%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW187+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 : n008.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 5.67s 1.41s
% Output : Refutation 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 120 ( 27 unt; 8 def)
% Number of atoms : 278 ( 62 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 280 ( 122 ~; 132 |; 3 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 8 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 99 ( 0 sgn 99 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) = c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__single) ).
fof(f5,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(f6,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(f9,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(f16,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(f44,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(f319,axiom,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f530,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(f548,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(f1185,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(f1186,conjecture,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f1187,negated_conjecture,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(negated_conjecture,[status(cth)],[f1186]) ).
fof(f1188,axiom,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
fof(f1189,plain,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(flattening,[],[f1187]) ).
fof(f1355,plain,
! [X0,X1,X2,X3] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f6]) ).
fof(f1356,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,[],[f5]) ).
fof(f1358,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) = c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f3]) ).
fof(f1373,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,[],[f548]) ).
fof(f1374,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,[],[f1373]) ).
fof(f1389,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,[],[f44]) ).
fof(f1393,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,[],[f16]) ).
fof(f1397,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,[],[f9]) ).
fof(f1398,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,[],[f1397]) ).
fof(f1423,plain,
! [X0] :
( class_Groups_Ozero(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1004]) ).
fof(f1424,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f998]) ).
fof(f1541,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f530]) ).
fof(f1840,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,[],[f1356]) ).
fof(f1987,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,[],[f1185]) ).
fof(f1988,plain,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(cnf_transformation,[],[f1189]) ).
fof(f1989,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(cnf_transformation,[],[f1188]) ).
fof(f2054,plain,
! [X2,X3,X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f1355]) ).
fof(f2055,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,[],[f1840]) ).
fof(f2058,plain,
! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f1358]) ).
fof(f2071,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,[],[f1374]) ).
fof(f2080,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,[],[f1389]) ).
fof(f2085,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,[],[f1393]) ).
fof(f2089,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,[],[f1398]) ).
fof(f2120,plain,
! [X0] :
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f1423]) ).
fof(f2121,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f1424]) ).
fof(f2278,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1541]) ).
fof(f2352,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f319]) ).
fof(f2724,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(definition_unfolding,[],[f2080,f2352]) ).
fof(f2726,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(definition_unfolding,[],[f2089,f2352]) ).
fof(f2746,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f2278,f2352]) ).
fof(f2852,definition,
~ sP13(c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h))),
introduced(definition,[new_symbols(definition,[sP13])],[inequality_splitting_name_introduction]) ).
fof(f2853,plain,
sP13(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p))),
inference(inequality_splitting,[],[f1988,f2852]) ).
fof(f2975,plain,
( sP13(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a) ),
inference(superposition,[],[f2853,f2726]) ).
fof(f2978,definition,
( spl14_1
<=> class_Groups_Ozero(t_a) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f2979,plain,
( class_Groups_Ozero(t_a)
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f2978]) ).
fof(f2980,plain,
( ~ class_Groups_Ozero(t_a)
| spl14_1 ),
inference(avatar_component_clause,[],[f2978]) ).
fof(f2982,definition,
( spl14_2
<=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f2983,plain,
( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| spl14_2 ),
inference(avatar_component_clause,[],[f2982]) ).
fof(f2984,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f2982]) ).
fof(f2986,definition,
( spl14_3
<=> sP13(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p))) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f2988,plain,
( sP13(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)))
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f2986]) ).
fof(f2990,plain,
( ~ spl14_1
| spl14_2
| spl14_3 ),
inference(avatar_split_clause,[],[f2975,f2986,f2982,f2978]) ).
fof(f2991,plain,
( ~ sP13(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)))))
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(superposition,[],[f2852,f2054]) ).
fof(f2992,plain,
~ sP13(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))))),
inference(forward_subsumption_resolution,[],[f2991,f1989]) ).
fof(f2993,plain,
class_Groups_Ozero(t_a),
inference(resolution,[],[f1989,f2120]) ).
fof(f2994,plain,
( $false
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f2993,f2980]) ).
