%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW253+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:29:56 PM UTC 2026
% Result : Theorem 5.27s 1.58s
% Output : Refutation 6.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 10 unt; 2 def)
% Number of atoms : 96 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 87 ( 39 ~; 40 |; 1 &)
% ( 4 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f144,axiom,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__divide__def) ).
fof(f145,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(f1184,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1185,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f1264,conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1265,negated_conjecture,
~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(negated_conjecture,[status(cth)],[f1264]) ).
fof(f1284,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<~> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(ennf_transformation,[],[f1265]) ).
fof(f1342,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f145]) ).
fof(f1831,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f2023,plain,
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(nnf_transformation,[],[f1284]) ).
fof(f2229,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f2023]) ).
fof(f2230,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f2023]) ).
fof(f2330,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1185]) ).
fof(f2331,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1184]) ).
fof(f2339,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)),
inference(cnf_transformation,[],[f144]) ).
fof(f2360,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f1342]) ).
fof(f2930,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f1831]) ).
fof(f3287,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(forward_demodulation,[],[f2229,f2339]) ).
fof(f3288,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(forward_demodulation,[],[f2230,f2339]) ).
fof(f3290,definition,
( spl29_1
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[spl29_1])],[avatar_definition]) ).
fof(f3291,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| spl29_1 ),
inference(avatar_component_clause,[],[f3290]) ).
fof(f3292,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl29_1 ),
inference(avatar_component_clause,[],[f3290]) ).
fof(f3294,definition,
( spl29_2
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[spl29_2])],[avatar_definition]) ).
fof(f3295,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| spl29_2 ),
inference(avatar_component_clause,[],[f3294]) ).
fof(f3296,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl29_2 ),
inference(avatar_component_clause,[],[f3294]) ).
fof(f3297,plain,
( spl29_1
| spl29_2 ),
inference(avatar_split_clause,[],[f3287,f3294,f3290]) ).
fof(f3298,plain,
( ~ spl29_1
| ~ spl29_2 ),
inference(avatar_split_clause,[],[f3288,f3294,f3290]) ).
fof(f3304,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| spl29_1 ),
inference(superposition,[],[f3291,f2360]) ).
fof(f3315,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| spl29_1 ),
inference(forward_subsumption_resolution,[],[f3304,f2330]) ).
fof(f3338,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl29_2 ),
inference(superposition,[],[f3296,f2930]) ).
fof(f3355,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| spl29_1
| ~ spl29_2 ),
inference(forward_subsumption_resolution,[],[f3338,f3315]) ).
fof(f3394,plain,
( $false
| spl29_1
| ~ spl29_2 ),
inference(forward_subsumption_resolution,[],[f3355,f2331]) ).
fof(f3395,plain,
( spl29_1
| ~ spl29_2 ),
inference(avatar_contradiction_clause,[],[f3394]) ).
fof(f3401,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ~ spl29_1 ),
inference(superposition,[],[f3292,f2360]) ).
fof(f3404,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl29_1 ),
inference(forward_subsumption_resolution,[],[f3401,f2330]) ).
fof(f3419,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| spl29_2 ),
inference(superposition,[],[f3295,f2930]) ).
fof(f3433,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl29_1
| spl29_2 ),
inference(forward_subsumption_resolution,[],[f3419,f3404]) ).
fof(f3446,plain,
( $false
| ~ spl29_1
| spl29_2 ),
inference(forward_subsumption_resolution,[],[f3433,f2331]) ).
fof(f3447,plain,
( ~ spl29_1
| spl29_2 ),
inference(avatar_contradiction_clause,[],[f3446]) ).
cnf(s1,plain,
( spl29_1
| spl29_2 ),
inference(sat_conversion,[],[f3297]) ).
cnf(s2,plain,
( ~ spl29_1
| ~ spl29_2 ),
inference(sat_conversion,[],[f3298]) ).
cnf(s16,plain,
( spl29_1
| ~ spl29_2 ),
inference(sat_conversion,[],[f3395]) ).
cnf(s22,plain,
( ~ spl29_1
| spl29_2 ),
inference(sat_conversion,[],[f3447]) ).
cnf(s23,plain,
spl29_1,
inference(rat,[],[s1,s16]) ).
cnf(s24,plain,
spl29_2,
inference(rat,[],[s22,s23]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s2,s24,s23]) ).
fof(f3448,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW253+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 13:19:36 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.27/1.58 % (3546031)Detected formulas, will run a generic FOF schedule.
