%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW289+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:30:02 PM UTC 2026
% Result : Theorem 11.35s 2.38s
% Output : Refutation 12.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of formulae : 136 ( 48 unt; 5 def)
% Number of atoms : 263 ( 99 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 235 ( 108 ~; 102 |; 6 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 182 ( 0 sgn 182 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,v_q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms) ).
fof(f5,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( X1 = c_Groups_Ozero__class_Ozero(X2)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X1)
=> ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
=> c_Rings_Odvd__class_Odvd(X3,X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(f40,axiom,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__0) ).
fof(f60,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(f70,axiom,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(f87,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
fof(f88,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
fof(f94,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f118,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f126,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(f156,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Rings_Odvd__class_Odvd(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(f180,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f451,axiom,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
fof(f607,axiom,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
fof(f1100,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(f1101,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1102,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f1120,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(f1151,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(f1180,conjecture,
c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_q)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1181,negated_conjecture,
~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_q)),
inference(negated_conjecture,[status(cth)],[f1180]) ).
fof(f1183,plain,
~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_q)),
inference(flattening,[],[f1181]) ).
fof(f1225,plain,
! [X0,X1,X2] :
( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( X1 = c_Groups_Ozero__class_Ozero(X2)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f1230,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f1231,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f1230]) ).
fof(f1266,plain,
! [X0,X1] :
( c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f1290,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,[],[f60]) ).
fof(f1301,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(ennf_transformation,[],[f70]) ).
fof(f1319,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f87]) ).
fof(f1320,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f88]) ).
fof(f1324,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f94]) ).
fof(f1348,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,[],[f118]) ).
fof(f1356,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f126]) ).
fof(f1394,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f156]) ).
fof(f1420,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f180]) ).
fof(f2307,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1151]) ).
fof(f2340,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 )
& ( ( X1 = c_Groups_Ozero__class_Ozero(X2)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
| c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Groups_Ozero(X2) ),
inference(nnf_transformation,[],[f1225]) ).
fof(f2341,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 )
& ( ( X1 = c_Groups_Ozero__class_Ozero(X2)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
| c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f2340]) ).
fof(f2636,plain,
c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,v_q),
inference(cnf_transformation,[],[f2]) ).
fof(f2641,plain,
! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2341]) ).
fof(f2647,plain,
! [X2,X3,X0,X1] :
( ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
| c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f2691,plain,
! [X0,X1] :
( c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[],[f1266]) ).
fof(f2718,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,[],[f1290]) ).
fof(f2729,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
inference(cnf_transformation,[],[f1301]) ).
fof(f2752,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0))) ),
inference(cnf_transformation,[],[f1319]) ).
fof(f2753,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))) ),
inference(cnf_transformation,[],[f1320]) ).
fof(f2759,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
inference(cnf_transformation,[],[f1324]) ).
fof(f2790,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,[],[f1348]) ).
fof(f2802,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(cnf_transformation,[],[f1356]) ).
fof(f2840,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f1394]) ).
fof(f2869,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(cnf_transformation,[],[f1420]) ).
fof(f3243,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(cnf_transformation,[],[f451]) ).
fof(f3486,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
inference(cnf_transformation,[],[f607]) ).
fof(f4077,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1100]) ).
fof(f4078,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1101]) ).
fof(f4079,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1102]) ).
fof(f4097,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1120]) ).
fof(f4128,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2307]) ).
fof(f4157,plain,
~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_q)),
inference(cnf_transformation,[],[f1183]) ).
fof(f4277,plain,
! [X2,X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| ~ class_Groups_Ozero(X2) ),
inference(equality_resolution,[],[f2641]) ).
fof(f4278,plain,
! [X2] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
inference(equality_resolution,[],[f4277]) ).
fof(f4516,definition,
sF28 = tc_Polynomial_Opoly(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f4517,plain,
tc_Polynomial_Opoly(tc_Complex_Ocomplex) = sF28,
inference(reorient_equations,[],[f4516]) ).
