%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW258+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 01:29:57 PM UTC 2026
% Result : Theorem 5.97s 1.77s
% Output : Refutation 7.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 65 ( 26 unt; 4 def)
% Number of atoms : 126 ( 10 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 115 ( 54 ~; 47 |; 1 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m_I1_J) ).
fof(f3,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w0) ).
fof(f11,axiom,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
<=> X0 != c_Groups_Ozero__class_Ozero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(f146,axiom,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(f160,axiom,
! [X0,X1] :
( class_Fields_Olinordered__field(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
fof(f208,axiom,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(f256,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(f1133,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(f1137,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(f1181,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1272,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1273,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
inference(negated_conjecture,[status(cth)],[f1272]) ).
fof(f1276,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
inference(flattening,[],[f1273]) ).
fof(f1291,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
<=> X0 != c_Groups_Ozero__class_Ozero(X1) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f1500,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f146]) ).
fof(f1501,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f1500]) ).
fof(f1527,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field(X1) ),
inference(ennf_transformation,[],[f160]) ).
fof(f1528,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field(X1) ),
inference(flattening,[],[f1527]) ).
fof(f1649,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(ennf_transformation,[],[f256]) ).
fof(f1650,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(flattening,[],[f1649]) ).
fof(f2421,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0 )
& ( X0 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(nnf_transformation,[],[f1291]) ).
fof(f2780,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(cnf_transformation,[],[f2]) ).
fof(f2781,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f3]) ).
fof(f2790,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f2421]) ).
fof(f2972,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f1501]) ).
fof(f2989,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field(X1) ),
inference(cnf_transformation,[],[f1528]) ).
fof(f3051,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
inference(cnf_transformation,[],[f208]) ).
fof(f3121,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(cnf_transformation,[],[f1650]) ).
fof(f4309,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1133]) ).
fof(f4313,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1137]) ).
fof(f4357,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1181]) ).
fof(f4448,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
inference(cnf_transformation,[],[f1276]) ).
fof(f4799,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(forward_demodulation,[],[f4448,f3051]) ).
fof(f4801,definition,
( spl40_1
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) ),
introduced(definition,[new_symbols(definition,[spl40_1])],[avatar_definition]) ).
fof(f4803,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))
| spl40_1 ),
inference(avatar_component_clause,[],[f4801]) ).
fof(f4804,plain,
~ spl40_1,
inference(avatar_split_clause,[],[f4799,f4801]) ).
fof(f4811,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ class_Fields_Olinordered__field(tc_RealDef_Oreal)
| spl40_1 ),
inference(resolution,[],[f4803,f2989]) ).
fof(f5137,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| spl40_1 ),
inference(forward_subsumption_resolution,[],[f4811,f4313]) ).
fof(f6422,definition,
( spl40_7
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
introduced(definition,[new_symbols(definition,[spl40_7])],[avatar_definition]) ).
fof(f6424,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| spl40_7 ),
inference(avatar_component_clause,[],[f6422]) ).
fof(f6425,plain,
( ~ spl40_7
| spl40_1 ),
inference(avatar_split_clause,[],[f5137,f4801,f6422]) ).
fof(f6426,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| spl40_7 ),
inference(resolution,[],[f6424,f3121]) ).
fof(f6757,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| spl40_7 ),
inference(forward_subsumption_resolution,[],[f6426,f2780]) ).
fof(f8688,definition,
( spl40_15
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
introduced(definition,[new_symbols(definition,[spl40_15])],[avatar_definition]) ).
fof(f8690,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| spl40_15 ),
inference(avatar_component_clause,[],[f8688]) ).
fof(f8691,plain,
( ~ spl40_15
| spl40_7 ),
inference(avatar_split_clause,[],[f6757,f6422,f8688]) ).
fof(f8697,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| spl40_15 ),
inference(resolution,[],[f8690,f2972]) ).
fof(f9015,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| spl40_15 ),
inference(forward_subsumption_resolution,[],[f8697,f4309]) ).
fof(f9030,definition,
( spl40_16
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
introduced(definition,[new_symbols(definition,[spl40_16])],[avatar_definition]) ).
fof(f9032,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| spl40_16 ),
inference(avatar_component_clause,[],[f9030]) ).
fof(f9033,plain,
( ~ spl40_16
| spl40_15 ),
inference(avatar_split_clause,[],[f9015,f8688,f9030]) ).
fof(f9196,plain,
( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| spl40_16 ),
inference(resolution,[],[f9032,f2790]) ).
fof(f9504,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| spl40_16 ),
inference(forward_subsumption_resolution,[],[f9196,f2781]) ).
fof(f9526,plain,
( $false
| spl40_16 ),
inference(forward_subsumption_resolution,[],[f9504,f4357]) ).
fof(f9527,plain,
spl40_16,
inference(avatar_contradiction_clause,[],[f9526]) ).
cnf(s1,plain,
~ spl40_1,
inference(sat_conversion,[],[f4804]) ).
