%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW269+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 : n013.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 01:29:59 PM UTC 2026
% Result : Theorem 7.75s 1.98s
% Output : Refutation 9.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 95 ( 43 unt; 5 def)
% Number of atoms : 187 ( 116 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 160 ( 68 ~; 70 |; 8 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 84 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
=> X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(f2,axiom,
v_d____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096d_A_061_A0_096) ).
fof(f3,axiom,
! [X0] :
( X0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons_Oprems) ).
fof(f5,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( X1 = c_Groups_Ozero__class_Ozero(X2)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( class_Int_Oring__char__0(X2)
& class_Rings_Oidom(X2) )
=> ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(f17,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(f154,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(f215,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X0,hAPP(c_Polynomial_Opoly(X3,X1),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(f1070,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1071,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f1084,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f1090,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(f1092,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(f1159,conjecture,
c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1160,negated_conjecture,
c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(negated_conjecture,[status(cth)],[f1159]) ).
fof(f1162,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(flattening,[],[f1160]) ).
fof(f1231,plain,
! [X0,X1] :
( X1 = X0
| ? [X2] : hAPP(X1,X2) != hAPP(X0,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1232,plain,
! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ),
inference(ennf_transformation,[],[f3]) ).
fof(f1234,plain,
! [X0,X1,X2] :
( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( X1 = c_Groups_Ozero__class_Ozero(X2)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f1244,plain,
! [X0,X1,X2] :
( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X1 = X0 )
| ~ class_Int_Oring__char__0(X2)
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f1245,plain,
! [X0,X1,X2] :
( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X1 = X0 )
| ~ class_Int_Oring__char__0(X2)
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f1244]) ).
fof(f1248,plain,
! [X0,X1] :
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f1374,plain,
! [X0,X1] :
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f154]) ).
fof(f1436,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X0,hAPP(c_Polynomial_Opoly(X3,X1),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f215]) ).
fof(f2390,plain,
! [X0,X1] :
( X1 = X0
| hAPP(X1,sK4(X0,X1)) != hAPP(X0,sK4(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f1231]) ).
fof(f2391,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 )
& ( ( X1 = c_Groups_Ozero__class_Ozero(X2)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
| c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Groups_Ozero(X2) ),
inference(nnf_transformation,[],[f1234]) ).
fof(f2392,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 )
& ( ( X1 = c_Groups_Ozero__class_Ozero(X2)
& X0 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) )
| c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f2391]) ).
fof(f2397,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
| X0 != X1 )
& ( X1 = X0
| c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0) ) )
| ~ class_Int_Oring__char__0(X2)
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f1245]) ).
fof(f2719,plain,
! [X0,X1] :
( hAPP(X1,sK4(X0,X1)) != hAPP(X0,sK4(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f2390]) ).
fof(f2720,plain,
v_d____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f2]) ).
fof(f2721,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ),
inference(cnf_transformation,[],[f1232]) ).
fof(f2725,plain,
! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2392]) ).
fof(f2739,plain,
! [X2,X0,X1] :
( c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0)
| X0 = X1
| ~ class_Int_Oring__char__0(X2)
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2397]) ).
fof(f2743,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
inference(cnf_transformation,[],[f1248]) ).
fof(f2928,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f1374]) ).
fof(f3009,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X0,hAPP(c_Polynomial_Opoly(X3,X1),X0))) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f4116,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1070]) ).
fof(f4117,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1071]) ).
fof(f4130,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1084]) ).
fof(f4136,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1090]) ).
fof(f4138,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1092]) ).
fof(f4205,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f1162]) ).
fof(f4337,plain,
! [X2,X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| ~ class_Groups_Ozero(X2) ),
inference(equality_resolution,[],[f2725]) ).
fof(f4338,plain,
! [X2] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) ),
inference(equality_resolution,[],[f4337]) ).
fof(f4584,definition,
sF28 = c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f4585,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____) = sF28,
inference(reorient_equations,[],[f4584]) ).
fof(f4586,definition,
sF29 = tc_Polynomial_Opoly(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f4587,plain,
tc_Polynomial_Opoly(tc_Complex_Ocomplex) = sF29,
inference(reorient_equations,[],[f4586]) ).
fof(f4588,definition,
sF30 = c_Groups_Ozero__class_Ozero(sF29),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f4589,plain,
c_Groups_Ozero__class_Ozero(sF29) = sF30,
inference(reorient_equations,[],[f4588]) ).
fof(f4590,plain,
sF28 != sF30,
inference(definition_folding,[],[f4205,f4589,f4587,f4585]) ).
