%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW188+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 : n003.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 01:29:48 PM UTC 2026
% Result : Theorem 5.33s 1.52s
% Output : Refutation 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 29
% Syntax : Number of formulae : 164 ( 37 unt; 8 def)
% Number of atoms : 454 ( 84 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 478 ( 188 ~; 251 |; 9 &)
% ( 12 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 8 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 134 ( 0 sgn 134 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
fof(f7,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__eq) ).
fof(f20,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( ( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
=> c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__eq__if) ).
fof(f36,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f157,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__le) ).
fof(f353,axiom,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(f546,axiom,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(f557,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(f560,axiom,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(f567,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
& X1 != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(f599,axiom,
! [X0,X1] :
( X1 != X0
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(f600,axiom,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(f622,axiom,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(f780,axiom,
! [X0,X1,X2] :
( class_Groups_Ocomm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
=> c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) = c_Polynomial_Odegree(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__right) ).
fof(f998,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Groups_Ocomm__monoid__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).
fof(f1004,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Groups_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).
fof(f1101,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(f1176,axiom,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Polynomial_Odegree(t_a,v_p),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1177,axiom,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f1178,conjecture,
c_Polynomial_Odegree(t_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,v_p)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(f1179,negated_conjecture,
c_Polynomial_Odegree(t_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,v_p)),
inference(negated_conjecture,[status(cth)],[f1178]) ).
fof(f1180,axiom,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
fof(f1181,plain,
c_Polynomial_Odegree(t_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,v_p)),
inference(flattening,[],[f1179]) ).
fof(f1271,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f599]) ).
fof(f1272,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(flattening,[],[f1271]) ).
fof(f1287,plain,
! [X0,X1,X2] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f1294,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) = c_Polynomial_Odegree(X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ),
inference(ennf_transformation,[],[f780]) ).
fof(f1295,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) = c_Polynomial_Odegree(X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ),
inference(flattening,[],[f1294]) ).
fof(f1324,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f157]) ).
fof(f1328,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 )
& ( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f1332,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f1333,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f1332]) ).
fof(f1446,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f557]) ).
fof(f1506,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> X1 = X0 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f546]) ).
fof(f1536,plain,
! [X0] :
( class_Groups_Ozero(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1004]) ).
fof(f1537,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f998]) ).
fof(f1831,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f622]) ).
fof(f1832,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f1831]) ).
fof(f1863,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 = X1 )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
& X1 != X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f567]) ).
fof(f1864,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 = X1 )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
& X1 != X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(flattening,[],[f1863]) ).
fof(f1888,plain,
! [X0,X1,X2] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 )
& ( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0) ) )
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(nnf_transformation,[],[f1287]) ).
fof(f1963,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| X0 != X1 )
& ( X1 = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(nnf_transformation,[],[f1506]) ).
fof(f2044,plain,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Polynomial_Odegree(t_a,v_p),
inference(cnf_transformation,[],[f1176]) ).
fof(f2045,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cnf_transformation,[],[f1177]) ).
fof(f2046,plain,
c_Polynomial_Odegree(t_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,v_p)),
inference(cnf_transformation,[],[f1181]) ).
fof(f2047,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(cnf_transformation,[],[f1180]) ).
fof(f2052,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1272]) ).
fof(f2058,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f1864]) ).
fof(f2109,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(cnf_transformation,[],[f36]) ).
fof(f2113,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f1888]) ).
fof(f2119,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ),
inference(cnf_transformation,[],[f1295]) ).
fof(f2138,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f1324]) ).
fof(f2142,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f1328]) ).
fof(f2148,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Nat_OSuc(c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f1333]) ).
fof(f2323,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
inference(cnf_transformation,[],[f560]) ).
fof(f2327,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f1446]) ).
fof(f2354,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f353]) ).
fof(f2448,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| X0 != X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1963]) ).
fof(f2509,plain,
! [X0] :
( class_Groups_Ozero(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f1536]) ).
fof(f2510,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f2602,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f600]) ).
fof(f2830,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1101]) ).
fof(f2845,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f1832]) ).
