%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV102+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 01:08:08 PM UTC 2026
% Result : Theorem 2.87s 0.97s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 27
% Syntax : Number of formulae : 139 ( 57 unt; 19 def)
% Number of atoms : 604 ( 180 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 565 ( 100 ~; 383 |; 75 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',sel2_update_2) ).
fof(f53,conjecture,
( ( a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use )
=> ( a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2) = use ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0014) ).
fof(f54,negated_conjecture,
~ ( ( a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use )
=> ( a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1) = use
& a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2) = use ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f82,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
fof(f83,axiom,
succ(succ(succ(succ(succ(n0))))) = n5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
fof(f84,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(f85,axiom,
succ(succ(n0)) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
fof(f86,axiom,
succ(succ(succ(n0))) = n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
fof(f102,plain,
( ( use != a_select2(sigma_defuse,n0)
| use != a_select2(sigma_defuse,n1)
| use != a_select2(sigma_defuse,n2)
| use != a_select2(sigma_defuse,n3)
| use != a_select2(sigma_defuse,n4)
| use != a_select2(sigma_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(xinit_defuse,n3)
| use != a_select2(xinit_defuse,n4)
| use != a_select2(xinit_defuse,n5)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2) )
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(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_select2(sigma_defuse,n0)
| use != a_select2(sigma_defuse,n1)
| use != a_select2(sigma_defuse,n2)
| use != a_select2(sigma_defuse,n3)
| use != a_select2(sigma_defuse,n4)
| use != a_select2(sigma_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(xinit_defuse,n3)
| use != a_select2(xinit_defuse,n4)
| use != a_select2(xinit_defuse,n5)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2) )
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_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(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(f119,plain,
use = a_select2(xinit_defuse,n5),
inference(cnf_transformation,[],[f103]) ).
fof(f120,plain,
use = a_select2(xinit_defuse,n4),
inference(cnf_transformation,[],[f103]) ).
fof(f121,plain,
use = a_select2(xinit_defuse,n3),
inference(cnf_transformation,[],[f103]) ).
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_select2(sigma_defuse,n5),
inference(cnf_transformation,[],[f103]) ).
fof(f126,plain,
use = a_select2(sigma_defuse,n4),
inference(cnf_transformation,[],[f103]) ).
fof(f127,plain,
use = a_select2(sigma_defuse,n3),
inference(cnf_transformation,[],[f103]) ).
fof(f128,plain,
use = a_select2(sigma_defuse,n2),
inference(cnf_transformation,[],[f103]) ).
fof(f129,plain,
use = a_select2(sigma_defuse,n1),
inference(cnf_transformation,[],[f103]) ).
fof(f130,plain,
use = a_select2(sigma_defuse,n0),
inference(cnf_transformation,[],[f103]) ).
fof(f131,plain,
( use != a_select2(sigma_defuse,n0)
| use != a_select2(sigma_defuse,n1)
| use != a_select2(sigma_defuse,n2)
| use != a_select2(sigma_defuse,n3)
| use != a_select2(sigma_defuse,n4)
| use != a_select2(sigma_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(xinit_defuse,n3)
| use != a_select2(xinit_defuse,n4)
| use != a_select2(xinit_defuse,n5)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1)
| use != a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f132,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f84]) ).
fof(f134,plain,
n2 = succ(succ(n0)),
inference(cnf_transformation,[],[f85]) ).
fof(f136,plain,
n3 = succ(succ(succ(n0))),
inference(cnf_transformation,[],[f86]) ).
fof(f138,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(cnf_transformation,[],[f82]) ).
fof(f140,plain,
n5 = succ(succ(succ(succ(succ(n0))))),
inference(cnf_transformation,[],[f83]) ).
fof(f145,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(f146,plain,
! [X2,X0,X1] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(cnf_transformation,[],[f48]) ).
fof(f147,definition,
~ sP1(use),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
fof(f148,definition,
~ sP2(use),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f149,definition,
~ sP3(use),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f150,definition,
~ sP4(use),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f151,definition,
~ sP5(use),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f152,definition,
~ sP6(use),
introduced(definition,[new_symbols(definition,[sP6])],[inequality_splitting_name_introduction]) ).
