%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW256+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 : n026.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 8.37s 1.83s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 60 ( 31 unt; 2 def)
% Number of atoms : 122 ( 72 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 116 ( 54 ~; 46 |; 6 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 77 ( 0 sgn 73 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I2_J) ).
fof(f3,axiom,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I1_J) ).
fof(f43,axiom,
! [X0,X1,X2] :
( class_Rings_Oring__1__no__zero__divisors(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(f65,axiom,
! [X0,X1,X2] :
( class_Rings_Oring__no__zero__divisors(X2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X1 = c_Groups_Ozero__class_Ozero(X2)
| X0 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(f211,axiom,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f212,axiom,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(f310,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(f461,axiom,
! [X0,X1,X2] :
( class_Power_Opower(X2)
=> ( ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = c_Groups_Oone__class_Oone(X2) )
& ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(f1187,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(f1189,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(f1217,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(f1284,conjecture,
? [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1285,negated_conjecture,
~ ? [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(negated_conjecture,[status(cth)],[f1284]) ).
fof(f1314,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f1315,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(flattening,[],[f1314]) ).
fof(f1333,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X1 = c_Groups_Ozero__class_Ozero(X2)
| X0 = c_Groups_Ozero__class_Ozero(X2) ) )
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(ennf_transformation,[],[f65]) ).
fof(f1772,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = c_Groups_Oone__class_Oone(X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) )
| ~ class_Power_Opower(X2) ),
inference(ennf_transformation,[],[f461]) ).
fof(f2445,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(ennf_transformation,[],[f1285]) ).
fof(f2465,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| ( c_Groups_Ozero__class_Ozero(X2) != X1
& c_Groups_Ozero__class_Ozero(X2) != X0 ) )
& ( X1 = c_Groups_Ozero__class_Ozero(X2)
| X0 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) ) )
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(nnf_transformation,[],[f1333]) ).
fof(f2466,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| ( c_Groups_Ozero__class_Ozero(X2) != X1
& c_Groups_Ozero__class_Ozero(X2) != X0 ) )
& ( X1 = c_Groups_Ozero__class_Ozero(X2)
| X0 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) ) )
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(flattening,[],[f2465]) ).
fof(f2801,plain,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f2]) ).
fof(f2802,plain,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f3]) ).
fof(f2856,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(cnf_transformation,[],[f1315]) ).
fof(f2882,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(cnf_transformation,[],[f2466]) ).
fof(f3074,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f211]) ).
fof(f3075,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f212]) ).
fof(f3218,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f310]) ).
fof(f3450,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ class_Power_Opower(X2) ),
inference(cnf_transformation,[],[f1772]) ).
fof(f4386,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1187]) ).
fof(f4388,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1189]) ).
fof(f4416,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1217]) ).
fof(f4483,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(cnf_transformation,[],[f2445]) ).
fof(f4533,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definition_unfolding,[],[f3075,f3074]) ).
fof(f4631,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(definition_unfolding,[],[f4483,f3074,f3074]) ).
fof(f4648,plain,
! [X2,X0] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),X0)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(equality_resolution,[],[f2882]) ).
fof(f4844,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(forward_demodulation,[],[f4631,f4533]) ).
fof(f4845,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(forward_demodulation,[],[f4844,f3218]) ).
fof(f4847,definition,
( spl40_1
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
introduced(definition,[new_symbols(definition,[spl40_1])],[avatar_definition]) ).
fof(f4848,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ spl40_1 ),
inference(avatar_component_clause,[],[f4847]) ).
fof(f4849,plain,
spl40_1,
inference(avatar_split_clause,[],[f4845,f4847]) ).
fof(f5263,plain,
( ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)
| v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(tc_Complex_Ocomplex) )
| ~ spl40_1 ),
inference(superposition,[],[f3450,f4848]) ).
fof(f5533,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) )
| ~ spl40_1 ),
inference(superposition,[],[f4648,f4848]) ).
fof(f5613,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ spl40_1 ),
inference(forward_subsumption_resolution,[],[f5533,f4388]) ).