fof(f2863,plain,
c_Polynomial_Odegree(t_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,v_p),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definition_unfolding,[],[f2046,f2354]) ).
fof(f2865,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(definition_unfolding,[],[f2142,f2354]) ).
fof(f2866,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(definition_unfolding,[],[f2148,f2354]) ).
fof(f2938,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X0 != X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f2448,f2354]) ).
fof(f3001,definition,
~ sP8(c_Polynomial_Odegree(t_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
fof(f3002,plain,
sP8(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,v_p),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(inequality_splitting,[],[f2863,f3001]) ).
fof(f3064,plain,
! [X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1) ),
inference(equality_resolution,[],[f2938]) ).
fof(f3141,plain,
sP8(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p))),
inference(forward_demodulation,[],[f3002,f2109]) ).
fof(f3142,plain,
( ~ sP8(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| ~ class_Groups_Ocomm__monoid__add(t_a) ),
inference(superposition,[],[f3001,f2119]) ).
fof(f3145,definition,
( spl9_1
<=> class_Groups_Ocomm__monoid__add(t_a) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f3147,plain,
( ~ class_Groups_Ocomm__monoid__add(t_a)
| spl9_1 ),
inference(avatar_component_clause,[],[f3145]) ).
fof(f3149,definition,
( spl9_2
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f3150,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f3149]) ).
fof(f3151,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| spl9_2 ),
inference(avatar_component_clause,[],[f3149]) ).
fof(f3158,definition,
( spl9_4
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f3160,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| spl9_4 ),
inference(avatar_component_clause,[],[f3158]) ).
fof(f3162,definition,
( spl9_5
<=> sP8(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f3164,plain,
( ~ sP8(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| spl9_5 ),
inference(avatar_component_clause,[],[f3162]) ).
fof(f3165,plain,
( ~ spl9_1
| ~ spl9_4
| ~ spl9_5 ),
inference(avatar_split_clause,[],[f3142,f3162,f3158,f3145]) ).
fof(f3166,plain,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| spl9_1 ),
inference(resolution,[],[f3147,f2510]) ).
fof(f3167,plain,
( $false
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f3166,f2047]) ).
fof(f3168,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f3167]) ).
fof(f3193,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,v_p))
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(superposition,[],[f2138,f2044]) ).
fof(f3200,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,v_p)),
inference(forward_subsumption_resolution,[],[f3193,f2047]) ).
fof(f3212,definition,
( spl9_11
<=> class_Groups_Ozero(t_a) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f3213,plain,
( class_Groups_Ozero(t_a)
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f3212]) ).
fof(f3214,plain,
( ~ class_Groups_Ozero(t_a)
| spl9_11 ),
inference(avatar_component_clause,[],[f3212]) ).
fof(f3216,definition,
( spl9_12
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
fof(f3217,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| spl9_12 ),
inference(avatar_component_clause,[],[f3216]) ).
fof(f3218,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f3216]) ).
fof(f3229,plain,
( ~ sP8(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a)
| spl9_5 ),
inference(superposition,[],[f3164,f2866]) ).
fof(f3235,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| spl9_2 ),
inference(resolution,[],[f3151,f2052]) ).
fof(f3259,plain,
( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| spl9_2
| spl9_4 ),
inference(forward_subsumption_resolution,[],[f3235,f3160]) ).
fof(f3325,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a)
| spl9_2 ),
inference(superposition,[],[f3151,f2865]) ).
fof(f3343,plain,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| spl9_11 ),
inference(resolution,[],[f3214,f2509]) ).
fof(f3344,plain,
( $false
| spl9_11 ),
inference(forward_subsumption_resolution,[],[f3343,f2047]) ).
fof(f3345,plain,
spl9_11,
inference(avatar_contradiction_clause,[],[f3344]) ).
fof(f3347,plain,
( ~ sP8(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Ozero(t_a)
| spl9_5
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3229,f3217]) ).
fof(f3350,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| ~ class_Groups_Ozero(t_a)
| spl9_2
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3325,f3217]) ).