fof(f153,definition,
~ sP7(use),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
fof(f154,definition,
~ sP8(use),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
fof(f155,definition,
~ sP9(use),
introduced(definition,[new_symbols(definition,[sP9])],[inequality_splitting_name_introduction]) ).
fof(f156,definition,
~ sP10(use),
introduced(definition,[new_symbols(definition,[sP10])],[inequality_splitting_name_introduction]) ).
fof(f157,definition,
~ sP11(use),
introduced(definition,[new_symbols(definition,[sP11])],[inequality_splitting_name_introduction]) ).
fof(f158,definition,
~ sP12(use),
introduced(definition,[new_symbols(definition,[sP12])],[inequality_splitting_name_introduction]) ).
fof(f159,definition,
~ sP13(use),
introduced(definition,[new_symbols(definition,[sP13])],[inequality_splitting_name_introduction]) ).
fof(f160,definition,
~ sP14(use),
introduced(definition,[new_symbols(definition,[sP14])],[inequality_splitting_name_introduction]) ).
fof(f161,definition,
~ sP15(use),
introduced(definition,[new_symbols(definition,[sP15])],[inequality_splitting_name_introduction]) ).
fof(f162,plain,
( sP1(a_select2(sigma_defuse,n0))
| sP2(a_select2(sigma_defuse,n1))
| sP3(a_select2(sigma_defuse,n2))
| sP4(a_select2(sigma_defuse,n3))
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(inequality_splitting,[],[f131,f161,f160,f159,f158,f157,f156,f155,f154,f153,f152,f151,f150,f149,f148,f147]) ).
fof(f163,plain,
! [X2,X0,X1,X4] :
( a_select2(X2,X1) = a_select2(tptp_update2(X2,X0,X4),X1)
| X0 = X1 ),
inference(equality_resolution,[],[f145]) ).
fof(f164,plain,
use = a_select2(xinit_defuse,succ(succ(succ(succ(succ(n0)))))),
inference(forward_demodulation,[],[f119,f140]) ).
fof(f165,plain,
use = a_select2(xinit_defuse,succ(succ(succ(succ(n0))))),
inference(forward_demodulation,[],[f120,f138]) ).
fof(f166,plain,
use = a_select2(xinit_defuse,succ(succ(succ(n0)))),
inference(forward_demodulation,[],[f121,f136]) ).
fof(f167,plain,
use = a_select3(u_defuse,succ(succ(n0)),n0),
inference(forward_demodulation,[],[f122,f134]) ).
fof(f168,plain,
use = a_select3(u_defuse,succ(n0),n0),
inference(forward_demodulation,[],[f123,f132]) ).
fof(f169,plain,
use = a_select2(sigma_defuse,succ(succ(succ(succ(succ(n0)))))),
inference(forward_demodulation,[],[f125,f140]) ).
fof(f170,plain,
use = a_select2(sigma_defuse,succ(succ(succ(succ(n0))))),
inference(forward_demodulation,[],[f126,f138]) ).
fof(f171,plain,
use = a_select2(sigma_defuse,succ(succ(succ(n0)))),
inference(forward_demodulation,[],[f127,f136]) ).
fof(f172,plain,
use = a_select2(sigma_defuse,succ(succ(n0))),
inference(forward_demodulation,[],[f128,f134]) ).
fof(f173,plain,
use = a_select2(sigma_defuse,succ(n0)),
inference(forward_demodulation,[],[f129,f132]) ).
fof(f174,plain,
( sP1(use)
| sP2(a_select2(sigma_defuse,n1))
| sP3(a_select2(sigma_defuse,n2))
| sP4(a_select2(sigma_defuse,n3))
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f162,f130]) ).
fof(f175,plain,
( sP2(a_select2(sigma_defuse,n1))
| sP3(a_select2(sigma_defuse,n2))
| sP4(a_select2(sigma_defuse,n3))
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f174,f147]) ).