fof(f2995,plain,
spl14_1,
inference(avatar_contradiction_clause,[],[f2994]) ).
fof(f3007,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,[],[f2085,f1987]) ).
fof(f3010,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,[],[f3007,f1989]) ).
fof(f3018,definition,
( spl14_5
<=> 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,[spl14_5])],[avatar_definition]) ).
fof(f3019,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| spl14_5 ),
inference(avatar_component_clause,[],[f3018]) ).
fof(f3020,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f3018]) ).
fof(f3072,plain,
( ~ sP13(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,[],[f2992,f2071]) ).
fof(f3074,definition,
( spl14_12
<=> class_Groups_Ocomm__monoid__add(t_a) ),
introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition]) ).
fof(f3076,plain,
( ~ class_Groups_Ocomm__monoid__add(t_a)
| spl14_12 ),
inference(avatar_component_clause,[],[f3074]) ).
fof(f3078,definition,
( spl14_13
<=> 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,[spl14_13])],[avatar_definition]) ).
fof(f3080,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))))
| spl14_13 ),
inference(avatar_component_clause,[],[f3078]) ).
fof(f3082,definition,
( spl14_14
<=> sP13(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,[spl14_14])],[avatar_definition]) ).
fof(f3084,plain,
( ~ sP13(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))))
| spl14_14 ),
inference(avatar_component_clause,[],[f3082]) ).
fof(f3085,plain,
( ~ spl14_12
| ~ spl14_13
| ~ spl14_14 ),
inference(avatar_split_clause,[],[f3072,f3082,f3078,f3074]) ).
fof(f3095,plain,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| spl14_12 ),
inference(resolution,[],[f3076,f2121]) ).
fof(f3096,plain,
( $false
| spl14_12 ),
inference(forward_subsumption_resolution,[],[f3095,f1989]) ).
fof(f3097,plain,
spl14_12,
inference(avatar_contradiction_clause,[],[f3096]) ).
fof(f3098,plain,
( ~ sP13(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_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)
| spl14_14 ),
inference(superposition,[],[f3084,f2726]) ).
fof(f3101,plain,
( ~ sP13(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))))
| ~ class_Groups_Ozero(t_a)
| spl14_5
| spl14_14 ),
inference(forward_subsumption_resolution,[],[f3098,f3019]) ).
fof(f3103,plain,
( ~ sP13(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))))
| ~ spl14_1
| spl14_5
| spl14_14 ),
inference(forward_subsumption_resolution,[],[f3101,f2979]) ).
fof(f3105,plain,
( ~ sP13(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)))
| ~ spl14_1
| spl14_5
| spl14_14 ),
inference(forward_demodulation,[],[f3103,f1987]) ).
fof(f3108,plain,
( $false
| ~ spl14_1
| ~ spl14_3
| spl14_5
| spl14_14 ),
inference(forward_subsumption_resolution,[],[f3105,f2988]) ).
fof(f3109,plain,
( ~ spl14_1
| ~ spl14_3
| spl14_5
| spl14_14 ),
inference(avatar_contradiction_clause,[],[f3108]) ).
fof(f3425,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))))
| 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)
| spl14_13 ),
inference(superposition,[],[f3080,f2724]) ).
fof(f3426,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))))
| ~ class_Groups_Ozero(t_a)
| spl14_5
| spl14_13 ),
inference(forward_subsumption_resolution,[],[f3425,f3019]) ).
fof(f3441,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))))
| ~ spl14_1
| spl14_5
| spl14_13 ),
inference(forward_subsumption_resolution,[],[f3426,f2979]) ).
fof(f3444,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)))
| ~ spl14_1
| spl14_5
| spl14_13 ),
inference(forward_demodulation,[],[f3441,f1987]) ).
fof(f3449,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))
| ~ spl14_1
| spl14_5
| spl14_13 ),
inference(resolution,[],[f3444,f2746]) ).
fof(f3480,plain,
( $false
| ~ spl14_1
| spl14_5
| spl14_13 ),
inference(forward_subsumption_resolution,[],[f3449,f3010]) ).