fof(f4799,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,X2,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X2))),
inference(resolution,[],[f4117,f3009]) ).
fof(f4800,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0),
inference(resolution,[],[f2743,f4117]) ).
fof(f4801,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(sF29)),X0),
inference(forward_demodulation,[],[f4800,f4587]) ).
fof(f4802,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),X0),
inference(forward_demodulation,[],[f4801,f4589]) ).
fof(f4803,plain,
! [X0] : v_d____ = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),X0),
inference(forward_demodulation,[],[f4802,f2720]) ).
fof(f4826,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(resolution,[],[f4136,f4338]) ).
fof(f4827,plain,
c_Groups_Ozero__class_Ozero(sF29) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(sF29)),
inference(forward_demodulation,[],[f4826,f4587]) ).
fof(f4828,plain,
sF30 = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),sF30),
inference(forward_demodulation,[],[f4827,f4589]) ).
fof(f4829,plain,
sF30 = c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,sF30),
inference(forward_demodulation,[],[f4828,f2720]) ).
fof(f4841,plain,
! [X0] :
( v_d____ != hAPP(X0,sK4(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),X0))
| c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30) = X0 ),
inference(superposition,[],[f2719,f4803]) ).
fof(f4917,plain,
( v_d____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)) = c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = sK4(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____))) ),
inference(superposition,[],[f4841,f2721]) ).
fof(f4918,plain,
( c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)) = c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = sK4(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____))) ),
inference(forward_subsumption_resolution,[],[f4917,f2720]) ).
fof(f4924,plain,
( c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30) = c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = sK4(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____))) ),
inference(forward_demodulation,[],[f4918,f4585]) ).
fof(f4930,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = sK4(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28))
| c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30) = c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28) ),
inference(forward_demodulation,[],[f4924,f4585]) ).
fof(f4935,plain,
( v_d____ = sK4(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28))
| c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30) = c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28) ),
inference(forward_demodulation,[],[f4930,f2720]) ).
fof(f4940,definition,
( spl31_12
<=> c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30) = c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28) ),
introduced(definition,[new_symbols(definition,[spl31_12])],[avatar_definition]) ).
fof(f4941,plain,
( c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30) != c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28)
| spl31_12 ),
inference(avatar_component_clause,[],[f4940]) ).
fof(f4942,plain,
( c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30) = c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28)
| ~ spl31_12 ),
inference(avatar_component_clause,[],[f4940]) ).
fof(f4944,definition,
( spl31_13
<=> v_d____ = sK4(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28)) ),
introduced(definition,[new_symbols(definition,[spl31_13])],[avatar_definition]) ).
fof(f4946,plain,
( v_d____ = sK4(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28))
| ~ spl31_13 ),
inference(avatar_component_clause,[],[f4944]) ).
fof(f4947,plain,
( spl31_12
| spl31_13 ),
inference(avatar_split_clause,[],[f4935,f4944,f4940]) ).
fof(f5011,plain,
( ! [X0] :
( c_Polynomial_Opoly(tc_Complex_Ocomplex,X0) != c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28)
| sF30 = X0
| ~ class_Int_Oring__char__0(tc_Complex_Ocomplex)
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
| ~ spl31_12 ),
inference(superposition,[],[f2739,f4942]) ).
fof(f5013,plain,
( ! [X0] :
( c_Polynomial_Opoly(tc_Complex_Ocomplex,X0) != c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28)
| sF30 = X0
| ~ class_Rings_Oidom(tc_Complex_Ocomplex) )
| ~ spl31_12 ),
inference(forward_subsumption_resolution,[],[f5011,f4130]) ).
fof(f5015,plain,
( ! [X0] :
( c_Polynomial_Opoly(tc_Complex_Ocomplex,X0) != c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28)
| sF30 = X0 )
| ~ spl31_12 ),
inference(forward_subsumption_resolution,[],[f5013,f4138]) ).
fof(f5017,plain,
( sF28 = sF30
| ~ spl31_12 ),
inference(equality_resolution,[],[f5015]) ).
fof(f5018,plain,
( $false
| ~ spl31_12 ),
inference(forward_subsumption_resolution,[],[f5017,f4590]) ).
fof(f5019,plain,
~ spl31_12,
inference(avatar_contradiction_clause,[],[f5018]) ).
fof(f5020,plain,
( v_d____ != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28),v_d____)
| c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30) = c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28)
| ~ spl31_13 ),
inference(superposition,[],[f4841,f4946]) ).