fof(f176,plain,
( sP2(a_select2(sigma_defuse,succ(n0)))
| sP3(a_select2(sigma_defuse,n2))
| sP4(a_select2(sigma_defuse,n3))
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f175,f132]) ).
fof(f177,plain,
( sP2(use)
| sP3(a_select2(sigma_defuse,n2))
| sP4(a_select2(sigma_defuse,n3))
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f176,f173]) ).
fof(f178,plain,
( sP3(a_select2(sigma_defuse,n2))
| sP4(a_select2(sigma_defuse,n3))
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f177,f148]) ).
fof(f179,plain,
( sP3(a_select2(sigma_defuse,succ(succ(n0))))
| sP4(a_select2(sigma_defuse,n3))
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f178,f134]) ).
fof(f180,plain,
( sP3(use)
| sP4(a_select2(sigma_defuse,n3))
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f179,f172]) ).
fof(f181,plain,
( sP4(a_select2(sigma_defuse,n3))
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f180,f149]) ).
fof(f182,plain,
( sP4(a_select2(sigma_defuse,succ(succ(succ(n0)))))
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f181,f136]) ).
fof(f183,plain,
( sP4(use)
| sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f182,f171]) ).
fof(f184,plain,
( sP5(a_select2(sigma_defuse,n4))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f183,f150]) ).
fof(f185,plain,
( sP5(a_select2(sigma_defuse,succ(succ(succ(succ(n0))))))
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f184,f138]) ).
fof(f186,plain,
( sP5(use)
| sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f185,f170]) ).
fof(f187,plain,
( sP6(a_select2(sigma_defuse,n5))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f186,f151]) ).
fof(f188,plain,
( sP6(a_select2(sigma_defuse,succ(succ(succ(succ(succ(n0)))))))
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f187,f140]) ).
fof(f189,plain,
( sP6(use)
| sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f188,f169]) ).
fof(f190,plain,
( sP7(a_select3(u_defuse,n0,n0))
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f189,f152]) ).
fof(f191,plain,
( sP7(use)
| sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f190,f124]) ).
fof(f192,plain,
( sP8(a_select3(u_defuse,n1,n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f191,f153]) ).
fof(f193,plain,
( sP8(a_select3(u_defuse,succ(n0),n0))
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f192,f132]) ).
fof(f194,plain,
( sP8(use)
| sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f193,f168]) ).
fof(f195,plain,
( sP9(a_select3(u_defuse,n2,n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f194,f154]) ).
fof(f196,plain,
( sP9(a_select3(u_defuse,succ(succ(n0)),n0))
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f195,f134]) ).
fof(f197,plain,
( sP9(use)
| sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f196,f167]) ).
fof(f198,plain,
( sP10(a_select2(xinit_defuse,n3))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f197,f155]) ).
fof(f199,plain,
( sP10(a_select2(xinit_defuse,succ(succ(succ(n0)))))
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f198,f136]) ).
fof(f200,plain,
( sP10(use)
| sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f199,f166]) ).
fof(f201,plain,
( sP11(a_select2(xinit_defuse,n4))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f200,f156]) ).
fof(f202,plain,
( sP11(a_select2(xinit_defuse,succ(succ(succ(succ(n0))))))
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f201,f138]) ).
fof(f203,plain,
( sP11(use)
| sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f202,f165]) ).
fof(f204,plain,
( sP12(a_select2(xinit_defuse,n5))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f203,f157]) ).
fof(f205,plain,
( sP12(a_select2(xinit_defuse,succ(succ(succ(succ(succ(n0)))))))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f204,f140]) ).
fof(f206,plain,
( sP12(use)
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f205,f164]) ).
fof(f207,plain,
( sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_subsumption_resolution,[],[f206,f158]) ).
fof(f208,plain,
( sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),succ(succ(n0)),use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f207,f134]) ).
fof(f209,plain,
( sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),n0))
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n1))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f208,f132]) ).
fof(f210,plain,
( sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),n2,use),succ(n0)))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),n0))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f209,f132]) ).
fof(f211,plain,
( sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),succ(n0)))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),n0))
| sP15(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),n1,use),n2,use),n2)) ),
inference(forward_demodulation,[],[f210,f134]) ).