fof(f3355,plain,
( ~ sP8(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| spl9_5
| ~ spl9_11
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3347,f3213]) ).
fof(f3358,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| spl9_2
| ~ spl9_11
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3350,f3213]) ).
fof(f3363,plain,
( ~ sP8(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| spl9_5
| ~ spl9_11
| spl9_12 ),
inference(forward_demodulation,[],[f3355,f2109]) ).
fof(f3366,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| spl9_2
| ~ spl9_11
| spl9_12 ),
inference(forward_demodulation,[],[f3358,f2109]) ).
fof(f3371,plain,
( ~ sP8(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)))
| spl9_5
| ~ spl9_11
| spl9_12 ),
inference(forward_demodulation,[],[f3363,f2044]) ).
fof(f3374,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| spl9_2
| ~ spl9_11
| spl9_12 ),
inference(forward_demodulation,[],[f3366,f2044]) ).
fof(f3380,plain,
( $false
| spl9_5
| ~ spl9_11
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3371,f3141]) ).
fof(f3381,plain,
( spl9_5
| ~ spl9_11
| spl9_12 ),
inference(avatar_contradiction_clause,[],[f3380]) ).
fof(f3402,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ~ spl9_12 ),
inference(superposition,[],[f2113,f3218]) ).
fof(f3404,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f3402]) ).
fof(f3406,plain,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| ~ spl9_12 ),
inference(forward_subsumption_resolution,[],[f3404,f2045]) ).
fof(f3407,plain,
( $false
| ~ spl9_12 ),
inference(forward_subsumption_resolution,[],[f3406,f2047]) ).
fof(f3408,plain,
~ spl9_12,
inference(avatar_contradiction_clause,[],[f3407]) ).
fof(f3451,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| ~ class_Orderings_Oorder(tc_Nat_Onat) )
| spl9_4 ),
inference(resolution,[],[f3160,f2845]) ).
fof(f3455,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a)
| spl9_4 ),
inference(superposition,[],[f3160,f2865]) ).
fof(f3456,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Ozero(t_a)
| spl9_4
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3455,f3217]) ).
fof(f3459,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) )
| spl9_4 ),
inference(forward_subsumption_resolution,[],[f3451,f2830]) ).
fof(f3461,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3456,f3213]) ).
fof(f3466,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(forward_demodulation,[],[f3461,f2109]) ).
fof(f3468,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)))
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(forward_demodulation,[],[f3466,f2044]) ).
fof(f3475,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| spl9_2
| ~ spl9_11
| spl9_12 ),
inference(resolution,[],[f3374,f2052]) ).
fof(f3490,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| spl9_2
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3475,f3468]) ).
fof(f3499,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)),c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| ~ class_Rings_Ocomm__semiring__0(t_a)
| spl9_2
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(superposition,[],[f2138,f3490]) ).
fof(f3521,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)),c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| spl9_2
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3499,f2047]) ).
fof(f3543,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)),c_Polynomial_Odegree(t_a,v_p))
| spl9_2
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(forward_demodulation,[],[f3521,f2044]) ).
fof(f3582,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a)
| ~ spl9_2 ),
inference(superposition,[],[f3150,f2865]) ).
fof(f3584,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| ~ class_Groups_Ozero(t_a)
| ~ spl9_2
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3582,f3217]) ).
fof(f3586,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| ~ spl9_2
| ~ spl9_11
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f3584,f3213]) ).
fof(f3588,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| ~ spl9_2
| ~ spl9_11
| spl9_12 ),
inference(forward_demodulation,[],[f3586,f2109]) ).
fof(f3590,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| ~ spl9_2
| ~ spl9_11
| spl9_12 ),
inference(forward_demodulation,[],[f3588,f2044]) ).
fof(f3636,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,v_p))
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(resolution,[],[f3468,f2327]) ).
fof(f4069,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,v_p))
| c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(resolution,[],[f3636,f2058]) ).
fof(f4094,definition,
( spl9_33
<=> c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) ),
introduced(definition,[new_symbols(definition,[spl9_33])],[avatar_definition]) ).
