%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV104+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 01:08:09 PM UTC 2026
% Result : Theorem 3.00s 1.06s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 18
% Syntax : Number of formulae : 89 ( 31 unt; 10 def)
% Number of atoms : 236 ( 94 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 211 ( 64 ~; 107 |; 33 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f48,axiom,
! [X0,X1,X2] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_1) ).
fof(f49,axiom,
! [X0,X1,X2,X3,X4] :
( ( X0 != X1
& a_select2(X2,X1) = X3 )
=> a_select2(tptp_update2(X2,X0,X4),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_2) ).
fof(f53,conjecture,
( ( a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use )
=> ( a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5) = use ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_inuse_0016) ).
fof(f54,negated_conjecture,
~ ( ( a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use )
=> ( a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5) = use ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f82,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
fof(f83,axiom,
succ(succ(succ(succ(succ(n0))))) = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
fof(f84,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
fof(f85,axiom,
succ(succ(n0)) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_2) ).
fof(f86,axiom,
succ(succ(succ(n0))) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_3) ).
fof(f102,plain,
( ( use != a_select3(u_defuse,n0,n0)
| use != a_select3(u_defuse,n1,n0)
| use != a_select3(u_defuse,n2,n0)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5) )
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use ),
inference(ennf_transformation,[],[f54]) ).
fof(f103,plain,
( ( use != a_select3(u_defuse,n0,n0)
| use != a_select3(u_defuse,n1,n0)
| use != a_select3(u_defuse,n2,n0)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5) )
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use ),
inference(flattening,[],[f102]) ).
fof(f116,plain,
! [X0,X1,X2,X3,X4] :
( a_select2(tptp_update2(X2,X0,X4),X1) = X3
| X0 = X1
| a_select2(X2,X1) != X3 ),
inference(ennf_transformation,[],[f49]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4] :
( a_select2(tptp_update2(X2,X0,X4),X1) = X3
| X0 = X1
| a_select2(X2,X1) != X3 ),
inference(flattening,[],[f116]) ).
fof(f122,plain,
use = a_select3(u_defuse,n2,n0),
inference(cnf_transformation,[],[f103]) ).
fof(f123,plain,
use = a_select3(u_defuse,n1,n0),
inference(cnf_transformation,[],[f103]) ).
fof(f124,plain,
use = a_select3(u_defuse,n0,n0),
inference(cnf_transformation,[],[f103]) ).
fof(f125,plain,
( use != a_select3(u_defuse,n0,n0)
| use != a_select3(u_defuse,n1,n0)
| use != a_select3(u_defuse,n2,n0)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5) ),
inference(cnf_transformation,[],[f103]) ).
fof(f126,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f84]) ).
fof(f128,plain,
n2 = succ(succ(n0)),
inference(cnf_transformation,[],[f85]) ).
fof(f130,plain,
n3 = succ(succ(succ(n0))),
inference(cnf_transformation,[],[f86]) ).
fof(f132,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(cnf_transformation,[],[f82]) ).
fof(f134,plain,
n5 = succ(succ(succ(succ(succ(n0))))),
inference(cnf_transformation,[],[f83]) ).
fof(f139,plain,
! [X2,X3,X0,X1,X4] :
( a_select2(tptp_update2(X2,X0,X4),X1) = X3
| X0 = X1
| a_select2(X2,X1) != X3 ),
inference(cnf_transformation,[],[f117]) ).
fof(f140,plain,
! [X2,X0,X1] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(cnf_transformation,[],[f48]) ).
fof(f141,definition,
~ sP1(use),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
fof(f142,definition,
~ sP2(use),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f143,definition,
~ sP3(use),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f144,definition,
~ sP4(use),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f145,definition,
~ sP5(use),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f146,definition,
~ sP6(use),
introduced(definition,[new_symbols(definition,[sP6])],[inequality_splitting_name_introduction]) ).
fof(f147,plain,
( sP1(a_select3(u_defuse,n0,n0))
| sP2(a_select3(u_defuse,n1,n0))
| sP3(a_select3(u_defuse,n2,n0))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(inequality_splitting,[],[f125,f146,f145,f144,f143,f142,f141]) ).
fof(f148,plain,
! [X2,X0,X1,X4] :
( a_select2(X2,X1) = a_select2(tptp_update2(X2,X0,X4),X1)
| X0 = X1 ),
inference(equality_resolution,[],[f139]) ).
fof(f152,plain,
use = a_select3(u_defuse,succ(succ(n0)),n0),
inference(forward_demodulation,[],[f122,f128]) ).
fof(f153,plain,
use = a_select3(u_defuse,succ(n0),n0),
inference(forward_demodulation,[],[f123,f126]) ).