fof(f5723,plain,
( ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)
| ~ class_Power_Opower(tc_Complex_Ocomplex) )
| ~ spl40_1 ),
inference(forward_subsumption_resolution,[],[f5263,f2801]) ).
fof(f6026,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)
| ~ spl40_1 ),
inference(forward_subsumption_resolution,[],[f5723,f4416]) ).
fof(f6190,plain,
( ! [X1] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)
| ~ spl40_1 ),
inference(forward_demodulation,[],[f6026,f5613]) ).
fof(f6224,definition,
( spl40_2
<=> ! [X1] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____) ),
introduced(definition,[new_symbols(definition,[spl40_2])],[avatar_definition]) ).
fof(f6225,plain,
( ! [X1] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)
| ~ spl40_2 ),
inference(avatar_component_clause,[],[f6224]) ).
fof(f6226,plain,
( spl40_2
| ~ spl40_1 ),
inference(avatar_split_clause,[],[f6190,f4847,f6224]) ).
fof(f6238,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) )
| ~ spl40_2 ),
inference(superposition,[],[f2856,f6225]) ).
fof(f6338,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) )
| ~ spl40_2 ),
inference(trivial_inequality_removal,[],[f6238]) ).
fof(f6385,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| ~ spl40_2 ),
inference(forward_subsumption_resolution,[],[f6338,f4386]) ).
fof(f6420,plain,
( $false
| ~ spl40_2 ),
inference(backward_subsumption_resolution,[],[f2802,f6385]) ).
fof(f6425,plain,
~ spl40_2,
inference(avatar_contradiction_clause,[],[f6420]) ).
cnf(s1,plain,
spl40_1,
inference(sat_conversion,[],[f4849]) ).
cnf(s2,plain,
( ~ spl40_1
| spl40_2 ),
inference(sat_conversion,[],[f6226]) ).
cnf(s7,plain,
~ spl40_2,
inference(sat_conversion,[],[f6425]) ).
cnf(s8,plain,
~ spl40_1,
inference(rat,[],[s2,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8]) ).
fof(f6441,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW256+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 % Computer : n026.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8046.5625MB
% 0.09/0.26 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Mon Sep 28 13:27:57 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.30 Running first-order theorem proving
% 0.26/0.30 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
% 8.37/1.83 % (3847881)Detected formulas, will run a generic FOF schedule.
% 8.37/1.83 % (3847892)dis-21_1_sil=8000:lcm=predicate:random_seed=1652381869: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)
% 8.37/1.83 % (3847892)Instruction limit reached!
% 8.37/1.83 % (3847892)------------------------------
% 8.37/1.83 % (3847892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847892)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847892)Termination reason: Instruction limit
% 8.37/1.83 % (3847892)Termination phase: Saturation
% 8.37/1.83 % (3847892)Time elapsed: 0.037 s
% 8.37/1.83 % (3847892)Peak memory usage: 91 MB
% 8.37/1.83 % (3847892)Instructions burned: 130 (million)
% 8.37/1.83 % (3847888)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=1839673145:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.37/1.83 % (3847887)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=3652349026:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.37/1.83 % (3847890)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1952629178:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.37/1.83 % (3847886)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=1840338993:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.37/1.83 % (3847889)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3095825004:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.37/1.83 % (3847891)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2666885951:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.37/1.83 % (3847889)Refutation not found, incomplete strategy
% 8.37/1.83 % (3847889)------------------------------
% 8.37/1.83 % (3847889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847889)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847889)Termination reason: Refutation not found, incomplete strategy
% 8.37/1.83 % (3847889)Time elapsed: 0.019 s
% 8.37/1.83 % (3847889)Peak memory usage: 90 MB
% 8.37/1.83 % (3847889)Instructions burned: 33 (million)
% 8.37/1.83 % (3847890)Instruction limit reached!