fof(f4518,definition,
sF29 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f4519,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = sF29,
inference(reorient_equations,[],[f4518]) ).
fof(f4520,definition,
sF30 = c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,v_q),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f4521,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,v_q) = sF30,
inference(reorient_equations,[],[f4520]) ).
fof(f4522,plain,
~ c_Rings_Odvd__class_Odvd(sF28,v_p,sF30),
inference(definition_folding,[],[f4157,f4521,f4519,f4517]) ).
fof(f4596,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_HOL_Obool_Obool__size(c_fFalse),
inference(forward_demodulation,[],[f3243,f3486]) ).
fof(f4703,plain,
! [X0,X1] :
( c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_HOL_Obool_Obool__size(c_fFalse))
| ~ class_Groups_Ozero(X1) ),
inference(forward_demodulation,[],[f2691,f3486]) ).
fof(f4823,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_HOL_Obool_Obool__size(c_fTrue)) ),
inference(forward_demodulation,[],[f4703,f4596]) ).
fof(f4962,plain,
! [X0] :
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_q,X0)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,X0)
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(resolution,[],[f2647,f2636]) ).
fof(f4965,definition,
( spl31_3
<=> class_Rings_Ocomm__semiring__1(sF28) ),
introduced(definition,[new_symbols(definition,[spl31_3])],[avatar_definition]) ).
fof(f4966,plain,
( class_Rings_Ocomm__semiring__1(sF28)
| ~ spl31_3 ),
inference(avatar_component_clause,[],[f4965]) ).
fof(f4967,plain,
( ~ class_Rings_Ocomm__semiring__1(sF28)
| spl31_3 ),
inference(avatar_component_clause,[],[f4965]) ).
fof(f4969,definition,
( spl31_4
<=> ! [X0] :
( ~ c_Rings_Odvd__class_Odvd(sF28,v_q,X0)
| c_Rings_Odvd__class_Odvd(sF28,v_p,X0) ) ),
introduced(definition,[new_symbols(definition,[spl31_4])],[avatar_definition]) ).
fof(f4970,plain,
( ! [X0] :
( ~ c_Rings_Odvd__class_Odvd(sF28,v_q,X0)
| c_Rings_Odvd__class_Odvd(sF28,v_p,X0) )
| ~ spl31_4 ),
inference(avatar_component_clause,[],[f4969]) ).
fof(f4972,plain,
! [X0] :
( ~ c_Rings_Odvd__class_Odvd(sF28,v_q,X0)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,X0)
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(forward_demodulation,[],[f4962,f4517]) ).
fof(f4973,plain,
! [X0] :
( c_Rings_Odvd__class_Odvd(sF28,v_p,X0)
| ~ c_Rings_Odvd__class_Odvd(sF28,v_q,X0)
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(forward_demodulation,[],[f4972,f4517]) ).
fof(f4974,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__1(sF28)
| c_Rings_Odvd__class_Odvd(sF28,v_p,X0)
| ~ c_Rings_Odvd__class_Odvd(sF28,v_q,X0) ),
inference(forward_demodulation,[],[f4973,f4517]) ).
fof(f4975,plain,
( spl31_4
| ~ spl31_3 ),
inference(avatar_split_clause,[],[f4974,f4965,f4969]) ).
fof(f4984,plain,
( class_Rings_Ocomm__semiring__1(sF28)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[],[f4128,f4517]) ).
fof(f4985,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| spl31_3 ),
inference(forward_subsumption_resolution,[],[f4984,f4967]) ).
fof(f4986,plain,
( $false
| spl31_3 ),
inference(forward_subsumption_resolution,[],[f4985,f4078]) ).
fof(f4987,plain,
spl31_3,
inference(avatar_contradiction_clause,[],[f4986]) ).
fof(f4992,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,[],[f2718,f4078]) ).