fof(f5023,plain,
( v_d____ != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28),v_d____)
| spl31_12
| ~ spl31_13 ),
inference(forward_subsumption_resolution,[],[f5020,f4941]) ).
fof(f5120,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0),
inference(resolution,[],[f2928,f4116]) ).
fof(f5121,plain,
! [X0] : v_d____ = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,v_d____,X0),
inference(forward_demodulation,[],[f5120,f2720]) ).
fof(f5123,plain,
! [X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),v_d____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,v_d____),
inference(superposition,[],[f4799,f5121]) ).
fof(f5124,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF28),v_d____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_d____,v_d____),
inference(superposition,[],[f5123,f4585]) ).
fof(f5125,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF30),v_d____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_d____,v_d____),
inference(superposition,[],[f5123,f4829]) ).
fof(f5133,plain,
v_d____ = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_d____,v_d____),
inference(forward_demodulation,[],[f5125,f4803]) ).
fof(f5134,plain,
( v_d____ != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_d____,v_d____)
| spl31_12
| ~ spl31_13 ),
inference(superposition,[],[f5023,f5124]) ).
fof(f5137,plain,
( $false
| spl31_12
| ~ spl31_13 ),
inference(forward_subsumption_resolution,[],[f5134,f5133]) ).
fof(f5138,plain,
( spl31_12
| ~ spl31_13 ),
inference(avatar_contradiction_clause,[],[f5137]) ).
cnf(s8,plain,
( spl31_12
| spl31_13 ),
inference(sat_conversion,[],[f4947]) ).
cnf(s10,plain,
~ spl31_12,
inference(sat_conversion,[],[f5019]) ).
cnf(s14,plain,
( spl31_12
| ~ spl31_13 ),
inference(sat_conversion,[],[f5138]) ).
cnf(s16,plain,
~ spl31_13,
inference(rat,[],[s14,s10]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s8,s16,s10]) ).
fof(f5139,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW269+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n013.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 13:24:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.75/1.98 % (1174308)Detected formulas, will run a generic FOF schedule.
% 7.75/1.98 % (1174448)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=3640550931:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.75/1.98 % (1174453)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=890463470:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.75/1.98 % (1174450)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=3007539801:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.75/1.98 % (1174451)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4113981067:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.75/1.98 % (1174452)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3876041715:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.75/1.98 % (1174451)Refutation not found, incomplete strategy
% 7.75/1.98 % (1174451)------------------------------
% 7.75/1.98 % (1174451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.98 % (1174451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.98 % (1174451)CaDiCaL version: 2.1.3
% 7.75/1.98 % (1174451)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.98 % (1174451)Time elapsed: 0.006 s
% 7.75/1.98 % (1174451)Peak memory usage: 89 MB
% 7.75/1.98 % (1174451)Instructions burned: 4 (million)
% 7.75/1.98 % (1174449)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=3028372243:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.75/1.98 % (1174454)dis-21_1_sil=8000:lcm=predicate:random_seed=3809998873:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 7.75/1.98 % (1174453)Instruction limit reached!
% 7.75/1.98 % (1174453)------------------------------
% 7.75/1.98 % (1174453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.98 % (1174453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.98 % (1174453)CaDiCaL version: 2.1.3
% 7.75/1.98 % (1174453)Termination reason: Instruction limit
% 7.75/1.98 % (1174453)Termination phase: Saturation
% 7.75/1.98 % (1174453)Time elapsed: 0.131 s
% 7.75/1.98 % (1174453)Peak memory usage: 91 MB
% 7.75/1.98 % (1174453)Instructions burned: 139 (million)
% 7.75/1.98 % (1174452)Instruction limit reached!
% 7.75/1.98 % (1174452)------------------------------
% 7.75/1.98 % (1174452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.98 % (1174452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.98 % (1174452)CaDiCaL version: 2.1.3
% 7.75/1.98 % (1174452)Termination reason: Instruction limit
% 7.75/1.98 % (1174452)Termination phase: Saturation
% 7.75/1.98 % (1174452)Time elapsed: 0.123 s
% 7.75/1.98 % (1174452)Peak memory usage: 89 MB
% 7.75/1.98 % (1174452)Instructions burned: 119 (million)
% 7.75/1.98 % (1174454)Instruction limit reached!