fof(f3481,plain,
( ~ spl14_1
| spl14_5
| spl14_13 ),
inference(avatar_contradiction_clause,[],[f3480]) ).
fof(f3538,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)
| ~ spl14_5 ),
inference(superposition,[],[f2055,f3020]) ).
fof(f3540,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ~ spl14_5 ),
inference(trivial_inequality_removal,[],[f3538]) ).
fof(f3542,plain,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| spl14_2
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f3540,f2983]) ).
fof(f3556,plain,
( $false
| spl14_2
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f3542,f1989]) ).
fof(f3557,plain,
( spl14_2
| ~ spl14_5 ),
inference(avatar_contradiction_clause,[],[f3556]) ).
fof(f3560,plain,
( ~ sP13(c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h)))
| ~ spl14_2 ),
inference(superposition,[],[f2852,f2984]) ).
fof(f3561,plain,
( sP13(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))
| ~ spl14_2 ),
inference(superposition,[],[f2853,f2984]) ).
fof(f3605,plain,
( ~ sP13(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))
| ~ class_Rings_Ocomm__semiring__0(t_a)
| ~ spl14_2 ),
inference(superposition,[],[f3560,f2058]) ).
fof(f3614,plain,
( ~ sP13(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f3605,f1989]) ).
fof(f3637,plain,
( $false
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f3614,f3561]) ).
fof(f3638,plain,
~ spl14_2,
inference(avatar_contradiction_clause,[],[f3637]) ).
cnf(s2,plain,
( ~ spl14_1
| spl14_2
| spl14_3 ),
inference(sat_conversion,[],[f2990]) ).
cnf(s3,plain,
spl14_1,
inference(sat_conversion,[],[f2995]) ).
cnf(s11,plain,
( ~ spl14_12
| ~ spl14_13
| ~ spl14_14 ),
inference(sat_conversion,[],[f3085]) ).
cnf(s13,plain,
spl14_12,
inference(sat_conversion,[],[f3097]) ).
cnf(s15,plain,
( ~ spl14_1
| ~ spl14_3
| spl14_5
| spl14_14 ),
inference(sat_conversion,[],[f3109]) ).
cnf(s42,plain,
( ~ spl14_1
| spl14_5
| spl14_13 ),
inference(sat_conversion,[],[f3481]) ).
cnf(s47,plain,
( spl14_2
| ~ spl14_5 ),
inference(sat_conversion,[],[f3557]) ).
cnf(s56,plain,
~ spl14_2,
inference(sat_conversion,[],[f3638]) ).
cnf(s57,plain,
~ spl14_5,
inference(rat,[],[s47,s56]) ).
cnf(s58,plain,
( ~ spl14_1
| spl14_13 ),
inference(rat,[],[s42,s57]) ).
cnf(s65,plain,
( ~ spl14_1
| ~ spl14_3
| spl14_14 ),
inference(rat,[],[s15,s57]) ).
cnf(s68,plain,
( ~ spl14_13
| ~ spl14_14 ),
inference(rat,[],[s11,s13]) ).
cnf(s72,plain,
spl14_13,
inference(rat,[],[s58,s3]) ).
cnf(s74,plain,
~ spl14_14,
inference(rat,[],[s68,s72]) ).
cnf(s75,plain,
~ spl14_3,
inference(rat,[],[s65,s3,s74]) ).
cnf(s76,plain,
$false,
inference(rat,[],[s2,s75,s56,s3]) ).
fof(f3639,plain,
$false,
inference(avatar_sat_refutation,[],[s76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW187+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n008.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Mon Sep 28 13:13:39 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.28 Running first-order theorem proving
% 0.23/0.28 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
% 5.67/1.41 % (2242632)Detected formulas, will run a generic FOF schedule.