fof(f212,plain,
( sP15(use)
| sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),succ(n0)))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),n0)) ),
inference(forward_demodulation,[],[f211,f146]) ).
fof(f213,plain,
( sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),succ(n0)))
| sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),n0)) ),
inference(forward_subsumption_resolution,[],[f212,f161]) ).
fof(f215,definition,
( spl16_1
<=> sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),n0)) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f217,plain,
( sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),n0))
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f219,definition,
( spl16_2
<=> sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),succ(n0))) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f221,plain,
( sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(succ(n0)),use),succ(n0)))
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f222,plain,
( spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f213,f219,f215]) ).
fof(f223,plain,
( sP14(a_select2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(n0)))
| succ(n0) = succ(succ(n0))
| ~ spl16_2 ),
inference(superposition,[],[f221,f163]) ).
fof(f228,plain,
( sP14(use)
| succ(n0) = succ(succ(n0))
| ~ spl16_2 ),
inference(forward_demodulation,[],[f223,f146]) ).
fof(f247,plain,
( succ(n0) = succ(succ(n0))
| ~ spl16_2 ),
inference(forward_subsumption_resolution,[],[f228,f160]) ).
fof(f257,plain,
( sP14(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),succ(n0),use),succ(n0)))
| ~ spl16_2 ),
inference(superposition,[],[f221,f247]) ).
fof(f258,plain,
( sP14(use)
| ~ spl16_2 ),
inference(forward_demodulation,[],[f257,f146]) ).
fof(f260,plain,
( $false
| ~ spl16_2 ),
inference(forward_subsumption_resolution,[],[f258,f160]) ).
fof(f261,plain,
~ spl16_2,
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f262,plain,
( sP13(a_select2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),n0))
| n0 = succ(succ(n0))
| ~ spl16_1 ),
inference(superposition,[],[f217,f163]) ).
fof(f268,definition,
( spl16_7
<=> n0 = succ(succ(n0)) ),
introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition]) ).
fof(f270,plain,
( n0 = succ(succ(n0))
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f272,definition,
( spl16_8
<=> sP13(a_select2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),n0)) ),
introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition]) ).
fof(f274,plain,
( sP13(a_select2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),n0))
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( spl16_7
| spl16_8
| ~ spl16_1 ),
inference(avatar_split_clause,[],[f262,f215,f272,f268]) ).
fof(f300,plain,
( sP13(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse,n0,use),succ(n0),use),n0,use),n0))
| ~ spl16_1
| ~ spl16_7 ),
inference(superposition,[],[f217,f270]) ).
fof(f303,plain,
( sP13(use)
| ~ spl16_1
| ~ spl16_7 ),
inference(forward_demodulation,[],[f300,f146]) ).
fof(f305,plain,
( $false
| ~ spl16_1
| ~ spl16_7 ),
inference(forward_subsumption_resolution,[],[f303,f159]) ).
fof(f306,plain,
( ~ spl16_1
| ~ spl16_7 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f307,plain,
( sP13(a_select2(tptp_update2(rho_defuse,n0,use),n0))
| n0 = succ(n0)
| ~ spl16_8 ),
inference(superposition,[],[f274,f163]) ).
fof(f310,plain,
( sP13(use)
| n0 = succ(n0)
| ~ spl16_8 ),
inference(forward_demodulation,[],[f307,f146]) ).
fof(f311,plain,
( n0 = succ(n0)
| ~ spl16_8 ),
inference(forward_subsumption_resolution,[],[f310,f159]) ).
fof(f326,plain,
( sP13(a_select2(tptp_update2(tptp_update2(rho_defuse,n0,use),n0,use),n0))
| ~ spl16_8 ),
inference(superposition,[],[f274,f311]) ).
fof(f329,plain,
( sP13(use)
| ~ spl16_8 ),
inference(forward_demodulation,[],[f326,f146]) ).
fof(f336,plain,
( $false
| ~ spl16_8 ),
inference(forward_subsumption_resolution,[],[f329,f159]) ).