fof(f4995,plain,
c_Groups_Oone__class_Oone(sF28) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(sF28)),
inference(forward_demodulation,[],[f4992,f4517]) ).
fof(f5035,plain,
( ! [X0] :
( ~ class_Rings_Ocomm__semiring__1(sF28)
| c_Rings_Odvd__class_Odvd(sF28,v_p,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),v_q)) )
| ~ spl31_4 ),
inference(resolution,[],[f2840,f4970]) ).
fof(f5039,plain,
( ! [X0] : c_Rings_Odvd__class_Odvd(sF28,v_p,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),v_q))
| ~ spl31_3
| ~ spl31_4 ),
inference(forward_subsumption_resolution,[],[f5035,f4966]) ).
fof(f5042,plain,
( ! [X0,X1] : c_Groups_Oplus__class_Oplus(sF28,X1,X0) = c_Groups_Oplus__class_Oplus(sF28,X0,X1)
| ~ spl31_3 ),
inference(resolution,[],[f2869,f4966]) ).
fof(f5045,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(resolution,[],[f4278,f4097]) ).
fof(f5046,plain,
c_Groups_Ozero__class_Ozero(sF28) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(sF28)),
inference(forward_demodulation,[],[f5045,f4517]) ).
fof(f5047,plain,
c_Groups_Ozero__class_Ozero(sF28) = c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,c_Groups_Ozero__class_Ozero(sF28)),
inference(forward_demodulation,[],[f5046,f4519]) ).
fof(f5049,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),X2) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X2),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X2))),
inference(resolution,[],[f4079,f2753]) ).
fof(f5050,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),X2) = c_Groups_Oplus__class_Oplus(sF28,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X2),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X1),X2))),
inference(forward_demodulation,[],[f5049,f4517]) ).
fof(f5051,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),X2) = c_Groups_Oplus__class_Oplus(sF28,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X2),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X1),X2))),
inference(forward_demodulation,[],[f5050,f4519]) ).
fof(f5118,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X2))),
inference(resolution,[],[f2752,f4079]) ).
fof(f5119,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Oplus__class_Oplus(sF28,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),X2))),
inference(forward_demodulation,[],[f5118,f4517]) ).
fof(f5120,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Oplus__class_Oplus(sF28,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),X2))),
inference(forward_demodulation,[],[f5119,f4519]) ).
fof(f5258,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X1),X0)
| ~ spl31_3 ),
inference(resolution,[],[f2759,f4966]) ).
fof(f5371,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0,
inference(resolution,[],[f2729,f4077]) ).
fof(f5372,plain,
! [X0] : c_Groups_Oplus__class_Oplus(sF28,X0,c_Groups_Ozero__class_Ozero(sF28)) = X0,
inference(forward_demodulation,[],[f5371,f4517]) ).
fof(f5377,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(sF28,c_Groups_Ozero__class_Ozero(sF28),X0) = X0
| ~ spl31_3 ),
inference(superposition,[],[f5042,f5372]) ).
fof(f5527,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Groups_Oone__class_Oone(sF28)) = X0
| ~ spl31_3 ),
inference(resolution,[],[f2802,f4966]) ).
fof(f5909,plain,
! [X0] : c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,c_HOL_Obool_Obool__size(c_fTrue)),
inference(resolution,[],[f4823,f4097]) ).
fof(f5913,plain,
! [X0] : c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(sF28)) = c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f5909,f4517]) ).
fof(f5929,plain,
c_Groups_Oone__class_Oone(sF28) = c_Polynomial_Omonom(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Obool_Obool__size(c_fTrue)),
inference(superposition,[],[f4995,f5913]) ).
fof(f5930,plain,
c_Groups_Ozero__class_Ozero(sF28) = c_Polynomial_Omonom(tc_Complex_Ocomplex,sF29,c_HOL_Obool_Obool__size(c_fTrue)),
inference(superposition,[],[f5047,f5913]) ).
