inference(sat_conversion,[],[f4555]) ).
cnf(s4,plain,
( ~ spl27_2
| ~ spl27_4
| ~ spl27_6 ),
inference(sat_conversion,[],[f4565]) ).
cnf(s5,plain,
( ~ spl27_3
| spl27_5 ),
inference(sat_conversion,[],[f4567]) ).
cnf(s6,plain,
( ~ spl27_3
| ~ spl27_6 ),
inference(sat_conversion,[],[f4568]) ).
cnf(s11,plain,
( ~ spl27_2
| spl27_6 ),
inference(sat_conversion,[],[f4672]) ).
cnf(s14,plain,
( spl27_3
| spl27_10
| spl27_11 ),
inference(sat_conversion,[],[f4710]) ).
cnf(s53,plain,
( ~ spl27_1
| spl27_3
| ~ spl27_10
| spl27_11 ),
inference(sat_conversion,[],[f7051]) ).
cnf(s54,plain,
( spl27_3
| spl27_4
| ~ spl27_11 ),
inference(sat_conversion,[],[f7080]) ).
cnf(s62,plain,
( ~ spl27_1
| spl27_2
| ~ spl27_4 ),
inference(sat_conversion,[],[f7901]) ).
cnf(s199,plain,
( ~ spl27_3
| ~ spl27_5
| spl27_6 ),
inference(sat_conversion,[],[f21999]) ).
cnf(s209,plain,
~ spl27_3,
inference(rat,[],[s199,s5,s6]) ).
cnf(s210,plain,
spl27_1,
inference(rat,[],[s4,s11,s1,s2,s209]) ).
cnf(s211,plain,
spl27_11,
inference(rat,[],[s53,s14,s209,s210]) ).
cnf(s212,plain,
spl27_4,
inference(rat,[],[s54,s209,s211]) ).
cnf(s213,plain,
spl27_2,
inference(rat,[],[s62,s210,s212]) ).
cnf(s216,plain,
spl27_6,
inference(rat,[],[s11,s213]) ).
cnf(s217,plain,
$false,
inference(rat,[],[s4,s212,s216,s213]) ).
fof(f22005,plain,
$false,
inference(avatar_sat_refutation,[],[s217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW283+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 13:29:34 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running first-order theorem proving
% 0.09/0.12 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
% 8.04/1.55 % (3376542)Detected formulas, will run a generic FOF schedule.
% 8.04/1.55 % (3376552)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3476572292:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.04/1.55 % (3376553)dis-21_1_sil=8000:lcm=predicate:random_seed=2496626654: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)
% 8.04/1.55 % (3376551)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=979351002:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.04/1.55 % (3376548)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=1454666827:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.04/1.55 % (3376550)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=454373545:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.04/1.55 % (3376549)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=4109659222:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.04/1.55 % (3376547)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=1613318143:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.04/1.55 % (3376550)Refutation not found, incomplete strategy
% 8.04/1.55 % (3376550)------------------------------
% 8.04/1.55 % (3376550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/1.55 % (3376550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/1.55 % (3376550)CaDiCaL version: 2.1.3
% 8.04/1.55 % (3376550)Termination reason: Refutation not found, incomplete strategy
% 8.04/1.55 % (3376550)Time elapsed: 0.007 s
% 8.04/1.55 % (3376550)Peak memory usage: 89 MB
% 8.04/1.55 % (3376550)Instructions burned: 22 (million)
% 8.04/1.55 % (3376553)Instruction limit reached!
% 8.04/1.55 % (3376553)------------------------------
% 8.04/1.55 % (3376553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/1.55 % (3376553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/1.55 % (3376553)CaDiCaL version: 2.1.3
% 8.04/1.55 % (3376553)Termination reason: Instruction limit
% 8.04/1.55 % (3376553)Termination phase: Saturation
% 8.04/1.55 % (3376553)Time elapsed: 0.036 s
% 8.04/1.55 % (3376553)Peak memory usage: 90 MB
% 8.04/1.55 % (3376553)Instructions burned: 131 (million)
% 8.04/1.55 % (3376551)Instruction limit reached!
% 8.04/1.55 % (3376551)------------------------------
% 8.04/1.55 % (3376551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/1.55 % (3376551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/1.55 % (3376551)CaDiCaL version: 2.1.3
% 8.04/1.55 % (3376551)Termination reason: Instruction limit
% 8.04/1.55 % (3376551)Termination phase: Saturation
% 8.04/1.55 % (3376551)Time elapsed: 0.038 s
% 8.04/1.55 % (3376551)Peak memory usage: 89 MB
% 8.04/1.55 % (3376551)Instructions burned: 120 (million)
% 8.04/1.55 % (3376552)Instruction limit reached!