fof(f337,plain,
~ spl16_8,
inference(avatar_contradiction_clause,[],[f336]) ).
cnf(s1,plain,
( spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f222]) ).
cnf(s4,plain,
~ spl16_2,
inference(sat_conversion,[],[f261]) ).
cnf(s5,plain,
( ~ spl16_1
| spl16_7
| spl16_8 ),
inference(sat_conversion,[],[f275]) ).
cnf(s9,plain,
( ~ spl16_1
| ~ spl16_7 ),
inference(sat_conversion,[],[f306]) ).
cnf(s11,plain,
~ spl16_8,
inference(sat_conversion,[],[f337]) ).
cnf(s13,plain,
( ~ spl16_1
| spl16_7 ),
inference(rat,[],[s5,s11]) ).
cnf(s14,plain,
spl16_1,
inference(rat,[],[s1,s4]) ).
cnf(s15,plain,
~ spl16_7,
inference(rat,[],[s9,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s13,s15,s14]) ).
fof(f343,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV102+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.14 % Computer : n012.cluster.edu
% 0.07/0.14 % Model : x86_64 x86_64
% 0.07/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.14 % Memory : 8046.5625MB
% 0.07/0.14 % OS : Linux 6.8.0-71-generic
% 0.07/0.14 % CPULimit : 300
% 0.07/0.14 % WCLimit : 300
% 0.07/0.14 % DateTime : Mon Sep 28 09:53:49 UTC 2026
% 0.07/0.15 % CPUTime :
% 0.07/0.15 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 Running first-order theorem proving
% 0.07/0.17 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
% 2.87/0.97 % (3274038)Detected formulas, will run a generic FOF schedule.
% 2.87/0.97 % (3274053)dis-21_1_sil=8000:lcm=predicate:random_seed=3909695758: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)
% 2.87/0.97 % (3274047)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=4111630466:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.87/0.97 % (3274052)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2768122522:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.87/0.97 % (3274050)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1947060498:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.87/0.97 % (3274048)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=1961176592:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.87/0.97 % (3274049)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=2837186709:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.87/0.97 % (3274051)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2808036320:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.87/0.97 % (3274050)First to succeed.
% 2.87/0.97 % (3274051)Also succeeded, but the first one will report.
% 2.87/0.97 % (3274050)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3274038"
% 2.87/0.97 % (3274052)Also succeeded, but the first one will report.
% 2.87/0.97 % (3274053)Instruction limit reached!
% 2.87/0.97 % (3274053)------------------------------
% 2.87/0.97 % (3274053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/0.97 % (3274053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/0.97 % (3274053)CaDiCaL version: 2.1.3
% 2.87/0.97 % (3274053)Termination reason: Instruction limit
% 2.87/0.97 % (3274053)Termination phase: Saturation
% 2.87/0.97 % (3274053)Time elapsed: 0.042 s
% 2.87/0.97 % (3274053)Peak memory usage: 89 MB
% 2.87/0.97 % (3274053)Instructions burned: 131 (million)
% 2.87/0.97 % (3274061)lrs+10_1_sil=8000:sp=occurrence:random_seed=1961053408:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.87/0.97 % (3274061)Also succeeded, but the first one will report.
% 2.87/0.97 % (3274050)Refutation found. Thanks to Tanya!
% 2.87/0.97 % SZS status Theorem for theBenchmark
% 2.87/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.16 % (3274050)------------------------------
% 3.69/1.16 % (3274050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.16 % (3274050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.16 % (3274050)CaDiCaL version: 2.1.3
% 3.69/1.16 % (3274050)Termination reason: Refutation
% 3.69/1.16 % (3274050)Time elapsed: 0.008 s
% 3.69/1.16 % (3274050)Peak memory usage: 89 MB
% 3.69/1.16 % (3274050)Instructions burned: 13 (million)
% 3.69/1.16 % (3274050)------------------------------
% 3.69/1.16 % (3274050)------------------------------
% 3.69/1.16 % (3274038)Success in time 0.451 s
% 3.69/1.16 % Vampire exiting
%------------------------------------------------------------------------------