fof(f4096,plain,
( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| ~ spl9_33 ),
inference(avatar_component_clause,[],[f4094]) ).
fof(f4103,plain,
( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f4069,f3200]) ).
fof(f4113,plain,
( spl9_33
| spl9_4
| ~ spl9_11
| spl9_12 ),
inference(avatar_split_clause,[],[f4103,f3216,f3212,f3158,f4094]) ).
fof(f4131,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)),c_Polynomial_Odegree(t_a,v_p))
| ~ spl9_2
| ~ spl9_11
| spl9_12
| ~ spl9_33 ),
inference(superposition,[],[f3590,f4096]) ).
fof(f4166,plain,
( $false
| ~ spl9_2
| ~ spl9_11
| spl9_12
| ~ spl9_33 ),
inference(forward_subsumption_resolution,[],[f4131,f2323]) ).
fof(f4167,plain,
( ~ spl9_2
| ~ spl9_11
| spl9_12
| ~ spl9_33 ),
inference(avatar_contradiction_clause,[],[f4166]) ).
fof(f4173,plain,
( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| spl9_2
| spl9_4
| ~ spl9_33 ),
inference(forward_demodulation,[],[f3259,f4096]) ).
fof(f4837,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| spl9_4 ),
inference(resolution,[],[f3459,f3064]) ).
fof(f4871,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| spl9_4 ),
inference(forward_subsumption_resolution,[],[f4837,f2602]) ).
fof(f4907,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Polynomial_Odegree(t_a,v_p))
| spl9_2
| spl9_4
| ~ spl9_33 ),
inference(forward_demodulation,[],[f4871,f4173]) ).
fof(f4942,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))),c_Polynomial_Odegree(t_a,v_p))
| spl9_2
| spl9_4
| ~ spl9_33 ),
inference(forward_demodulation,[],[f4907,f2109]) ).
fof(f4965,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)),c_Polynomial_Odegree(t_a,v_p))
| spl9_2
| spl9_4
| ~ spl9_33 ),
inference(forward_demodulation,[],[f4942,f4096]) ).
fof(f4972,plain,
( $false
| spl9_2
| spl9_4
| ~ spl9_11
| spl9_12
| ~ spl9_33 ),
inference(forward_subsumption_resolution,[],[f4965,f3543]) ).
fof(f4973,plain,
( spl9_2
| spl9_4
| ~ spl9_11
| spl9_12
| ~ spl9_33 ),
inference(avatar_contradiction_clause,[],[f4972]) ).
cnf(s2,plain,
( ~ spl9_1
| ~ spl9_4
| ~ spl9_5 ),
inference(sat_conversion,[],[f3165]) ).
cnf(s3,plain,
spl9_1,
inference(sat_conversion,[],[f3168]) ).
cnf(s28,plain,
spl9_11,
inference(sat_conversion,[],[f3345]) ).
cnf(s30,plain,
( spl9_5
| ~ spl9_11
| spl9_12 ),
inference(sat_conversion,[],[f3381]) ).
cnf(s31,plain,
~ spl9_12,
inference(sat_conversion,[],[f3408]) ).
cnf(s74,plain,
( spl9_4
| ~ spl9_11
| spl9_12
| spl9_33 ),
inference(sat_conversion,[],[f4113]) ).
cnf(s84,plain,
( ~ spl9_2
| ~ spl9_11
| spl9_12
| ~ spl9_33 ),
inference(sat_conversion,[],[f4167]) ).
cnf(s98,plain,
( spl9_2
| spl9_4
| ~ spl9_11
| spl9_12
| ~ spl9_33 ),
inference(sat_conversion,[],[f4973]) ).
cnf(s99,plain,
( spl9_5
| ~ spl9_11 ),
inference(rat,[],[s30,s31]) ).
cnf(s101,plain,
spl9_5,
inference(rat,[],[s99,s28]) ).
cnf(s104,plain,
~ spl9_4,
inference(rat,[],[s2,s101,s3]) ).
cnf(s105,plain,
spl9_33,
inference(rat,[],[s74,s28,s31,s104]) ).
cnf(s106,plain,
~ spl9_2,
inference(rat,[],[s84,s28,s31,s105]) ).
cnf(s107,plain,
$false,
inference(rat,[],[s98,s104,s31,s28,s105,s106]) ).
fof(f4974,plain,
$false,
inference(avatar_sat_refutation,[],[s107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW188+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 13:16:35 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 5.33/1.52 % (1575473)Detected formulas, will run a generic FOF schedule.