% 8.04/1.55 % (3376552)------------------------------
% 8.04/1.55 % (3376552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/1.55 % (3376552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/1.55 % (3376552)CaDiCaL version: 2.1.3
% 8.04/1.55 % (3376552)Termination reason: Instruction limit
% 8.04/1.55 % (3376552)Termination phase: Saturation
% 8.04/1.55 % (3376552)Time elapsed: 0.042 s
% 8.04/1.55 % (3376552)Peak memory usage: 91 MB
% 8.04/1.55 % (3376552)Instructions burned: 139 (million)
% 8.04/1.55 % (3376561)lrs+10_1_sil=8000:sp=occurrence:random_seed=666558185:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.04/1.55 % (3376563)lrs+1011_1_sil=32000:sp=occurrence:random_seed=378874552:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 8.04/1.55 % (3376562)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3029248590:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 8.04/1.55 % (3376550)------------------------------
% 8.04/1.55 % (3376550)------------------------------
% 8.04/1.55 % (3376562)Instruction limit reached!
% 8.04/1.55 % (3376562)------------------------------
% 8.04/1.55 % (3376562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.97/2.07 % (3376562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.97/2.07 % (3376562)CaDiCaL version: 2.1.3
% 11.97/2.07 % (3376562)Termination reason: Instruction limit
% 11.97/2.07 % (3376562)Termination phase: Saturation
% 11.97/2.07 % (3376562)Time elapsed: 0.049 s
% 11.97/2.07 % (3376562)Peak memory usage: 91 MB
% 11.97/2.07 % (3376562)Instructions burned: 157 (million)
% 11.97/2.07 % (3376561)Instruction limit reached!
% 11.97/2.07 % (3376561)------------------------------
% 11.97/2.07 % (3376561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.97/2.07 % (3376561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.97/2.07 % (3376561)CaDiCaL version: 2.1.3
% 11.97/2.07 % (3376561)Termination reason: Instruction limit
% 11.97/2.07 % (3376561)Termination phase: Saturation
% 11.97/2.07 % (3376561)Time elapsed: 0.096 s
% 11.97/2.07 % (3376561)Peak memory usage: 92 MB
% 11.97/2.07 % (3376561)Instructions burned: 287 (million)
% 11.97/2.07 % (3376563)Instruction limit reached!
% 11.97/2.07 % (3376563)------------------------------
% 11.97/2.07 % (3376563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.97/2.07 % (3376563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.97/2.07 % (3376563)CaDiCaL version: 2.1.3
% 11.97/2.07 % (3376563)Termination reason: Instruction limit
% 11.97/2.07 % (3376563)Termination phase: Saturation
% 11.97/2.07 % (3376563)Time elapsed: 0.109 s
% 11.97/2.07 % (3376563)Peak memory usage: 91 MB
% 11.97/2.07 % (3376563)Instructions burned: 328 (million)
% 11.97/2.07 % (3376568)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2300602720:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2997 on theBenchmark for (2997ds/294Mi)
% 11.97/2.07 % (3376567)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=3366266032:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 11.97/2.07 % (3376570)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4107720771:cts=off:i=113:fsr=off:ss=included:sgt=4_2996 on theBenchmark for (2996ds/113Mi)
% 11.97/2.07 % (3376569)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=580880695:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 11.97/2.07 % (3376567)Instruction limit reached!
% 11.97/2.07 % (3376567)------------------------------
% 11.97/2.07 % (3376567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.97/2.07 % (3376567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.97/2.07 % (3376567)CaDiCaL version: 2.1.3
% 11.97/2.07 % (3376567)Termination reason: Instruction limit
% 11.97/2.07 % (3376567)Termination phase: Saturation
% 11.97/2.07 % (3376567)Time elapsed: 0.085 s
% 11.97/2.07 % (3376567)Peak memory usage: 92 MB
% 11.97/2.07 % (3376567)Instructions burned: 248 (million)
% 11.97/2.07 % (3376568)Instruction limit reached!
% 11.97/2.07 % (3376568)------------------------------
% 11.97/2.07 % (3376568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.97/2.07 % (3376568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.97/2.07 % (3376568)CaDiCaL version: 2.1.3
% 11.97/2.07 % (3376568)Termination reason: Instruction limit
% 11.97/2.07 % (3376568)Termination phase: Saturation
% 11.97/2.07 % (3376568)Time elapsed: 0.091 s
% 11.97/2.07 % (3376568)Peak memory usage: 92 MB
% 11.97/2.07 % (3376568)Instructions burned: 296 (million)
% 11.97/2.07 % (3376570)Instruction limit reached!