% 8.37/1.83 % (3847890)------------------------------
% 8.37/1.83 % (3847890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847890)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847890)Termination reason: Instruction limit
% 8.37/1.83 % (3847890)Termination phase: Saturation
% 8.37/1.83 % (3847890)Time elapsed: 0.070 s
% 8.37/1.83 % (3847890)Peak memory usage: 89 MB
% 8.37/1.83 % (3847890)Instructions burned: 119 (million)
% 8.37/1.83 % (3847891)Instruction limit reached!
% 8.37/1.83 % (3847891)------------------------------
% 8.37/1.83 % (3847891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847891)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847891)Termination reason: Instruction limit
% 8.37/1.83 % (3847891)Termination phase: Saturation
% 8.37/1.83 % (3847891)Time elapsed: 0.077 s
% 8.37/1.83 % (3847891)Peak memory usage: 91 MB
% 8.37/1.83 % (3847891)Instructions burned: 139 (million)
% 8.37/1.83 % (3847900)lrs+10_1_sil=8000:sp=occurrence:random_seed=1083871372:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.37/1.83 % (3847900)Instruction limit reached!
% 8.37/1.83 % (3847900)------------------------------
% 8.37/1.83 % (3847900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847900)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847900)Termination reason: Instruction limit
% 8.37/1.83 % (3847900)Termination phase: Saturation
% 8.37/1.83 % (3847900)Time elapsed: 0.101 s
% 8.37/1.83 % (3847900)Peak memory usage: 92 MB
% 8.37/1.83 % (3847900)Instructions burned: 287 (million)
% 8.37/1.83 % (3847901)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3371982210:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.37/1.83 % (3847902)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1371418650:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.37/1.83 % (3847889)------------------------------
% 8.37/1.83 % (3847889)------------------------------
% 8.37/1.83 % (3847904)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=904304662:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 8.37/1.83 % (3847901)Instruction limit reached!
% 8.37/1.83 % (3847901)------------------------------
% 8.37/1.83 % (3847901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847901)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847901)Termination reason: Instruction limit
% 8.37/1.83 % (3847901)Termination phase: Saturation
% 8.37/1.83 % (3847901)Time elapsed: 0.094 s
% 8.37/1.83 % (3847901)Peak memory usage: 91 MB
% 8.37/1.83 % (3847901)Instructions burned: 158 (million)
% 8.37/1.83 % (3847904)Instruction limit reached!
% 8.37/1.83 % (3847904)------------------------------
% 8.37/1.83 % (3847904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847904)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847904)Termination reason: Instruction limit
% 8.37/1.83 % (3847904)Termination phase: Saturation
% 8.37/1.83 % (3847904)Time elapsed: 0.077 s
% 8.37/1.83 % (3847904)Peak memory usage: 92 MB
% 8.37/1.83 % (3847904)Instructions burned: 248 (million)
% 8.37/1.83 % (3847907)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=550601728:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.37/1.83 % (3847902)Instruction limit reached!
% 8.37/1.83 % (3847902)------------------------------
% 8.37/1.83 % (3847902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847902)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847902)Termination reason: Instruction limit
% 8.37/1.83 % (3847902)Termination phase: Saturation
% 8.37/1.83 % (3847902)Time elapsed: 0.207 s
% 8.37/1.83 % (3847902)Peak memory usage: 92 MB
% 8.37/1.83 % (3847902)Instructions burned: 326 (million)
% 8.37/1.83 % (3847909)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3697603042:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 8.37/1.83 % (3847910)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1778161387:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.37/1.83 % (3847910)Instruction limit reached!
% 8.37/1.83 % (3847910)------------------------------
% 8.37/1.83 % (3847910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847910)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847910)Termination reason: Instruction limit
% 8.37/1.83 % (3847910)Termination phase: Saturation
% 8.37/1.83 % (3847910)Time elapsed: 0.031 s
% 8.37/1.83 % (3847910)Peak memory usage: 90 MB
% 8.37/1.83 % (3847910)Instructions burned: 114 (million)
% 8.37/1.83 % (3847913)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1008536546:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.37/1.83 % (3847915)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4146983581:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 8.37/1.83 % (3847907)Instruction limit reached!