% 5.33/1.52 % (1575479)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=2790846836:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.33/1.52 % (1575483)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=698001276:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.33/1.52 % (1575480)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=4025254015:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.33/1.52 % (1575478)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=1227110282:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.33/1.52 % (1575481)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3998059075:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.33/1.52 % (1575482)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=977794686:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.33/1.52 % (1575484)dis-21_1_sil=8000:lcm=predicate:random_seed=2153558496: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)
% 5.33/1.52 % (1575481)Instruction limit reached!
% 5.33/1.52 % (1575481)------------------------------
% 5.33/1.52 % (1575481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/1.52 % (1575481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.52 % (1575481)CaDiCaL version: 2.1.3
% 5.33/1.52 % (1575481)Termination reason: Instruction limit
% 5.33/1.52 % (1575481)Termination phase: Saturation
% 5.33/1.52 % (1575481)Time elapsed: 0.061 s
% 5.33/1.52 % (1575481)Peak memory usage: 90 MB
% 5.33/1.52 % (1575481)Instructions burned: 109 (million)
% 5.33/1.52 % (1575484)Instruction limit reached!
% 5.33/1.52 % (1575484)------------------------------
% 5.33/1.52 % (1575484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/1.52 % (1575484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.52 % (1575484)CaDiCaL version: 2.1.3
% 5.33/1.52 % (1575484)Termination reason: Instruction limit
% 5.33/1.52 % (1575484)Termination phase: Saturation
% 5.33/1.52 % (1575484)Time elapsed: 0.069 s
% 5.33/1.52 % (1575484)Peak memory usage: 90 MB
% 5.33/1.52 % (1575484)Instructions burned: 130 (million)
% 5.33/1.52 % (1575482)Instruction limit reached!
% 5.33/1.52 % (1575482)------------------------------
% 5.33/1.52 % (1575482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/1.52 % (1575482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.52 % (1575482)CaDiCaL version: 2.1.3
% 5.33/1.52 % (1575482)Termination reason: Instruction limit
% 5.33/1.52 % (1575482)Termination phase: Saturation
% 5.33/1.52 % (1575482)Time elapsed: 0.070 s
% 5.33/1.52 % (1575482)Peak memory usage: 89 MB
% 5.33/1.52 % (1575482)Instructions burned: 119 (million)
% 5.33/1.52 % (1575483)Instruction limit reached!
% 5.33/1.52 % (1575483)------------------------------
% 5.33/1.52 % (1575483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/1.52 % (1575483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.52 % (1575483)CaDiCaL version: 2.1.3
% 5.33/1.52 % (1575483)Termination reason: Instruction limit
% 5.33/1.52 % (1575483)Termination phase: Saturation
% 5.33/1.52 % (1575483)Time elapsed: 0.080 s
% 5.33/1.52 % (1575483)Peak memory usage: 90 MB
% 5.33/1.52 % (1575483)Instructions burned: 140 (million)
% 5.33/1.52 % (1575493)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3286532333:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.33/1.52 % (1575494)lrs+1011_1_sil=32000:sp=occurrence:random_seed=133360361:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.33/1.52 % (1575492)lrs+10_1_sil=8000:sp=occurrence:random_seed=2769349026:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.33/1.52 % (1575495)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=909356142:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.33/1.52 % (1575493)Instruction limit reached!