% 11.97/2.07 % (3376570)------------------------------
% 11.97/2.07 % (3376570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.97/2.07 % (3376570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.97/2.07 % (3376570)CaDiCaL version: 2.1.3
% 11.97/2.07 % (3376570)Termination reason: Instruction limit
% 11.97/2.07 % (3376570)Termination phase: Saturation
% 11.97/2.07 % (3376570)Time elapsed: 0.032 s
% 11.97/2.07 % (3376570)Peak memory usage: 90 MB
% 11.97/2.07 % (3376570)Instructions burned: 115 (million)
% 11.97/2.07 % (3376577)lrs+10_1_sil=8000:sp=occurrence:random_seed=1892719244:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2995 on theBenchmark for (2995ds/907Mi)
% 11.97/2.07 % (3376575)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3997589149:i=127:av=off:fsr=off:sup=off_2995 on theBenchmark for (2995ds/127Mi)
% 11.97/2.07 % (3376576)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3707124247:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2995 on theBenchmark for (2995ds/114Mi)
% 12.60/2.16 % (3376576)Instruction limit reached!
% 12.60/2.16 % (3376576)------------------------------
% 12.60/2.16 % (3376576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376576)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376576)Termination reason: Instruction limit
% 12.60/2.16 % (3376576)Termination phase: Saturation
% 12.60/2.16 % (3376576)Time elapsed: 0.030 s
% 12.60/2.16 % (3376576)Peak memory usage: 89 MB
% 12.60/2.16 % (3376576)Instructions burned: 117 (million)
% 12.60/2.16 % (3376575)Instruction limit reached!
% 12.60/2.16 % (3376575)------------------------------
% 12.60/2.16 % (3376575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376575)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376575)Termination reason: Instruction limit
% 12.60/2.16 % (3376575)Termination phase: Saturation
% 12.60/2.16 % (3376575)Time elapsed: 0.032 s
% 12.60/2.16 % (3376575)Peak memory usage: 90 MB
% 12.60/2.16 % (3376575)Instructions burned: 129 (million)
% 12.60/2.16 % (3376581)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=46625574:i=437:sd=1:aac=none:ss=included_2994 on theBenchmark for (2994ds/437Mi)
% 12.60/2.16 % (3376582)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2166214836:i=5202:ss=axioms:sgt=16_2994 on theBenchmark for (2994ds/5202Mi)
% 12.60/2.16 % (3376581)Instruction limit reached!
% 12.60/2.16 % (3376581)------------------------------
% 12.60/2.16 % (3376581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376581)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376581)Termination reason: Instruction limit
% 12.60/2.16 % (3376581)Termination phase: Saturation
% 12.60/2.16 % (3376581)Time elapsed: 0.134 s
% 12.60/2.16 % (3376581)Peak memory usage: 95 MB
% 12.60/2.16 % (3376581)Instructions burned: 441 (million)
% 12.60/2.16 % (3376577)Instruction limit reached!
% 12.60/2.16 % (3376577)------------------------------
% 12.60/2.16 % (3376577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376577)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376577)Termination reason: Instruction limit
% 12.60/2.16 % (3376577)Termination phase: Saturation
% 12.60/2.16 % (3376577)Time elapsed: 0.302 s
% 12.60/2.16 % (3376577)Peak memory usage: 97 MB
% 12.60/2.16 % (3376577)Instructions burned: 909 (million)
% 12.60/2.16 % (3376585)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2328696847:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2991 on theBenchmark for (2991ds/134Mi)
% 12.60/2.16 % (3376585)Instruction limit reached!
% 12.60/2.16 % (3376585)------------------------------
% 12.60/2.16 % (3376585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376585)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376585)Termination reason: Instruction limit
% 12.60/2.16 % (3376585)Termination phase: Saturation
% 12.60/2.16 % (3376585)Time elapsed: 0.041 s
% 12.60/2.16 % (3376585)Peak memory usage: 92 MB
% 12.60/2.16 % (3376585)Instructions burned: 135 (million)
% 12.60/2.16 % (3376586)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3153065221:st=8:i=592:sd=3:ep=RST:ss=axioms_2991 on theBenchmark for (2991ds/592Mi)
% 12.60/2.16 % (3376588)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1690040587:st=3:i=13193:sd=3:ss=axioms_2990 on theBenchmark for (2990ds/13193Mi)
% 12.60/2.16 % (3376586)Instruction limit reached!
% 12.60/2.16 % (3376586)------------------------------
% 12.60/2.16 % (3376586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376586)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376586)Termination reason: Instruction limit
% 12.60/2.16 % (3376586)Termination phase: Saturation
% 12.60/2.16 % (3376586)Time elapsed: 0.188 s
% 12.60/2.16 % (3376586)Peak memory usage: 96 MB
% 12.60/2.16 % (3376586)Instructions burned: 594 (million)
% 12.60/2.16 % (3376591)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=758930122:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2988 on theBenchmark for (2988ds/125Mi)
% 12.60/2.16 % (3376569)Instruction limit reached!