% 8.37/1.83 % (3847907)------------------------------
% 8.37/1.83 % (3847907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847907)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847907)Termination reason: Instruction limit
% 8.37/1.83 % (3847907)Termination phase: Saturation
% 8.37/1.83 % (3847907)Time elapsed: 0.164 s
% 8.37/1.83 % (3847907)Peak memory usage: 92 MB
% 8.37/1.83 % (3847907)Instructions burned: 294 (million)
% 8.37/1.83 % (3847915)Instruction limit reached!
% 8.37/1.83 % (3847915)------------------------------
% 8.37/1.83 % (3847915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847915)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847915)Termination reason: Instruction limit
% 8.37/1.83 % (3847915)Termination phase: Saturation
% 8.37/1.83 % (3847915)Time elapsed: 0.032 s
% 8.37/1.83 % (3847915)Peak memory usage: 90 MB
% 8.37/1.83 % (3847915)Instructions burned: 117 (million)
% 8.37/1.83 % (3847913)Refutation not found, incomplete strategy
% 8.37/1.83 % (3847913)------------------------------
% 8.37/1.83 % (3847913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847913)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847913)Termination reason: Refutation not found, incomplete strategy
% 8.37/1.83 % (3847913)Time elapsed: 0.060 s
% 8.37/1.83 % (3847913)Peak memory usage: 90 MB
% 8.37/1.83 % (3847913)Instructions burned: 120 (million)
% 8.37/1.83 % (3847919)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3329080570:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 8.37/1.83 % (3847918)lrs+10_1_sil=8000:sp=occurrence:random_seed=995536837:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.37/1.83 % (3847919)Instruction limit reached!
% 8.37/1.83 % (3847919)------------------------------
% 8.37/1.83 % (3847919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847919)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847919)Termination reason: Instruction limit
% 8.37/1.83 % (3847919)Termination phase: Saturation
% 8.37/1.83 % (3847919)Time elapsed: 0.127 s
% 8.37/1.83 % (3847919)Peak memory usage: 94 MB
% 8.37/1.83 % (3847919)Instructions burned: 439 (million)
% 8.37/1.83 % (3847913)------------------------------
% 8.37/1.83 % (3847913)------------------------------
% 8.37/1.83 % (3847888)First to succeed.
% 8.37/1.83 % (3847888)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3847881"
% 8.37/1.83 % (3847922)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3126029669:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 8.37/1.83 % (3847923)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2159427760:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 8.37/1.83 % (3847923)Instruction limit reached!
% 8.37/1.83 % (3847923)------------------------------
% 8.37/1.83 % (3847923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/1.83 % (3847923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/1.83 % (3847923)CaDiCaL version: 2.1.3
% 8.37/1.83 % (3847923)Termination reason: Instruction limit
% 8.37/1.83 % (3847923)Termination phase: Saturation
% 8.37/1.83 % (3847923)Time elapsed: 0.070 s
% 8.37/1.83 % (3847923)Peak memory usage: 92 MB
% 8.37/1.83 % (3847923)Instructions burned: 135 (million)
% 8.37/1.83 % (3847888)Refutation found. Thanks to Tanya!
% 8.37/1.83 % SZS status Theorem for theBenchmark
% 8.37/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/2.03 % (3847888)------------------------------
% 0.27/2.03 % (3847888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.03 % (3847888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.03 % (3847888)CaDiCaL version: 2.1.3
% 0.27/2.03 % (3847888)Termination reason: Refutation
% 0.27/2.03 % (3847888)Time elapsed: 0.903 s
% 0.27/2.03 % (3847888)Peak memory usage: 148 MB
% 0.27/2.03 % (3847888)Instructions burned: 1410 (million)
% 0.27/2.03 % (3847888)------------------------------
% 0.27/2.03 % (3847888)------------------------------
% 0.27/2.03 % (3847881)Success in time 1.341 s
% 0.27/2.03 % Vampire exiting
%------------------------------------------------------------------------------