%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV199+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 : n014.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 01:08:22 PM UTC 2026
% Result : Theorem 3.03s 1.12s
% Output : Refutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 22
% Syntax : Number of formulae : 126 ( 33 unt; 17 def)
% Number of atoms : 562 ( 271 equ)
% Maximal formula atoms : 51 ( 4 avg)
% Number of connectives : 623 ( 187 ~; 165 |; 248 &)
% ( 11 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 12 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 18 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = 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(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n2)
& leq(X1,pred(pv5)) )
=> a_select3(u_defuse,X0,X1) = use )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,pred(pv5)) )
=> a_select3(z_defuse,X2,X3) = use ) )
=> ! [X4,X5] :
( ( leq(n0,X4)
& leq(n0,X5)
& leq(X4,n2)
& leq(X5,pv5) )
=> ( ( ~ ( n0 = X4
& pv5 = X5 )
& ~ ( n1 = X4
& pv5 = X5 )
& ~ ( n2 = X4
& pv5 = X5 ) )
=> a_select3(z_defuse,X4,X5) = use ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0010) ).
fof(f54,negated_conjecture,
~ ( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = 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(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n2)
& leq(X1,pred(pv5)) )
=> a_select3(u_defuse,X0,X1) = use )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,pred(pv5)) )
=> a_select3(z_defuse,X2,X3) = use ) )
=> ! [X4,X5] :
( ( leq(n0,X4)
& leq(n0,X5)
& leq(X4,n2)
& leq(X5,pv5) )
=> ( ( ~ ( n0 = X4
& pv5 = X5 )
& ~ ( n1 = X4
& pv5 = X5 )
& ~ ( n2 = X4
& pv5 = X5 ) )
=> a_select3(z_defuse,X4,X5) = use ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f85,axiom,
! [X0] :
( ( leq(n0,X0)
& leq(X0,n0) )
=> X0 = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f87,axiom,
! [X0] :
( ( leq(n0,X0)
& leq(X0,n2) )
=> ( X0 = n0
| X0 = n1
| X0 = n2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_2) ).
fof(f91,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(f92,axiom,
succ(succ(n0)) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
fof(f94,plain,
( ? [X4,X5] :
( use != a_select3(z_defuse,X4,X5)
& ( n0 != X4
| pv5 != X5 )
& ( n1 != X4
| pv5 != X5 )
& ( n2 != X4
| pv5 != X5 )
& leq(n0,X4)
& leq(n0,X5)
& leq(X4,n2)
& leq(X5,pv5) )
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = 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(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ! [X0,X1] :
( a_select3(u_defuse,X0,X1) = use
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n2)
| ~ leq(X1,pred(pv5)) )
& ! [X2,X3] :
( a_select3(z_defuse,X2,X3) = use
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,pred(pv5)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ? [X4,X5] :
( use != a_select3(z_defuse,X4,X5)
& ( n0 != X4
| pv5 != X5 )
& ( n1 != X4
| pv5 != X5 )
& ( n2 != X4
| pv5 != X5 )
& leq(n0,X4)
& leq(n0,X5)
& leq(X4,n2)
& leq(X5,pv5) )
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = 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(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ! [X0,X1] :
( a_select3(u_defuse,X0,X1) = use
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n2)
| ~ leq(X1,pred(pv5)) )
& ! [X2,X3] :
( a_select3(z_defuse,X2,X3) = use
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,pred(pv5)) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f97,plain,
! [X0] :
( X0 = n0
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(flattening,[],[f96]) ).
fof(f105,plain,
! [X0] :
( X0 = n0
| X0 = n1
| X0 = n2
| ~ leq(n0,X0)
| ~ leq(X0,n2) ),
inference(ennf_transformation,[],[f87]) ).
fof(f106,plain,
! [X0] :
( X0 = n0
| X0 = n1
| X0 = n2
| ~ leq(n0,X0)
| ~ leq(X0,n2) ),
inference(flattening,[],[f105]) ).