cnf(s7,plain,
( spl40_1
| ~ spl40_7 ),
inference(sat_conversion,[],[f6425]) ).
cnf(s15,plain,
( spl40_7
| ~ spl40_15 ),
inference(sat_conversion,[],[f8691]) ).
cnf(s16,plain,
( spl40_15
| ~ spl40_16 ),
inference(sat_conversion,[],[f9033]) ).
cnf(s18,plain,
spl40_16,
inference(sat_conversion,[],[f9527]) ).
cnf(s19,plain,
spl40_15,
inference(rat,[],[s16,s18]) ).
cnf(s20,plain,
spl40_7,
inference(rat,[],[s15,s19]) ).
cnf(s21,plain,
spl40_1,
inference(rat,[],[s7,s20]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s1,s21]) ).
fof(f9539,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW258+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 % Computer : n013.cluster.edu
% 0.07/0.22 % Model : x86_64 x86_64
% 0.07/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.22 % Memory : 8046.5625MB
% 0.07/0.22 % OS : Linux 6.8.0-71-generic
% 0.07/0.22 % CPULimit : 300
% 0.07/0.22 % WCLimit : 300
% 0.07/0.22 % DateTime : Mon Sep 28 13:24:37 UTC 2026
% 0.07/0.22 % CPUTime :
% 0.07/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.26 Running first-order theorem proving
% 0.07/0.26 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
% 5.97/1.77 % (1173553)Detected formulas, will run a generic FOF schedule.
% 5.97/1.77 % (1173576)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=3696653962:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.97/1.77 % (1173574)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=2039826216:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.97/1.77 % (1173580)dis-21_1_sil=8000:lcm=predicate:random_seed=3352197493: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)
% 5.97/1.77 % (1173577)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4083358384:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.97/1.77 % (1173575)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=4109042792:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.97/1.77 % (1173578)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1308133327:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.97/1.77 % (1173579)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=854039349:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.97/1.77 % (1173577)Instruction limit reached!
% 5.97/1.77 % (1173577)------------------------------
% 5.97/1.77 % (1173577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173577)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173577)Termination reason: Instruction limit
% 5.97/1.77 % (1173577)Termination phase: Saturation
% 5.97/1.77 % (1173577)Time elapsed: 0.063 s
% 5.97/1.77 % (1173577)Peak memory usage: 90 MB
% 5.97/1.77 % (1173577)Instructions burned: 110 (million)
% 5.97/1.77 % (1173580)Instruction limit reached!
% 5.97/1.77 % (1173580)------------------------------
% 5.97/1.77 % (1173580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173580)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173580)Termination reason: Instruction limit
% 5.97/1.77 % (1173580)Termination phase: Saturation
% 5.97/1.77 % (1173580)Time elapsed: 0.068 s
% 5.97/1.77 % (1173580)Peak memory usage: 91 MB
% 5.97/1.77 % (1173580)Instructions burned: 130 (million)
% 5.97/1.77 % (1173578)Instruction limit reached!
% 5.97/1.77 % (1173578)------------------------------
% 5.97/1.77 % (1173578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173578)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173578)Termination reason: Instruction limit
% 5.97/1.77 % (1173578)Termination phase: Saturation
% 5.97/1.77 % (1173578)Time elapsed: 0.085 s
% 5.97/1.77 % (1173578)Peak memory usage: 89 MB
% 5.97/1.77 % (1173578)Instructions burned: 120 (million)
% 5.97/1.77 % (1173579)Instruction limit reached!
% 5.97/1.77 % (1173579)------------------------------
% 5.97/1.77 % (1173579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173579)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173579)Termination reason: Instruction limit
% 5.97/1.77 % (1173579)Termination phase: Saturation
% 5.97/1.77 % (1173579)Time elapsed: 0.077 s
% 5.97/1.77 % (1173579)Peak memory usage: 91 MB
% 5.97/1.77 % (1173579)Instructions burned: 140 (million)
% 5.97/1.77 % (1173589)lrs+10_1_sil=8000:sp=occurrence:random_seed=858107046:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.97/1.77 % (1173590)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1336323652:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.97/1.77 % (1173591)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4276474927:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.97/1.77 % (1173592)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=3912157784:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.97/1.77 % (1173590)Instruction limit reached!
% 5.97/1.77 % (1173590)------------------------------
% 5.97/1.77 % (1173590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173590)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173590)Termination reason: Instruction limit
% 5.97/1.77 % (1173590)Termination phase: Saturation
% 5.97/1.77 % (1173590)Time elapsed: 0.087 s
% 5.97/1.77 % (1173590)Peak memory usage: 90 MB
% 5.97/1.77 % (1173590)Instructions burned: 157 (million)
% 5.97/1.77 % (1173592)Instruction limit reached!