fof(f6145,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(sF28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Groups_Ozero__class_Ozero(sF28))
| ~ spl31_3 ),
inference(resolution,[],[f2790,f4966]) ).
fof(f6223,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(sF28))) = c_Groups_Oplus__class_Oplus(sF28,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,c_Groups_Ozero__class_Ozero(sF28)))
| ~ spl31_3 ),
inference(superposition,[],[f5120,f6145]) ).
fof(f6238,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(sF28))) = c_Groups_Oplus__class_Oplus(sF28,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X0),c_Groups_Ozero__class_Ozero(sF28))
| ~ spl31_3 ),
inference(forward_demodulation,[],[f6223,f5047]) ).
fof(f6242,plain,
( ! [X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(sF28)))
| ~ spl31_3 ),
inference(forward_demodulation,[],[f6238,f5372]) ).
fof(f6245,plain,
( ! [X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Polynomial_Omonom(tc_Complex_Ocomplex,X1,c_HOL_Obool_Obool__size(c_fTrue)))
| ~ spl31_3 ),
inference(forward_demodulation,[],[f6242,f5913]) ).
fof(f6273,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Groups_Ozero__class_Ozero(sF28)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,sF29,X0)
| ~ spl31_3 ),
inference(superposition,[],[f6245,f5930]) ).
fof(f6303,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(sF28) = c_Polynomial_Osmult(tc_Complex_Ocomplex,sF29,X0)
| ~ spl31_3 ),
inference(forward_demodulation,[],[f6273,f6145]) ).
fof(f6344,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,X1)) = c_Groups_Oplus__class_Oplus(sF28,c_Groups_Ozero__class_Ozero(sF28),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),X1)))
| ~ spl31_3 ),
inference(superposition,[],[f5120,f6303]) ).
fof(f6345,plain,
( ! [X0,X1] : c_Groups_Oplus__class_Oplus(sF28,c_Groups_Ozero__class_Ozero(sF28),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),X1))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,X0)),X1)
| ~ spl31_3 ),
inference(superposition,[],[f5051,f6303]) ).
fof(f6346,plain,
( ! [X0,X1] : c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,X0)),X1)
| ~ spl31_3 ),
inference(forward_demodulation,[],[f6345,f5377]) ).
fof(f6347,plain,
( ! [X0,X1] : c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,X1))
| ~ spl31_3 ),
inference(forward_demodulation,[],[f6344,f5377]) ).
fof(f6348,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,X0)),X1)
| ~ spl31_3 ),
inference(forward_demodulation,[],[f6347,f6346]) ).
fof(f6549,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Groups_Oone__class_Oone(sF28)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)
| ~ spl31_3 ),
inference(superposition,[],[f6245,f5929]) ).
fof(f6551,plain,
( ! [X0] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0) = X0
| ~ spl31_3 ),
inference(forward_demodulation,[],[f6549,f5527]) ).
fof(f6859,plain,
( ! [X0] : c_Rings_Odvd__class_Odvd(sF28,v_p,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,sF29,v_q)))
| ~ spl31_3
| ~ spl31_4 ),
inference(superposition,[],[f5039,f6348]) ).
fof(f6869,plain,
( ! [X0] : c_Rings_Odvd__class_Odvd(sF28,v_p,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),X0),sF30))
| ~ spl31_3
| ~ spl31_4 ),
inference(forward_demodulation,[],[f6859,f4521]) ).
fof(f6897,plain,
( ! [X0] : c_Rings_Odvd__class_Odvd(sF28,v_p,hAPP(hAPP(c_Groups_Otimes__class_Otimes(sF28),sF30),X0))
| ~ spl31_3
| ~ spl31_4 ),
inference(superposition,[],[f6869,f5258]) ).