fof(f113,plain,
( ? [X0,X1] :
( use != a_select3(z_defuse,X0,X1)
& ( n0 != X0
| pv5 != X1 )
& ( n1 != X0
| pv5 != X1 )
& ( n2 != X0
| pv5 != X1 )
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,n2)
& leq(X1,pv5) )
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = 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(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ! [X2,X3] :
( use = a_select3(u_defuse,X2,X3)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,pred(pv5)) )
& ! [X4,X5] :
( use = a_select3(z_defuse,X4,X5)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n2)
| ~ leq(X5,pred(pv5)) ) ),
inference(rectify,[],[f95]) ).
fof(f114,plain,
( use != a_select3(z_defuse,sK0,sK1)
& ( n0 != sK0
| pv5 != sK1 )
& ( n1 != sK0
| pv5 != sK1 )
& ( n2 != sK0
| pv5 != sK1 )
& leq(n0,sK0)
& leq(n0,sK1)
& leq(sK0,n2)
& leq(sK1,pv5)
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = 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(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ! [X2,X3] :
( use = a_select3(u_defuse,X2,X3)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,pred(pv5)) )
& ! [X4,X5] :
( use = a_select3(z_defuse,X4,X5)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n2)
| ~ leq(X5,pred(pv5)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f113]) ).
fof(f119,plain,
leq(pv5,n0),
inference(cnf_transformation,[],[f114]) ).
fof(f120,plain,
leq(n0,pv5),
inference(cnf_transformation,[],[f114]) ).
fof(f148,plain,
leq(sK1,pv5),
inference(cnf_transformation,[],[f114]) ).
fof(f149,plain,
leq(sK0,n2),
inference(cnf_transformation,[],[f114]) ).
fof(f150,plain,
leq(n0,sK1),
inference(cnf_transformation,[],[f114]) ).
fof(f151,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f114]) ).
fof(f152,plain,
( n2 != sK0
| pv5 != sK1 ),
inference(cnf_transformation,[],[f114]) ).
fof(f153,plain,
( n1 != sK0
| pv5 != sK1 ),
inference(cnf_transformation,[],[f114]) ).
fof(f154,plain,
( n0 != sK0
| pv5 != sK1 ),
inference(cnf_transformation,[],[f114]) ).
fof(f160,plain,
! [X0] :
( ~ leq(n0,X0)
| n0 = X0
| ~ leq(X0,n0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f165,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f91]) ).
fof(f168,plain,
n2 = succ(succ(n0)),
inference(cnf_transformation,[],[f92]) ).
fof(f169,plain,
! [X0] :
( ~ leq(n0,X0)
| n1 = X0
| n2 = X0
| n0 = X0
| ~ leq(X0,n2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f199,definition,
~ sP3(n0),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f200,definition,
~ sP4(pv5),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f201,plain,
( sP3(sK0)
| sP4(sK1) ),
inference(inequality_splitting,[],[f154,f200,f199]) ).
fof(f202,definition,
~ sP5(n1),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f203,definition,
~ sP6(pv5),
introduced(definition,[new_symbols(definition,[sP6])],[inequality_splitting_name_introduction]) ).
fof(f204,plain,
( sP5(sK0)
| sP6(sK1) ),
inference(inequality_splitting,[],[f153,f203,f202]) ).
fof(f205,definition,
~ sP7(n2),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
fof(f206,definition,
~ sP8(pv5),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
fof(f207,plain,
( sP7(sK0)
| sP8(sK1) ),
inference(inequality_splitting,[],[f152,f206,f205]) ).
fof(f208,plain,
~ sP5(succ(n0)),
inference(forward_demodulation,[],[f202,f165]) ).
fof(f209,plain,
~ sP7(succ(succ(n0))),
inference(forward_demodulation,[],[f205,f168]) ).
fof(f234,plain,
leq(sK0,succ(succ(n0))),
inference(forward_demodulation,[],[f149,f168]) ).
fof(f236,definition,
( spl9_1
<=> sP8(sK1) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f238,plain,
( sP8(sK1)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f240,definition,
( spl9_2
<=> sP7(sK0) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f242,plain,
( sP7(sK0)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f243,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f207,f240,f236]) ).