% 5.97/1.77 % (1173592)------------------------------
% 5.97/1.77 % (1173592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173592)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173592)Termination reason: Instruction limit
% 5.97/1.77 % (1173592)Termination phase: Saturation
% 5.97/1.77 % (1173592)Time elapsed: 0.142 s
% 5.97/1.77 % (1173592)Peak memory usage: 92 MB
% 5.97/1.77 % (1173592)Instructions burned: 249 (million)
% 5.97/1.77 % (1173589)Instruction limit reached!
% 5.97/1.77 % (1173589)------------------------------
% 5.97/1.77 % (1173589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173589)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173589)Termination reason: Instruction limit
% 5.97/1.77 % (1173589)Termination phase: Saturation
% 5.97/1.77 % (1173589)Time elapsed: 0.183 s
% 5.97/1.77 % (1173589)Peak memory usage: 92 MB
% 5.97/1.77 % (1173589)Instructions burned: 285 (million)
% 5.97/1.77 % (1173591)Instruction limit reached!
% 5.97/1.77 % (1173591)------------------------------
% 5.97/1.77 % (1173591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173591)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173591)Termination reason: Instruction limit
% 5.97/1.77 % (1173591)Termination phase: Saturation
% 5.97/1.77 % (1173591)Time elapsed: 0.203 s
% 5.97/1.77 % (1173591)Peak memory usage: 92 MB
% 5.97/1.77 % (1173591)Instructions burned: 327 (million)
% 5.97/1.77 % (1173642)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=128498563:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.97/1.77 % (1173665)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2788227680:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.97/1.77 % (1173670)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1493341601:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.97/1.77 % (1173679)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=250245496:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.97/1.77 % (1173670)Instruction limit reached!
% 5.97/1.77 % (1173670)------------------------------
% 5.97/1.77 % (1173670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173670)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173670)Termination reason: Instruction limit
% 5.97/1.77 % (1173670)Termination phase: Saturation
% 5.97/1.77 % (1173670)Time elapsed: 0.059 s
% 5.97/1.77 % (1173670)Peak memory usage: 90 MB
% 5.97/1.77 % (1173670)Instructions burned: 115 (million)
% 5.97/1.77 % (1173642)Instruction limit reached!
% 5.97/1.77 % (1173642)------------------------------
% 5.97/1.77 % (1173642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173642)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173642)Termination reason: Instruction limit
% 5.97/1.77 % (1173642)Termination phase: Saturation
% 5.97/1.77 % (1173642)Time elapsed: 0.169 s
% 5.97/1.77 % (1173642)Peak memory usage: 91 MB
% 5.97/1.77 % (1173642)Instructions burned: 294 (million)
% 5.97/1.77 % (1173679)Instruction limit reached!
% 5.97/1.77 % (1173679)------------------------------
% 5.97/1.77 % (1173679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173679)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173679)Termination reason: Instruction limit
% 5.97/1.77 % (1173679)Termination phase: Saturation
% 5.97/1.77 % (1173679)Time elapsed: 0.060 s
% 5.97/1.77 % (1173679)Peak memory usage: 90 MB
% 5.97/1.77 % (1173679)Instructions burned: 128 (million)
% 5.97/1.77 % (1173576)First to succeed.
% 5.97/1.77 % (1173576)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1173553"
% 5.97/1.77 % (1173710)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1953192400:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 5.97/1.77 % (1173711)lrs+10_1_sil=8000:sp=occurrence:random_seed=2069717644:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 5.97/1.77 % (1173712)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2640025436:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 5.97/1.77 % (1173710)Instruction limit reached!
% 5.97/1.77 % (1173710)------------------------------
% 5.97/1.77 % (1173710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/1.77 % (1173710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/1.77 % (1173710)CaDiCaL version: 2.1.3
% 5.97/1.77 % (1173710)Termination reason: Instruction limit
% 5.97/1.77 % (1173710)Termination phase: Saturation
% 5.97/1.77 % (1173710)Time elapsed: 0.057 s
% 5.97/1.77 % (1173710)Peak memory usage: 90 MB
% 5.97/1.77 % (1173710)Instructions burned: 114 (million)
% 5.97/1.77 % (1173576)Refutation found. Thanks to Tanya!
% 5.97/1.77 % SZS status Theorem for theBenchmark
% 5.97/1.77 % SZS output start Proof for theBenchmark
% See solution above
% 7.26/1.96 % (1173576)------------------------------
% 7.26/1.96 % (1173576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.26/1.96 % (1173576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.26/1.96 % (1173576)CaDiCaL version: 2.1.3
% 7.26/1.96 % (1173576)Termination reason: Refutation
% 7.26/1.96 % (1173576)Time elapsed: 0.650 s
% 7.26/1.96 % (1173576)Peak memory usage: 141 MB
% 7.26/1.96 % (1173576)Instructions burned: 1879 (million)
% 7.26/1.96 % (1173576)------------------------------
% 7.26/1.96 % (1173576)------------------------------
% 7.26/1.96 % (1173553)Success in time 0.961 s
% 7.26/1.96 % Vampire exiting
%------------------------------------------------------------------------------