fof(f154,plain,
( sP1(use)
| sP2(a_select3(u_defuse,n1,n0))
| sP3(a_select3(u_defuse,n2,n0))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f147,f124]) ).
fof(f155,plain,
( sP2(a_select3(u_defuse,n1,n0))
| sP3(a_select3(u_defuse,n2,n0))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_subsumption_resolution,[],[f154,f141]) ).
fof(f156,plain,
( sP2(a_select3(u_defuse,succ(n0),n0))
| sP3(a_select3(u_defuse,n2,n0))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f155,f126]) ).
fof(f157,plain,
( sP2(use)
| sP3(a_select3(u_defuse,n2,n0))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f156,f153]) ).
fof(f158,plain,
( sP3(a_select3(u_defuse,n2,n0))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_subsumption_resolution,[],[f157,f142]) ).
fof(f159,plain,
( sP3(a_select3(u_defuse,succ(succ(n0)),n0))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f158,f128]) ).
fof(f160,plain,
( sP3(use)
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f159,f152]) ).
fof(f161,plain,
( sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n3))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_subsumption_resolution,[],[f160,f143]) ).
fof(f162,plain,
( sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),n4,use),n5,use),succ(succ(succ(n0)))))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f161,f130]) ).
fof(f163,plain,
( sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),n4,use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(n0)))))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f162,f134]) ).
fof(f164,plain,
( sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(n0)))))
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n4))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f163,f132]) ).
fof(f165,plain,
( sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),succ(succ(succ(succ(n0)))),use),n5,use),succ(succ(succ(succ(n0))))))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(n0)))))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f164,f132]) ).
fof(f166,plain,
( sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(succ(n0))))))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(n0)))))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f165,f134]) ).
fof(f167,plain,
( sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(succ(n0))))))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(n0)))))
| sP6(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,n3,use),n4,use),n5,use),n5)) ),
inference(forward_demodulation,[],[f166,f130]) ).
fof(f168,plain,
( sP6(use)
| sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(succ(n0))))))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(n0))))) ),
inference(forward_demodulation,[],[f167,f140]) ).
fof(f169,plain,
( sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(succ(n0))))))
| sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(n0))))) ),
inference(forward_subsumption_resolution,[],[f168,f146]) ).
fof(f171,definition,
( spl7_1
<=> sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(n0))))) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f173,plain,
( sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(n0)))))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f175,definition,
( spl7_2
<=> sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(succ(n0)))))) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f177,plain,
( sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(succ(n0))))),use),succ(succ(succ(succ(n0))))))
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f169,f175,f171]) ).
fof(f179,plain,
( sP5(a_select2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(n0))))))
| succ(succ(succ(succ(n0)))) = succ(succ(succ(succ(succ(n0)))))
| ~ spl7_2 ),
inference(superposition,[],[f177,f148]) ).
fof(f184,plain,
( sP5(use)
| succ(succ(succ(succ(n0)))) = succ(succ(succ(succ(succ(n0)))))
| ~ spl7_2 ),
inference(forward_demodulation,[],[f179,f140]) ).
fof(f203,plain,
( succ(succ(succ(succ(n0)))) = succ(succ(succ(succ(succ(n0)))))
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f184,f145]) ).
fof(f205,plain,
( sP5(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(succ(n0))))))
| ~ spl7_2 ),
inference(superposition,[],[f177,f203]) ).
fof(f207,plain,
( sP5(use)
| ~ spl7_2 ),
inference(forward_demodulation,[],[f205,f140]) ).
fof(f208,plain,
( $false
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f207,f145]) ).
fof(f209,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f208]) ).
fof(f210,plain,
( sP4(a_select2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(n0)))))
| succ(succ(succ(n0))) = succ(succ(succ(succ(succ(n0)))))
| ~ spl7_1 ),
inference(superposition,[],[f173,f148]) ).
fof(f216,definition,
( spl7_7
<=> succ(succ(succ(n0))) = succ(succ(succ(succ(succ(n0))))) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
fof(f218,plain,
( succ(succ(succ(n0))) = succ(succ(succ(succ(succ(n0)))))
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f220,definition,
( spl7_8
<=> sP4(a_select2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(n0))))) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
fof(f222,plain,
( sP4(a_select2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(n0)))))
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f223,plain,
( spl7_7
| spl7_8
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f210,f171,f220,f216]) ).
fof(f240,plain,
( sP4(a_select2(tptp_update2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(succ(n0)))),use),succ(succ(succ(n0))),use),succ(succ(succ(n0)))))
| ~ spl7_1
| ~ spl7_7 ),
inference(superposition,[],[f173,f218]) ).
fof(f242,plain,
( sP4(use)
| ~ spl7_1
| ~ spl7_7 ),
inference(forward_demodulation,[],[f240,f140]) ).