% 7.75/1.98 % (1174454)------------------------------
% 7.75/1.98 % (1174454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.98 % (1174454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.98 % (1174454)CaDiCaL version: 2.1.3
% 7.75/1.98 % (1174454)Termination reason: Instruction limit
% 7.75/1.98 % (1174454)Termination phase: Saturation
% 7.75/1.98 % (1174454)Time elapsed: 0.125 s
% 7.75/1.98 % (1174454)Peak memory usage: 91 MB
% 7.75/1.98 % (1174454)Instructions burned: 129 (million)
% 7.75/1.98 % (1174469)lrs+10_1_sil=8000:sp=occurrence:random_seed=3277373671:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 7.75/1.98 % (1174451)------------------------------
% 7.75/1.98 % (1174451)------------------------------
% 7.75/1.98 % (1174470)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3910399315:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 7.75/1.98 % (1174470)Refutation not found, incomplete strategy
% 7.75/1.98 % (1174470)------------------------------
% 7.75/1.98 % (1174470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.98 % (1174470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.98 % (1174470)CaDiCaL version: 2.1.3
% 7.75/1.98 % (1174470)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.98 % (1174470)Time elapsed: 0.016 s
% 7.75/1.98 % (1174470)Peak memory usage: 90 MB
% 7.75/1.98 % (1174470)Instructions burned: 15 (million)
% 7.75/1.98 % (1174473)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2751460810:i=325:sd=1:ss=axioms:sgt=32_2994 on theBenchmark for (2994ds/325Mi)
% 7.75/1.98 % (1174473)Refutation not found, incomplete strategy
% 7.75/1.98 % (1174473)------------------------------
% 7.75/1.98 % (1174473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.98 % (1174473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.98 % (1174473)CaDiCaL version: 2.1.3
% 7.75/1.98 % (1174473)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.98 % (1174473)Time elapsed: 0.007 s
% 7.75/1.98 % (1174473)Peak memory usage: 89 MB
% 7.75/1.98 % (1174473)Instructions burned: 4 (million)
% 7.75/1.98 % (1174469)Instruction limit reached!
% 7.75/1.98 % (1174469)------------------------------
% 7.75/1.98 % (1174469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.98 % (1174469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.98 % (1174469)CaDiCaL version: 2.1.3
% 7.75/1.98 % (1174469)Termination reason: Instruction limit
% 7.75/1.98 % (1174469)Termination phase: Saturation
% 7.75/1.98 % (1174469)Time elapsed: 0.289 s
% 7.75/1.98 % (1174469)Peak memory usage: 92 MB
% 7.75/1.98 % (1174469)Instructions burned: 286 (million)
% 7.75/1.98 % (1174478)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=3312431884:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 7.75/1.98 % (1174448)First to succeed.
% 7.75/1.98 % (1174448)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1174308"
% 7.75/1.98 % (1174480)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1024015650:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2990 on theBenchmark for (2990ds/294Mi)
% 7.75/1.98 % (1174470)------------------------------
% 7.75/1.98 % (1174470)------------------------------
% 7.75/1.98 % (1174473)------------------------------
% 7.75/1.98 % (1174473)------------------------------
% 7.75/1.98 % (1174478)Instruction limit reached!
% 7.75/1.98 % (1174478)------------------------------
% 7.75/1.98 % (1174478)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.98 % (1174478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.98 % (1174478)CaDiCaL version: 2.1.3
% 7.75/1.98 % (1174478)Termination reason: Instruction limit
% 7.75/1.98 % (1174478)Termination phase: Saturation
% 7.75/1.98 % (1174478)Time elapsed: 0.224 s
% 7.75/1.98 % (1174478)Peak memory usage: 92 MB
% 7.75/1.98 % (1174478)Instructions burned: 249 (million)
% 7.75/1.98 % (1174448)Refutation found. Thanks to Tanya!
% 7.75/1.98 % SZS status Theorem for theBenchmark
% 7.75/1.98 % SZS output start Proof for theBenchmark
% See solution above
% 9.26/2.27 % (1174448)------------------------------
% 9.26/2.27 % (1174448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.27 % (1174448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.27 % (1174448)CaDiCaL version: 2.1.3
% 9.26/2.27 % (1174448)Termination reason: Refutation
% 9.26/2.27 % (1174448)Time elapsed: 0.771 s
% 9.26/2.27 % (1174448)Peak memory usage: 147 MB
% 9.26/2.27 % (1174448)Instructions burned: 1538 (million)
% 9.26/2.27 % (1174448)------------------------------
% 9.26/2.27 % (1174448)------------------------------
% 9.26/2.27 % (1174308)Success in time 1.292 s
% 9.26/2.27 % Vampire exiting
%------------------------------------------------------------------------------