fof(f245,definition,
( spl9_3
<=> sP6(sK1) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f247,plain,
( sP6(sK1)
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f249,definition,
( spl9_4
<=> sP5(sK0) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f251,plain,
( sP5(sK0)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f252,plain,
( spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f204,f249,f245]) ).
fof(f254,definition,
( spl9_5
<=> sP4(sK1) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f256,plain,
( sP4(sK1)
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,definition,
( spl9_6
<=> sP3(sK0) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
fof(f260,plain,
( sP3(sK0)
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,plain,
( spl9_5
| spl9_6 ),
inference(avatar_split_clause,[],[f201,f258,f254]) ).
fof(f276,definition,
( spl9_9
<=> n0 = pv5 ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
fof(f277,plain,
( n0 != pv5
| spl9_9 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f278,plain,
( n0 = pv5
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f289,plain,
( n0 = pv5
| ~ leq(pv5,n0) ),
inference(resolution,[],[f120,f160]) ).
fof(f303,definition,
( spl9_12
<=> n0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
fof(f304,plain,
( n0 != sK1
| spl9_12 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f305,plain,
( n0 = sK1
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f308,plain,
( ~ leq(pv5,n0)
| spl9_9 ),
inference(forward_subsumption_resolution,[],[f289,f277]) ).
fof(f323,plain,
( $false
| spl9_9 ),
inference(forward_subsumption_resolution,[],[f308,f119]) ).
fof(f324,plain,
spl9_9,
inference(avatar_contradiction_clause,[],[f323]) ).
fof(f397,plain,
( n0 = sK1
| ~ leq(sK1,n0) ),
inference(resolution,[],[f150,f160]) ).
fof(f404,plain,
( n1 = sK0
| n2 = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(resolution,[],[f151,f169]) ).
fof(f410,definition,
( spl9_25
<=> n0 = sK0 ),
introduced(definition,[new_symbols(definition,[spl9_25])],[avatar_definition]) ).
fof(f412,plain,
( n0 = sK0
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f424,plain,
( succ(n0) = sK0
| n2 = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(forward_demodulation,[],[f404,f165]) ).
fof(f429,plain,
( succ(succ(n0)) = sK0
| succ(n0) = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(forward_demodulation,[],[f424,f168]) ).
fof(f434,definition,
( spl9_28
<=> succ(n0) = sK0 ),
introduced(definition,[new_symbols(definition,[spl9_28])],[avatar_definition]) ).
fof(f436,plain,
( succ(n0) = sK0
| ~ spl9_28 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f442,plain,
( ~ leq(sK0,succ(succ(n0)))
| succ(succ(n0)) = sK0
| succ(n0) = sK0
| n0 = sK0 ),
inference(forward_demodulation,[],[f429,f168]) ).
fof(f446,plain,
( succ(succ(n0)) = sK0
| succ(n0) = sK0
| n0 = sK0 ),
inference(forward_subsumption_resolution,[],[f442,f234]) ).
fof(f451,definition,
( spl9_30
<=> succ(succ(n0)) = sK0 ),
introduced(definition,[new_symbols(definition,[spl9_30])],[avatar_definition]) ).
fof(f453,plain,
( succ(succ(n0)) = sK0
| ~ spl9_30 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f454,plain,
( spl9_25
| spl9_28
| spl9_30 ),
inference(avatar_split_clause,[],[f446,f451,f434,f410]) ).
fof(f508,plain,
( leq(sK1,n0)
| ~ spl9_9 ),
inference(superposition,[],[f148,f278]) ).
fof(f509,plain,
( ~ sP4(n0)
| ~ spl9_9 ),
inference(superposition,[],[f200,f278]) ).
fof(f510,plain,
( ~ sP6(n0)
| ~ spl9_9 ),
inference(superposition,[],[f203,f278]) ).
fof(f511,plain,
( ~ sP8(n0)
| ~ spl9_9 ),
inference(superposition,[],[f206,f278]) ).
fof(f548,plain,
( sP6(n0)
| ~ spl9_3
| ~ spl9_12 ),
inference(superposition,[],[f247,f305]) ).
fof(f549,plain,
( sP4(n0)
| ~ spl9_5
| ~ spl9_12 ),
inference(superposition,[],[f256,f305]) ).