% 5.67/1.41 % (2242642)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4192538476:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.67/1.41 % (2242643)dis-21_1_sil=8000:lcm=predicate:random_seed=4290686474: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)
% 5.67/1.41 % (2242639)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=1159338193:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.67/1.41 % (2242641)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4127629692:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.67/1.41 % (2242638)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=1591488973:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.67/1.41 % (2242640)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=59125021:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.67/1.41 % (2242637)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=1183635385:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.67/1.41 % (2242640)Refutation not found, incomplete strategy
% 5.67/1.41 % (2242640)------------------------------
% 5.67/1.41 % (2242640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.41 % (2242640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.41 % (2242640)CaDiCaL version: 2.1.3
% 5.67/1.41 % (2242640)Termination reason: Refutation not found, incomplete strategy
% 5.67/1.41 % (2242640)Time elapsed: 0.005 s
% 5.67/1.41 % (2242640)Peak memory usage: 89 MB
% 5.67/1.41 % (2242640)Instructions burned: 5 (million)
% 5.67/1.41 % (2242642)Instruction limit reached!
% 5.67/1.41 % (2242642)------------------------------
% 5.67/1.41 % (2242642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.41 % (2242642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.41 % (2242642)CaDiCaL version: 2.1.3
% 5.67/1.41 % (2242642)Termination reason: Instruction limit
% 5.67/1.41 % (2242642)Termination phase: Saturation
% 5.67/1.41 % (2242642)Time elapsed: 0.045 s
% 5.67/1.41 % (2242642)Peak memory usage: 91 MB
% 5.67/1.41 % (2242642)Instructions burned: 140 (million)
% 5.67/1.41 % (2242643)Instruction limit reached!
% 5.67/1.41 % (2242643)------------------------------
% 5.67/1.41 % (2242643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.41 % (2242643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.41 % (2242643)CaDiCaL version: 2.1.3
% 5.67/1.41 % (2242643)Termination reason: Instruction limit
% 5.67/1.41 % (2242643)Termination phase: Saturation
% 5.67/1.41 % (2242643)Time elapsed: 0.069 s
% 5.67/1.41 % (2242643)Peak memory usage: 90 MB
% 5.67/1.41 % (2242643)Instructions burned: 130 (million)
% 5.67/1.41 % (2242641)Instruction limit reached!
% 5.67/1.41 % (2242641)------------------------------
% 5.67/1.41 % (2242641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.41 % (2242641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.41 % (2242641)CaDiCaL version: 2.1.3
% 5.67/1.41 % (2242641)Termination reason: Instruction limit
% 5.67/1.41 % (2242641)Termination phase: Saturation
% 5.67/1.41 % (2242641)Time elapsed: 0.072 s
% 5.67/1.41 % (2242641)Peak memory usage: 89 MB
% 5.67/1.41 % (2242641)Instructions burned: 120 (million)
% 5.67/1.41 % (2242651)lrs+10_1_sil=8000:sp=occurrence:random_seed=197183307:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.67/1.41 % (2242653)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2746108256:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.67/1.41 % (2242652)lrs+10_1_sil=32000:urr=on:br=off:random_seed=81598163:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.67/1.41 % (2242652)Refutation not found, incomplete strategy
% 5.67/1.41 % (2242652)------------------------------
% 5.67/1.41 % (2242652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.41 % (2242652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.41 % (2242652)CaDiCaL version: 2.1.3
% 5.67/1.41 % (2242652)Termination reason: Refutation not found, incomplete strategy
% 5.67/1.41 % (2242652)Time elapsed: 0.010 s
% 5.67/1.41 % (2242652)Peak memory usage: 89 MB
% 5.67/1.41 % (2242652)Instructions burned: 18 (million)
% 5.67/1.41 % (2242651)Instruction limit reached!
% 5.67/1.41 % (2242651)------------------------------
% 5.67/1.41 % (2242651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.41 % (2242651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.41 % (2242651)CaDiCaL version: 2.1.3
% 5.67/1.41 % (2242651)Termination reason: Instruction limit
% 5.67/1.41 % (2242651)Termination phase: Saturation
% 5.67/1.41 % (2242651)Time elapsed: 0.099 s
% 5.67/1.41 % (2242651)Peak memory usage: 92 MB
% 5.67/1.41 % (2242651)Instructions burned: 287 (million)
% 5.67/1.41 % (2242640)------------------------------
% 5.67/1.41 % (2242640)------------------------------
% 5.67/1.41 % (2242657)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=4097397498:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.67/1.41 % (2242653)Instruction limit reached!