% 5.33/1.52 % (1575493)------------------------------
% 5.33/1.52 % (1575493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/1.52 % (1575493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.52 % (1575493)CaDiCaL version: 2.1.3
% 5.33/1.52 % (1575493)Termination reason: Instruction limit
% 5.33/1.52 % (1575493)Termination phase: Saturation
% 5.33/1.52 % (1575493)Time elapsed: 0.087 s
% 5.33/1.52 % (1575493)Peak memory usage: 90 MB
% 5.33/1.52 % (1575493)Instructions burned: 158 (million)
% 5.33/1.52 % (1575495)Instruction limit reached!
% 5.33/1.52 % (1575495)------------------------------
% 5.33/1.52 % (1575495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/1.52 % (1575495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.52 % (1575495)CaDiCaL version: 2.1.3
% 5.33/1.52 % (1575495)Termination reason: Instruction limit
% 5.33/1.52 % (1575495)Termination phase: Saturation
% 5.33/1.52 % (1575495)Time elapsed: 0.132 s
% 5.33/1.52 % (1575495)Peak memory usage: 92 MB
% 5.33/1.52 % (1575495)Instructions burned: 249 (million)
% 5.33/1.52 % (1575492)Instruction limit reached!
% 5.33/1.52 % (1575492)------------------------------
% 5.33/1.52 % (1575492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/1.52 % (1575492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.52 % (1575492)CaDiCaL version: 2.1.3
% 5.33/1.52 % (1575492)Termination reason: Instruction limit
% 5.33/1.52 % (1575492)Termination phase: Saturation
% 5.33/1.52 % (1575492)Time elapsed: 0.182 s
% 5.33/1.52 % (1575492)Peak memory usage: 92 MB
% 5.33/1.52 % (1575492)Instructions burned: 286 (million)
% 5.33/1.52 % (1575494)Instruction limit reached!
% 5.33/1.52 % (1575494)------------------------------
% 5.33/1.52 % (1575494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/1.52 % (1575494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.52 % (1575494)CaDiCaL version: 2.1.3
% 5.33/1.52 % (1575494)Termination reason: Instruction limit
% 5.33/1.52 % (1575494)Termination phase: Saturation
% 5.33/1.52 % (1575494)Time elapsed: 0.205 s
% 5.33/1.52 % (1575494)Peak memory usage: 91 MB
% 5.33/1.52 % (1575494)Instructions burned: 325 (million)
% 5.33/1.52 % (1575500)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2278548181:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.33/1.52 % (1575500)First to succeed.
% 5.33/1.52 % (1575500)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1575473"
% 5.33/1.52 % (1575501)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1542749255:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.33/1.52 % (1575502)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=815265429:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.33/1.52 % (1575504)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3684684648:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.33/1.52 % (1575502)Instruction limit reached!
% 5.33/1.52 % (1575502)------------------------------
% 5.33/1.52 % (1575502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/1.52 % (1575502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.52 % (1575502)CaDiCaL version: 2.1.3
% 5.33/1.52 % (1575502)Termination reason: Instruction limit
% 5.33/1.52 % (1575502)Termination phase: Saturation
% 5.33/1.52 % (1575502)Time elapsed: 0.062 s
% 5.33/1.52 % (1575502)Peak memory usage: 91 MB
% 5.33/1.52 % (1575502)Instructions burned: 113 (million)
% 5.33/1.52 % (1575500)Refutation found. Thanks to Tanya!
% 5.33/1.52 % SZS status Theorem for theBenchmark
% 5.33/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 6.37/1.72 % (1575500)------------------------------
% 6.37/1.72 % (1575500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.37/1.72 % (1575500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.37/1.72 % (1575500)CaDiCaL version: 2.1.3
% 6.37/1.72 % (1575500)Termination reason: Refutation
% 6.37/1.72 % (1575500)Time elapsed: 0.047 s
% 6.37/1.72 % (1575500)Peak memory usage: 92 MB
% 6.37/1.72 % (1575500)Instructions burned: 154 (million)
% 6.37/1.72 % (1575500)------------------------------
% 6.37/1.72 % (1575500)------------------------------
% 6.37/1.72 % (1575473)Success in time 0.856 s
% 6.37/1.72 % Vampire exiting
%------------------------------------------------------------------------------