fof(f551,plain,
( $false
| ~ spl9_5
| ~ spl9_9
| ~ spl9_12 ),
inference(forward_subsumption_resolution,[],[f549,f509]) ).
fof(f552,plain,
( ~ spl9_5
| ~ spl9_9
| ~ spl9_12 ),
inference(avatar_contradiction_clause,[],[f551]) ).
fof(f553,plain,
( $false
| ~ spl9_3
| ~ spl9_9
| ~ spl9_12 ),
inference(forward_subsumption_resolution,[],[f548,f510]) ).
fof(f554,plain,
( ~ spl9_3
| ~ spl9_9
| ~ spl9_12 ),
inference(avatar_contradiction_clause,[],[f553]) ).
fof(f559,plain,
( ~ leq(sK1,n0)
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f397,f304]) ).
fof(f565,plain,
( $false
| ~ spl9_9
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f559,f508]) ).
fof(f566,plain,
( ~ spl9_9
| spl9_12 ),
inference(avatar_contradiction_clause,[],[f565]) ).
fof(f659,plain,
( sP7(succ(succ(n0)))
| ~ spl9_2
| ~ spl9_30 ),
inference(superposition,[],[f242,f453]) ).
fof(f668,plain,
( $false
| ~ spl9_2
| ~ spl9_30 ),
inference(forward_subsumption_resolution,[],[f659,f209]) ).
fof(f669,plain,
( ~ spl9_2
| ~ spl9_30 ),
inference(avatar_contradiction_clause,[],[f668]) ).
fof(f675,plain,
( sP3(n0)
| ~ spl9_6
| ~ spl9_25 ),
inference(forward_demodulation,[],[f260,f412]) ).
fof(f678,plain,
( $false
| ~ spl9_6
| ~ spl9_25 ),
inference(forward_subsumption_resolution,[],[f675,f199]) ).
fof(f679,plain,
( ~ spl9_6
| ~ spl9_25 ),
inference(avatar_contradiction_clause,[],[f678]) ).
fof(f683,plain,
( sP5(succ(n0))
| ~ spl9_4
| ~ spl9_28 ),
inference(forward_demodulation,[],[f251,f436]) ).
fof(f687,plain,
( $false
| ~ spl9_4
| ~ spl9_28 ),
inference(forward_subsumption_resolution,[],[f683,f208]) ).
fof(f688,plain,
( ~ spl9_4
| ~ spl9_28 ),
inference(avatar_contradiction_clause,[],[f687]) ).
fof(f689,plain,
( sP8(n0)
| ~ spl9_1
| ~ spl9_12 ),
inference(forward_demodulation,[],[f238,f305]) ).
fof(f694,plain,
( $false
| ~ spl9_1
| ~ spl9_9
| ~ spl9_12 ),
inference(forward_subsumption_resolution,[],[f689,f511]) ).
fof(f695,plain,
( ~ spl9_1
| ~ spl9_9
| ~ spl9_12 ),
inference(avatar_contradiction_clause,[],[f694]) ).
cnf(s1,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f243]) ).
cnf(s2,plain,
( spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f252]) ).
cnf(s3,plain,
( spl9_5
| spl9_6 ),
inference(sat_conversion,[],[f261]) ).
cnf(s8,plain,
spl9_9,
inference(sat_conversion,[],[f324]) ).
cnf(s18,plain,
( spl9_25
| spl9_28
| spl9_30 ),
inference(sat_conversion,[],[f454]) ).
cnf(s24,plain,
( ~ spl9_5
| ~ spl9_9
| ~ spl9_12 ),
inference(sat_conversion,[],[f552]) ).
cnf(s25,plain,
( ~ spl9_3
| ~ spl9_9
| ~ spl9_12 ),
inference(sat_conversion,[],[f554]) ).
cnf(s26,plain,
( ~ spl9_9
| spl9_12 ),
inference(sat_conversion,[],[f566]) ).
cnf(s36,plain,
( ~ spl9_2
| ~ spl9_30 ),
inference(sat_conversion,[],[f669]) ).