% 5.27/1.58 % (3546036)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=35490744:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.27/1.58 % (3546041)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2309214907:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.27/1.58 % (3546038)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=13506809:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.27/1.58 % (3546040)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=910619364:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.27/1.58 % (3546039)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3740190977:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.27/1.58 % (3546037)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=1609377020:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.27/1.58 % (3546042)dis-21_1_sil=8000:lcm=predicate:random_seed=362631173: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)
% 5.27/1.58 % (3546039)Instruction limit reached!
% 5.27/1.58 % (3546039)------------------------------
% 5.27/1.58 % (3546039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.58 % (3546039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.58 % (3546039)CaDiCaL version: 2.1.3
% 5.27/1.58 % (3546039)Termination reason: Instruction limit
% 5.27/1.58 % (3546039)Termination phase: Saturation
% 5.27/1.58 % (3546039)Time elapsed: 0.052 s
% 5.27/1.58 % (3546039)Peak memory usage: 89 MB
% 5.27/1.58 % (3546039)Instructions burned: 110 (million)
% 5.27/1.58 % (3546040)Instruction limit reached!
% 5.27/1.58 % (3546040)------------------------------
% 5.27/1.58 % (3546040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.58 % (3546040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.58 % (3546040)CaDiCaL version: 2.1.3
% 5.27/1.58 % (3546040)Termination reason: Instruction limit
% 5.27/1.58 % (3546040)Termination phase: Saturation
% 5.27/1.58 % (3546040)Time elapsed: 0.071 s
% 5.27/1.58 % (3546040)Peak memory usage: 89 MB
% 5.27/1.58 % (3546040)Instructions burned: 120 (million)
% 5.27/1.58 % (3546042)Instruction limit reached!
% 5.27/1.58 % (3546042)------------------------------
% 5.27/1.58 % (3546042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.58 % (3546042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.58 % (3546042)CaDiCaL version: 2.1.3
% 5.27/1.58 % (3546042)Termination reason: Instruction limit
% 5.27/1.58 % (3546042)Termination phase: Saturation
% 5.27/1.58 % (3546042)Time elapsed: 0.067 s
% 5.27/1.58 % (3546042)Peak memory usage: 91 MB
% 5.27/1.58 % (3546042)Instructions burned: 129 (million)
% 5.27/1.58 % (3546041)Instruction limit reached!
% 5.27/1.58 % (3546041)------------------------------
% 5.27/1.58 % (3546041)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.58 % (3546041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.58 % (3546041)CaDiCaL version: 2.1.3
% 5.27/1.58 % (3546041)Termination reason: Instruction limit
% 5.27/1.58 % (3546041)Termination phase: Saturation
% 5.27/1.58 % (3546041)Time elapsed: 0.078 s
% 5.27/1.58 % (3546041)Peak memory usage: 91 MB
% 5.27/1.58 % (3546041)Instructions burned: 139 (million)
% 5.27/1.58 % (3546050)lrs+10_1_sil=8000:sp=occurrence:random_seed=3217143237:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.27/1.58 % (3546051)lrs+10_1_sil=32000:urr=on:br=off:random_seed=683087585:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.27/1.58 % (3546052)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1555510818:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.27/1.58 % (3546053)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=1069734679:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.27/1.58 % (3546051)Instruction limit reached!
% 5.27/1.58 % (3546051)------------------------------
% 5.27/1.58 % (3546051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.58 % (3546051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.58 % (3546051)CaDiCaL version: 2.1.3
% 5.27/1.58 % (3546051)Termination reason: Instruction limit
% 5.27/1.58 % (3546051)Termination phase: Saturation
% 5.27/1.58 % (3546051)Time elapsed: 0.091 s
% 5.27/1.58 % (3546051)Peak memory usage: 91 MB
% 5.27/1.58 % (3546051)Instructions burned: 158 (million)
% 5.27/1.58 % (3546050)Instruction limit reached!