fof(f6907,plain,
( ! [X0] : c_Rings_Odvd__class_Odvd(sF28,v_p,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,sF30))
| ~ spl31_3
| ~ spl31_4 ),
inference(superposition,[],[f6897,f6245]) ).
fof(f6933,plain,
( c_Rings_Odvd__class_Odvd(sF28,v_p,sF30)
| ~ spl31_3
| ~ spl31_4 ),
inference(superposition,[],[f6907,f6551]) ).
fof(f6934,plain,
( $false
| ~ spl31_3
| ~ spl31_4 ),
inference(forward_subsumption_resolution,[],[f6933,f4522]) ).
fof(f6935,plain,
( ~ spl31_3
| ~ spl31_4 ),
inference(avatar_contradiction_clause,[],[f6934]) ).
cnf(s4,plain,
( ~ spl31_3
| spl31_4 ),
inference(sat_conversion,[],[f4975]) ).
cnf(s5,plain,
spl31_3,
inference(sat_conversion,[],[f4987]) ).
cnf(s29,plain,
( ~ spl31_3
| ~ spl31_4 ),
inference(sat_conversion,[],[f6935]) ).
cnf(s36,plain,
~ spl31_4,
inference(rat,[],[s29,s5]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s4,s36,s5]) ).
fof(f6937,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW289+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 13:25:52 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.35/2.38 % (3548293)Detected formulas, will run a generic FOF schedule.
% 11.35/2.38 % (3548302)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=835292311:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.35/2.38 % (3548300)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=2582702739:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.35/2.38 % (3548299)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=4143200112:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.35/2.38 % (3548298)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=550450470:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.35/2.38 % (3548301)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1095336474:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.35/2.38 % (3548303)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1247120950:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.35/2.38 % (3548304)dis-21_1_sil=8000:lcm=predicate:random_seed=4008796651: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)
% 11.35/2.38 % (3548302)Instruction limit reached!
% 11.35/2.38 % (3548302)------------------------------
% 11.35/2.38 % (3548302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548302)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548302)Termination reason: Instruction limit
% 11.35/2.38 % (3548302)Termination phase: Saturation
% 11.35/2.38 % (3548302)Time elapsed: 0.038 s
% 11.35/2.38 % (3548302)Peak memory usage: 89 MB
% 11.35/2.38 % (3548302)Instructions burned: 119 (million)
% 11.35/2.38 % (3548301)Refutation not found, incomplete strategy
% 11.35/2.38 % (3548301)------------------------------
% 11.35/2.38 % (3548301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548301)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548301)Termination reason: Refutation not found, incomplete strategy
% 11.35/2.38 % (3548301)Time elapsed: 0.007 s
% 11.35/2.38 % (3548301)Peak memory usage: 89 MB
% 11.35/2.38 % (3548301)Instructions burned: 10 (million)
% 11.35/2.38 % (3548304)Instruction limit reached!
% 11.35/2.38 % (3548304)------------------------------
% 11.35/2.38 % (3548304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548304)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548304)Termination reason: Instruction limit
% 11.35/2.38 % (3548304)Termination phase: Saturation
% 11.35/2.38 % (3548304)Time elapsed: 0.068 s
% 11.35/2.38 % (3548304)Peak memory usage: 90 MB
% 11.35/2.38 % (3548304)Instructions burned: 130 (million)
% 11.35/2.38 % (3548303)Instruction limit reached!
% 11.35/2.38 % (3548303)------------------------------
% 11.35/2.38 % (3548303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548303)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548303)Termination reason: Instruction limit
% 11.35/2.38 % (3548303)Termination phase: Saturation
% 11.35/2.38 % (3548303)Time elapsed: 0.080 s
% 11.35/2.38 % (3548303)Peak memory usage: 91 MB
% 11.35/2.38 % (3548303)Instructions burned: 139 (million)
% 11.35/2.38 % (3548312)lrs+10_1_sil=8000:sp=occurrence:random_seed=2221287013:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 11.35/2.38 % (3548312)Instruction limit reached!