fof(f243,plain,
( $false
| ~ spl7_1
| ~ spl7_7 ),
inference(forward_subsumption_resolution,[],[f242,f144]) ).
fof(f244,plain,
( ~ spl7_1
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f243]) ).
fof(f245,plain,
( sP4(a_select2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(n0)))))
| succ(succ(succ(n0))) = succ(succ(succ(succ(n0))))
| ~ spl7_8 ),
inference(superposition,[],[f222,f148]) ).
fof(f250,plain,
( sP4(use)
| succ(succ(succ(n0))) = succ(succ(succ(succ(n0))))
| ~ spl7_8 ),
inference(forward_demodulation,[],[f245,f140]) ).
fof(f265,plain,
( succ(succ(succ(n0))) = succ(succ(succ(succ(n0))))
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f250,f144]) ).
fof(f272,plain,
( sP4(a_select2(tptp_update2(tptp_update2(xinit_defuse,succ(succ(succ(n0))),use),succ(succ(succ(n0))),use),succ(succ(succ(n0)))))
| ~ spl7_8 ),
inference(superposition,[],[f222,f265]) ).
fof(f275,plain,
( sP4(use)
| ~ spl7_8 ),
inference(forward_demodulation,[],[f272,f140]) ).
fof(f281,plain,
( $false
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f275,f144]) ).
fof(f282,plain,
~ spl7_8,
inference(avatar_contradiction_clause,[],[f281]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f178]) ).
cnf(s4,plain,
~ spl7_2,
inference(sat_conversion,[],[f209]) ).
cnf(s5,plain,
( ~ spl7_1
| spl7_7
| spl7_8 ),
inference(sat_conversion,[],[f223]) ).
cnf(s8,plain,
( ~ spl7_1
| ~ spl7_7 ),
inference(sat_conversion,[],[f244]) ).
cnf(s12,plain,
~ spl7_8,
inference(sat_conversion,[],[f282]) ).
cnf(s14,plain,
( ~ spl7_1
| spl7_7 ),
inference(rat,[],[s5,s12]) ).
cnf(s15,plain,
spl7_1,
inference(rat,[],[s1,s4]) ).
cnf(s16,plain,
~ spl7_7,
inference(rat,[],[s8,s15]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s14,s16,s15]) ).
fof(f287,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV104+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:55:35 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 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
% 3.00/1.06 % (67795)Detected formulas, will run a generic FOF schedule.
% 3.00/1.06 % (67806)dis-21_1_sil=8000:lcm=predicate:random_seed=985345242: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)
% 3.00/1.06 % (67803)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2834976041:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.00/1.06 % (67803)First to succeed.
% 3.00/1.06 % (67803)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-67795"
% 3.00/1.06 % (67800)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=3326202306:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.00/1.06 % (67802)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=4251241239:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.00/1.06 % (67801)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=2849509407:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.00/1.06 % (67806)Instruction limit reached!
% 3.00/1.06 % (67806)------------------------------
% 3.00/1.06 % (67806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.06 % (67806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.06 % (67806)CaDiCaL version: 2.1.3
% 3.00/1.06 % (67806)Termination reason: Instruction limit
% 3.00/1.06 % (67806)Termination phase: Saturation
% 3.00/1.06 % (67806)Time elapsed: 0.040 s
% 3.00/1.06 % (67806)Peak memory usage: 89 MB
% 3.00/1.06 % (67806)Instructions burned: 132 (million)
% 3.00/1.06 % (67805)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2959251120:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.00/1.06 % (67804)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1597024144:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.00/1.06 % (67804)Also succeeded, but the first one will report.
% 3.00/1.06 % (67805)Also succeeded, but the first one will report.
% 3.00/1.06 % (67812)lrs+10_1_sil=8000:sp=occurrence:random_seed=62831505:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.00/1.06 % (67812)Also succeeded, but the first one will report.
% 3.00/1.06 % (67803)Refutation found. Thanks to Tanya!
% 3.00/1.06 % SZS status Theorem for theBenchmark
% 3.00/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.25 % (67803)------------------------------
% 3.46/1.25 % (67803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.25 % (67803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.25 % (67803)CaDiCaL version: 2.1.3
% 3.46/1.25 % (67803)Termination reason: Refutation
% 3.46/1.25 % (67803)Time elapsed: 0.007 s
% 3.46/1.25 % (67803)Peak memory usage: 89 MB
% 3.46/1.25 % (67803)Instructions burned: 9 (million)
% 3.46/1.25 % (67803)------------------------------
% 3.46/1.25 % (67803)------------------------------
% 3.46/1.25 % (67795)Success in time 0.406 s
% 3.46/1.25 % Vampire exiting
%------------------------------------------------------------------------------