% 5.27/1.58 % (3546050)------------------------------
% 5.27/1.58 % (3546050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.58 % (3546050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.58 % (3546050)CaDiCaL version: 2.1.3
% 5.27/1.58 % (3546050)Termination reason: Instruction limit
% 5.27/1.58 % (3546050)Termination phase: Saturation
% 5.27/1.58 % (3546050)Time elapsed: 0.174 s
% 5.27/1.58 % (3546050)Peak memory usage: 91 MB
% 5.27/1.58 % (3546050)Instructions burned: 285 (million)
% 5.27/1.58 % (3546053)Instruction limit reached!
% 5.27/1.58 % (3546053)------------------------------
% 5.27/1.58 % (3546053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.58 % (3546053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.58 % (3546053)CaDiCaL version: 2.1.3
% 5.27/1.58 % (3546053)Termination reason: Instruction limit
% 5.27/1.58 % (3546053)Termination phase: Saturation
% 5.27/1.58 % (3546053)Time elapsed: 0.146 s
% 5.27/1.58 % (3546053)Peak memory usage: 92 MB
% 5.27/1.58 % (3546053)Instructions burned: 249 (million)
% 5.27/1.58 % (3546052)Instruction limit reached!
% 5.27/1.58 % (3546052)------------------------------
% 5.27/1.58 % (3546052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.58 % (3546052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.58 % (3546052)CaDiCaL version: 2.1.3
% 5.27/1.58 % (3546052)Termination reason: Instruction limit
% 5.27/1.58 % (3546052)Termination phase: Saturation
% 5.27/1.58 % (3546052)Time elapsed: 0.199 s
% 5.27/1.58 % (3546052)Peak memory usage: 91 MB
% 5.27/1.58 % (3546052)Instructions burned: 326 (million)
% 5.27/1.58 % (3546058)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1942164764:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.27/1.58 % (3546058)First to succeed.
% 5.27/1.58 % (3546058)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3546031"
% 5.27/1.58 % (3546059)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2605890833:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.27/1.58 % (3546060)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3818303981:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.27/1.58 % (3546061)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3890116518:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.27/1.58 % (3546060)Instruction limit reached!
% 5.27/1.58 % (3546060)------------------------------
% 5.27/1.58 % (3546060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.58 % (3546060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.58 % (3546060)CaDiCaL version: 2.1.3
% 5.27/1.58 % (3546060)Termination reason: Instruction limit
% 5.27/1.58 % (3546060)Termination phase: Saturation
% 5.27/1.58 % (3546060)Time elapsed: 0.062 s
% 5.27/1.58 % (3546060)Peak memory usage: 91 MB
% 5.27/1.58 % (3546060)Instructions burned: 115 (million)
% 5.27/1.58 % (3546036)Also succeeded, but the first one will report.
% 5.27/1.58 % (3546061)Instruction limit reached!
% 5.27/1.58 % (3546061)------------------------------
% 5.27/1.58 % (3546061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.58 % (3546061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.58 % (3546061)CaDiCaL version: 2.1.3
% 5.27/1.58 % (3546061)Termination reason: Instruction limit
% 5.27/1.58 % (3546061)Termination phase: Saturation
% 5.27/1.58 % (3546061)Time elapsed: 0.063 s
% 5.27/1.58 % (3546061)Peak memory usage: 90 MB
% 5.27/1.58 % (3546061)Instructions burned: 128 (million)
% 5.27/1.58 % (3546066)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1410226350:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 5.27/1.58 % (3546058)Refutation found. Thanks to Tanya!
% 5.27/1.58 % SZS status Theorem for theBenchmark
% 5.27/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 6.76/1.76 % (3546058)------------------------------
% 6.76/1.76 % (3546058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/1.76 % (3546058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.76 % (3546058)CaDiCaL version: 2.1.3
% 6.76/1.76 % (3546058)Termination reason: Refutation
% 6.76/1.76 % (3546058)Time elapsed: 0.047 s
% 6.76/1.76 % (3546058)Peak memory usage: 92 MB
% 6.76/1.76 % (3546058)Instructions burned: 83 (million)
% 6.76/1.76 % (3546058)------------------------------
% 6.76/1.76 % (3546058)------------------------------
% 6.76/1.76 % (3546031)Success in time 0.915 s
% 6.76/1.76 % Vampire exiting
%------------------------------------------------------------------------------