% 11.35/2.38 % (3548312)------------------------------
% 11.35/2.38 % (3548312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548312)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548312)Termination reason: Instruction limit
% 11.35/2.38 % (3548312)Termination phase: Saturation
% 11.35/2.38 % (3548312)Time elapsed: 0.101 s
% 11.35/2.38 % (3548312)Peak memory usage: 92 MB
% 11.35/2.38 % (3548312)Instructions burned: 287 (million)
% 11.35/2.38 % (3548313)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1696650344:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.35/2.38 % (3548314)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4026905597:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 11.35/2.38 % (3548301)------------------------------
% 11.35/2.38 % (3548301)------------------------------
% 11.35/2.38 % (3548317)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=2446768990:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 11.35/2.38 % (3548313)Instruction limit reached!
% 11.35/2.38 % (3548313)------------------------------
% 11.35/2.38 % (3548313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548313)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548313)Termination reason: Instruction limit
% 11.35/2.38 % (3548313)Termination phase: Saturation
% 11.35/2.38 % (3548313)Time elapsed: 0.085 s
% 11.35/2.38 % (3548313)Peak memory usage: 91 MB
% 11.35/2.38 % (3548313)Instructions burned: 157 (million)
% 11.35/2.38 % (3548317)Instruction limit reached!
% 11.35/2.38 % (3548317)------------------------------
% 11.35/2.38 % (3548317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548317)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548317)Termination reason: Instruction limit
% 11.35/2.38 % (3548317)Termination phase: Saturation
% 11.35/2.38 % (3548317)Time elapsed: 0.076 s
% 11.35/2.38 % (3548317)Peak memory usage: 92 MB
% 11.35/2.38 % (3548317)Instructions burned: 250 (million)
% 11.35/2.38 % (3548319)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1873161805:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 11.35/2.38 % (3548314)Instruction limit reached!
% 11.35/2.38 % (3548314)------------------------------
% 11.35/2.38 % (3548314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548314)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548314)Termination reason: Instruction limit
% 11.35/2.38 % (3548314)Termination phase: Saturation
% 11.35/2.38 % (3548314)Time elapsed: 0.194 s
% 11.35/2.38 % (3548314)Peak memory usage: 91 MB
% 11.35/2.38 % (3548314)Instructions burned: 325 (million)
% 11.35/2.38 % (3548321)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2446076179:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 11.35/2.38 % (3548322)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1350820964:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 11.35/2.38 % (3548322)Instruction limit reached!
% 11.35/2.38 % (3548322)------------------------------
% 11.35/2.38 % (3548322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548322)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548322)Termination reason: Instruction limit
% 11.35/2.38 % (3548322)Termination phase: Saturation
% 11.35/2.38 % (3548322)Time elapsed: 0.032 s
% 11.35/2.38 % (3548322)Peak memory usage: 90 MB
% 11.35/2.38 % (3548322)Instructions burned: 115 (million)
% 11.35/2.38 % (3548325)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1085502890:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 11.35/2.38 % (3548319)Instruction limit reached!
% 11.35/2.38 % (3548319)------------------------------
% 11.35/2.38 % (3548319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548319)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548319)Termination reason: Instruction limit
% 11.35/2.38 % (3548319)Termination phase: Saturation
% 11.35/2.38 % (3548319)Time elapsed: 0.168 s
% 11.35/2.38 % (3548319)Peak memory usage: 93 MB
% 11.35/2.38 % (3548319)Instructions burned: 294 (million)
% 11.35/2.38 % (3548327)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4113906115:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 11.35/2.38 % (3548325)Instruction limit reached!