% 12.60/2.16 % (3376569)------------------------------
% 12.60/2.16 % (3376569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376569)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376569)Termination reason: Instruction limit
% 12.60/2.16 % (3376569)Termination phase: Saturation
% 12.60/2.16 % (3376569)Time elapsed: 0.809 s
% 12.60/2.16 % (3376569)Peak memory usage: 145 MB
% 12.60/2.16 % (3376569)Instructions burned: 2353 (million)
% 12.60/2.16 % (3376591)Instruction limit reached!
% 12.60/2.16 % (3376591)------------------------------
% 12.60/2.16 % (3376591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376591)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376591)Termination reason: Instruction limit
% 12.60/2.16 % (3376591)Termination phase: Saturation
% 12.60/2.16 % (3376591)Time elapsed: 0.036 s
% 12.60/2.16 % (3376591)Peak memory usage: 91 MB
% 12.60/2.16 % (3376591)Instructions burned: 127 (million)
% 12.60/2.16 % (3376594)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=585041870:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2987 on theBenchmark for (2987ds/141Mi)
% 12.60/2.16 % (3376593)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=4014197928:i=134:gtgl=5:slsql=off:gtg=exists_sym_2987 on theBenchmark for (2987ds/134Mi)
% 12.60/2.16 % (3376594)Refutation not found, incomplete strategy
% 12.60/2.16 % (3376594)------------------------------
% 12.60/2.16 % (3376594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376594)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376594)Termination reason: Refutation not found, incomplete strategy
% 12.60/2.16 % (3376594)Time elapsed: 0.004 s
% 12.60/2.16 % (3376594)Peak memory usage: 89 MB
% 12.60/2.16 % (3376594)Instructions burned: 11 (million)
% 12.60/2.16 % (3376593)Instruction limit reached!
% 12.60/2.16 % (3376593)------------------------------
% 12.60/2.16 % (3376593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376593)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376593)Termination reason: Instruction limit
% 12.60/2.16 % (3376593)Termination phase: Saturation
% 12.60/2.16 % (3376593)Time elapsed: 0.036 s
% 12.60/2.16 % (3376593)Peak memory usage: 90 MB
% 12.60/2.16 % (3376593)Instructions burned: 135 (million)
% 12.60/2.16 % (3376597)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=2751178326:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/431Mi)
% 12.60/2.16 % (3376594)------------------------------
% 12.60/2.16 % (3376594)------------------------------
% 12.60/2.16 % (3376599)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=3564663360:i=6060:aac=none:ins=25_2984 on theBenchmark for (2984ds/6060Mi)
% 12.60/2.16 % (3376597)Instruction limit reached!
% 12.60/2.16 % (3376597)------------------------------
% 12.60/2.16 % (3376597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376597)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376597)Termination reason: Instruction limit
% 12.60/2.16 % (3376597)Termination phase: Saturation
% 12.60/2.16 % (3376597)Time elapsed: 0.113 s
% 12.60/2.16 % (3376597)Peak memory usage: 93 MB
% 12.60/2.16 % (3376597)Instructions burned: 433 (million)
% 12.60/2.16 % (3376548)First to succeed.
% 12.60/2.16 % (3376548)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3376542"
% 12.60/2.16 % (3376601)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=1320378114:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2983 on theBenchmark for (2983ds/150Mi)
% 12.60/2.16 % (3376601)Instruction limit reached!
% 12.60/2.16 % (3376601)------------------------------
% 12.60/2.16 % (3376601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.60/2.16 % (3376601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.60/2.16 % (3376601)CaDiCaL version: 2.1.3
% 12.60/2.16 % (3376601)Termination reason: Instruction limit
% 12.60/2.16 % (3376601)Termination phase: Saturation
% 12.60/2.16 % (3376601)Time elapsed: 0.044 s
% 12.60/2.16 % (3376601)Peak memory usage: 91 MB
% 12.60/2.16 % (3376601)Instructions burned: 150 (million)
% 12.60/2.16 % (3376548)Refutation found. Thanks to Tanya!
% 12.60/2.16 % SZS status Theorem for theBenchmark
% 12.60/2.16 % SZS output start Proof for theBenchmark
% See solution above
% 13.02/2.26 % (3376548)------------------------------
% 13.02/2.26 % (3376548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.02/2.26 % (3376548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.02/2.26 % (3376548)CaDiCaL version: 2.1.3
% 13.02/2.26 % (3376548)Termination reason: Refutation
% 13.02/2.26 % (3376548)Time elapsed: 1.558 s
% 13.02/2.26 % (3376548)Peak memory usage: 162 MB
% 13.02/2.26 % (3376548)Instructions burned: 4433 (million)
% 13.02/2.26 % (3376548)------------------------------
% 13.02/2.26 % (3376548)------------------------------
% 13.02/2.26 % (3376542)Success in time 1.843 s
% 13.02/2.26 % Vampire exiting
%------------------------------------------------------------------------------