% 5.67/1.41 % (2242653)------------------------------
% 5.67/1.41 % (2242653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.41 % (2242653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.41 % (2242653)CaDiCaL version: 2.1.3
% 5.67/1.41 % (2242653)Termination reason: Instruction limit
% 5.67/1.41 % (2242653)Termination phase: Saturation
% 5.67/1.41 % (2242653)Time elapsed: 0.190 s
% 5.67/1.41 % (2242653)Peak memory usage: 92 MB
% 5.67/1.41 % (2242653)Instructions burned: 326 (million)
% 5.67/1.41 % (2242658)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4111195344:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.67/1.41 % (2242657)Instruction limit reached!
% 5.67/1.41 % (2242657)------------------------------
% 5.67/1.41 % (2242657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.41 % (2242657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.41 % (2242657)CaDiCaL version: 2.1.3
% 5.67/1.41 % (2242657)Termination reason: Instruction limit
% 5.67/1.41 % (2242657)Termination phase: Saturation
% 5.67/1.41 % (2242657)Time elapsed: 0.069 s
% 5.67/1.41 % (2242657)Peak memory usage: 92 MB
% 5.67/1.41 % (2242657)Instructions burned: 248 (million)
% 5.67/1.41 % (2242658)First to succeed.
% 5.67/1.41 % (2242658)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2242632"
% 5.67/1.41 % (2242652)------------------------------
% 5.67/1.41 % (2242652)------------------------------
% 5.67/1.41 % (2242662)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2059550712:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.67/1.41 % (2242662)Instruction limit reached!
% 5.67/1.41 % (2242662)------------------------------
% 5.67/1.41 % (2242662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.41 % (2242662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.41 % (2242662)CaDiCaL version: 2.1.3
% 5.67/1.41 % (2242662)Termination reason: Instruction limit
% 5.67/1.41 % (2242662)Termination phase: Saturation
% 5.67/1.41 % (2242662)Time elapsed: 0.034 s
% 5.67/1.41 % (2242662)Peak memory usage: 91 MB
% 5.67/1.41 % (2242662)Instructions burned: 114 (million)
% 5.67/1.41 % (2242661)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=959959285:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 5.67/1.41 % (2242663)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2648848848:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.67/1.41 % (2242663)Instruction limit reached!
% 5.67/1.41 % (2242663)------------------------------
% 5.67/1.41 % (2242663)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.41 % (2242663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.41 % (2242663)CaDiCaL version: 2.1.3
% 5.67/1.41 % (2242663)Termination reason: Instruction limit
% 5.67/1.41 % (2242663)Termination phase: Saturation
% 5.67/1.41 % (2242663)Time elapsed: 0.062 s
% 5.67/1.41 % (2242663)Peak memory usage: 90 MB
% 5.67/1.41 % (2242663)Instructions burned: 128 (million)
% 5.67/1.41 % (2242658)Refutation found. Thanks to Tanya!
% 5.67/1.41 % SZS status Theorem for theBenchmark
% 5.67/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 6.90/1.61 % (2242658)------------------------------
% 6.90/1.61 % (2242658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.90/1.61 % (2242658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.61 % (2242658)CaDiCaL version: 2.1.3
% 6.90/1.61 % (2242658)Termination reason: Refutation
% 6.90/1.61 % (2242658)Time elapsed: 0.055 s
% 6.90/1.61 % (2242658)Peak memory usage: 92 MB
% 6.90/1.61 % (2242658)Instructions burned: 92 (million)
% 6.90/1.61 % (2242658)------------------------------
% 6.90/1.61 % (2242658)------------------------------
% 6.90/1.61 % (2242632)Success in time 0.936 s
% 6.90/1.61 % Vampire exiting
%------------------------------------------------------------------------------