% 11.35/2.38 % (3548325)------------------------------
% 11.35/2.38 % (3548325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548325)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548325)Termination reason: Instruction limit
% 11.35/2.38 % (3548325)Termination phase: Saturation
% 11.35/2.38 % (3548325)Time elapsed: 0.063 s
% 11.35/2.38 % (3548325)Peak memory usage: 90 MB
% 11.35/2.38 % (3548325)Instructions burned: 128 (million)
% 11.35/2.38 % (3548327)Instruction limit reached!
% 11.35/2.38 % (3548327)------------------------------
% 11.35/2.38 % (3548327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548327)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548327)Termination reason: Instruction limit
% 11.35/2.38 % (3548327)Termination phase: Saturation
% 11.35/2.38 % (3548327)Time elapsed: 0.031 s
% 11.35/2.38 % (3548327)Peak memory usage: 90 MB
% 11.35/2.38 % (3548327)Instructions burned: 116 (million)
% 11.35/2.38 % (3548329)lrs+10_1_sil=8000:sp=occurrence:random_seed=287573610:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 11.35/2.38 % (3548332)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2133543987:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 11.35/2.38 % (3548331)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=161575354:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 11.35/2.38 % (3548331)Instruction limit reached!
% 11.35/2.38 % (3548331)------------------------------
% 11.35/2.38 % (3548331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548331)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548331)Termination reason: Instruction limit
% 11.35/2.38 % (3548331)Termination phase: Saturation
% 11.35/2.38 % (3548331)Time elapsed: 0.240 s
% 11.35/2.38 % (3548331)Peak memory usage: 95 MB
% 11.35/2.38 % (3548331)Instructions burned: 437 (million)
% 11.35/2.38 % (3548336)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=249905843:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 11.35/2.38 % (3548336)Instruction limit reached!
% 11.35/2.38 % (3548336)------------------------------
% 11.35/2.38 % (3548336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548336)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548336)Termination reason: Instruction limit
% 11.35/2.38 % (3548336)Termination phase: Saturation
% 11.35/2.38 % (3548336)Time elapsed: 0.075 s
% 11.35/2.38 % (3548336)Peak memory usage: 92 MB
% 11.35/2.38 % (3548336)Instructions burned: 135 (million)
% 11.35/2.38 % (3548298)First to succeed.
% 11.35/2.38 % (3548298)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3548293"
% 11.35/2.38 % (3548329)Instruction limit reached!
% 11.35/2.38 % (3548329)------------------------------
% 11.35/2.38 % (3548329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.35/2.38 % (3548329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.35/2.38 % (3548329)CaDiCaL version: 2.1.3
% 11.35/2.38 % (3548329)Termination reason: Instruction limit
% 11.35/2.38 % (3548329)Termination phase: Saturation
% 11.35/2.38 % (3548329)Time elapsed: 0.579 s
% 11.35/2.38 % (3548329)Peak memory usage: 98 MB
% 11.35/2.38 % (3548329)Instructions burned: 908 (million)
% 11.35/2.38 % (3548338)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3971980818:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 11.35/2.38 % (3548339)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2408795730:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 11.35/2.38 % (3548298)Refutation found. Thanks to Tanya!
% 11.35/2.38 % SZS status Theorem for theBenchmark
% 11.35/2.38 % SZS output start Proof for theBenchmark
% See solution above
% 12.48/2.57 % (3548298)------------------------------
% 12.48/2.57 % (3548298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.48/2.57 % (3548298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.48/2.57 % (3548298)CaDiCaL version: 2.1.3
% 12.48/2.57 % (3548298)Termination reason: Refutation
% 12.48/2.57 % (3548298)Time elapsed: 1.272 s
% 12.48/2.57 % (3548298)Peak memory usage: 146 MB
% 12.48/2.57 % (3548298)Instructions burned: 2015 (million)
% 12.48/2.57 % (3548298)------------------------------
% 12.48/2.57 % (3548298)------------------------------
% 12.48/2.57 % (3548293)Success in time 1.725 s
% 12.48/2.57 % Vampire exiting
%------------------------------------------------------------------------------