cnf(s38,plain,
( ~ spl9_6
| ~ spl9_25 ),
inference(sat_conversion,[],[f679]) ).
cnf(s40,plain,
( ~ spl9_4
| ~ spl9_28 ),
inference(sat_conversion,[],[f688]) ).
cnf(s42,plain,
( ~ spl9_1
| ~ spl9_9
| ~ spl9_12 ),
inference(sat_conversion,[],[f695]) ).
cnf(s43,plain,
spl9_12,
inference(rat,[],[s26,s8]) ).
cnf(s44,plain,
~ spl9_3,
inference(rat,[],[s25,s43,s8]) ).
cnf(s45,plain,
~ spl9_5,
inference(rat,[],[s24,s43,s8]) ).
cnf(s47,plain,
~ spl9_1,
inference(rat,[],[s42,s8,s43]) ).
cnf(s48,plain,
spl9_6,
inference(rat,[],[s3,s45]) ).
cnf(s49,plain,
~ spl9_25,
inference(rat,[],[s38,s48]) ).
cnf(s52,plain,
spl9_4,
inference(rat,[],[s2,s44]) ).
cnf(s53,plain,
~ spl9_28,
inference(rat,[],[s40,s52]) ).
cnf(s54,plain,
spl9_30,
inference(rat,[],[s18,s49,s53]) ).
cnf(s56,plain,
~ spl9_2,
inference(rat,[],[s36,s54]) ).
cnf(s60,plain,
$false,
inference(rat,[],[s1,s56,s47]) ).
fof(f696,plain,
$false,
inference(avatar_sat_refutation,[],[s60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV199+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.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 10:08:45 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.23 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
% 3.03/1.12 % (1684275)Detected formulas, will run a generic FOF schedule.
% 3.03/1.12 % (1684281)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=2943095709:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.03/1.12 % (1684285)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2902556399:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.03/1.12 % (1684284)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=829718230:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.03/1.12 % (1684282)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=4109583467:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.03/1.12 % (1684286)dis-21_1_sil=8000:lcm=predicate:random_seed=787391568: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)
% 3.03/1.12 % (1684280)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=2218393694:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.03/1.12 % (1684283)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1571122540:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.03/1.12 % (1684283)First to succeed.
% 3.03/1.12 % (1684284)Also succeeded, but the first one will report.
% 3.03/1.12 % (1684283)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1684275"
% 3.03/1.12 % (1684285)Also succeeded, but the first one will report.
% 3.03/1.12 % (1684286)Instruction limit reached!
% 3.03/1.12 % (1684286)------------------------------
% 3.03/1.12 % (1684286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.12 % (1684286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.12 % (1684286)CaDiCaL version: 2.1.3
% 3.03/1.12 % (1684286)Termination reason: Instruction limit
% 3.03/1.12 % (1684286)Termination phase: Saturation
% 3.03/1.12 % (1684286)Time elapsed: 0.068 s
% 3.03/1.12 % (1684286)Peak memory usage: 88 MB
% 3.03/1.12 % (1684286)Instructions burned: 130 (million)
% 3.03/1.12 % (1684294)lrs+10_1_sil=8000:sp=occurrence:random_seed=3133979947:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.03/1.12 % (1684294)Also succeeded, but the first one will report.
% 3.03/1.12 % (1684283)Refutation found. Thanks to Tanya!
% 3.03/1.12 % SZS status Theorem for theBenchmark
% 3.03/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 3.74/1.21 % (1684283)------------------------------
% 3.74/1.21 % (1684283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.21 % (1684283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.21 % (1684283)CaDiCaL version: 2.1.3
% 3.74/1.21 % (1684283)Termination reason: Refutation
% 3.74/1.21 % (1684283)Time elapsed: 0.012 s
% 3.74/1.21 % (1684283)Peak memory usage: 89 MB
% 3.74/1.21 % (1684283)Instructions burned: 18 (million)
% 3.74/1.21 % (1684283)------------------------------
% 3.74/1.21 % (1684283)------------------------------
% 3.74/1.21 % (1684275)Success in time 0.455 s
% 3.74/1.21 % Vampire exiting
%------------------------------------------------------------------------------