%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV197+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 : n011.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 01:08:21 PM UTC 2026
% Result : Theorem 0.63s 0.92s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 25
% Syntax : Number of formulae : 137 ( 35 unt; 18 def)
% Number of atoms : 584 ( 270 equ)
% Maximal formula atoms : 51 ( 4 avg)
% Number of connectives : 641 ( 194 ~; 172 |; 249 &)
% ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 13 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 18 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
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,pred(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_0008) ).
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,pred(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,pred(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,pred(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(f100,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
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,pred(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,pred(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(f115,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
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,pred(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(f158,plain,
! [X0,X1] :
( ~ leq(X0,pred(X1))
| gt(X1,X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f160,plain,
! [X0] :
( ~ leq(n0,X0)
| n0 = X0
| ~ leq(X0,n0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f162,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
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(f298,plain,
( n0 = sK1
| ~ leq(sK1,n0) ),
inference(resolution,[],[f150,f160]) ).
fof(f302,definition,
( spl9_11
<=> n0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f304,plain,
( n0 = sK1
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f311,definition,
( spl9_13
<=> leq(sK1,n0) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
fof(f313,plain,
( ~ leq(sK1,n0)
| spl9_13 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f314,plain,
( ~ spl9_13
| spl9_11 ),
inference(avatar_split_clause,[],[f298,f302,f311]) ).
fof(f383,plain,
( n1 = sK0
| n2 = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(resolution,[],[f151,f169]) ).
fof(f389,definition,
( spl9_24
<=> n0 = sK0 ),
introduced(definition,[new_symbols(definition,[spl9_24])],[avatar_definition]) ).
fof(f391,plain,
( n0 = sK0
| ~ spl9_24 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f403,plain,
( succ(n0) = sK0
| n2 = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(forward_demodulation,[],[f383,f165]) ).
fof(f408,plain,
( succ(succ(n0)) = sK0
| succ(n0) = sK0
| n0 = sK0
| ~ leq(sK0,n2) ),
inference(forward_demodulation,[],[f403,f168]) ).
fof(f413,definition,
( spl9_27
<=> succ(n0) = sK0 ),
introduced(definition,[new_symbols(definition,[spl9_27])],[avatar_definition]) ).
fof(f415,plain,
( succ(n0) = sK0
| ~ spl9_27 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f421,plain,
( ~ leq(sK0,succ(succ(n0)))
| succ(succ(n0)) = sK0
| succ(n0) = sK0
| n0 = sK0 ),
inference(forward_demodulation,[],[f408,f168]) ).
fof(f425,plain,
( succ(succ(n0)) = sK0
| succ(n0) = sK0
| n0 = sK0 ),
inference(forward_subsumption_resolution,[],[f421,f234]) ).
fof(f430,definition,
( spl9_29
<=> succ(succ(n0)) = sK0 ),
introduced(definition,[new_symbols(definition,[spl9_29])],[avatar_definition]) ).
fof(f432,plain,
( succ(succ(n0)) = sK0
| ~ spl9_29 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f433,plain,
( spl9_24
| spl9_27
| spl9_29 ),
inference(avatar_split_clause,[],[f425,f430,f413,f389]) ).
fof(f484,plain,
gt(pv5,sK1),
inference(resolution,[],[f148,f158]) ).
fof(f505,plain,
( ~ leq(pv5,n0)
| spl9_9 ),
inference(forward_subsumption_resolution,[],[f289,f277]) ).
fof(f512,plain,
( $false
| spl9_9 ),
inference(forward_subsumption_resolution,[],[f505,f119]) ).
fof(f513,plain,
spl9_9,
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f590,plain,
( gt(n0,sK1)
| ~ spl9_9 ),
inference(forward_demodulation,[],[f484,f278]) ).
fof(f605,plain,
( ~ sP4(n0)
| ~ spl9_9 ),
inference(superposition,[],[f200,f278]) ).
fof(f606,plain,
( ~ sP6(n0)
| ~ spl9_9 ),
inference(superposition,[],[f203,f278]) ).
fof(f607,plain,
( ~ sP8(n0)
| ~ spl9_9 ),
inference(superposition,[],[f206,f278]) ).
fof(f640,plain,
( leq(sK1,n0)
| ~ spl9_9 ),
inference(resolution,[],[f590,f162]) ).
fof(f641,plain,
( $false
| ~ spl9_9
| spl9_13 ),
inference(forward_subsumption_resolution,[],[f640,f313]) ).
fof(f642,plain,
( ~ spl9_9
| spl9_13 ),
inference(avatar_contradiction_clause,[],[f641]) ).
fof(f649,plain,
( sP6(n0)
| ~ spl9_3
| ~ spl9_11 ),
inference(superposition,[],[f247,f304]) ).
fof(f650,plain,
( sP4(n0)
| ~ spl9_5
| ~ spl9_11 ),
inference(superposition,[],[f256,f304]) ).
fof(f653,plain,
( $false
| ~ spl9_5
| ~ spl9_9
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f650,f605]) ).
fof(f654,plain,
( ~ spl9_5
| ~ spl9_9
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f653]) ).
fof(f655,plain,
( $false
| ~ spl9_3
| ~ spl9_9
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f649,f606]) ).
fof(f656,plain,
( ~ spl9_3
| ~ spl9_9
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f655]) ).
fof(f769,plain,
( sP7(succ(succ(n0)))
| ~ spl9_2
| ~ spl9_29 ),
inference(superposition,[],[f242,f432]) ).
fof(f778,plain,
( $false
| ~ spl9_2
| ~ spl9_29 ),
inference(forward_subsumption_resolution,[],[f769,f209]) ).
fof(f779,plain,
( ~ spl9_2
| ~ spl9_29 ),
inference(avatar_contradiction_clause,[],[f778]) ).
fof(f788,plain,
( sP3(n0)
| ~ spl9_6
| ~ spl9_24 ),
inference(forward_demodulation,[],[f260,f391]) ).
fof(f790,plain,
( $false
| ~ spl9_6
| ~ spl9_24 ),
inference(forward_subsumption_resolution,[],[f788,f199]) ).
fof(f791,plain,
( ~ spl9_6
| ~ spl9_24 ),
inference(avatar_contradiction_clause,[],[f790]) ).
fof(f796,plain,
( sP5(succ(n0))
| ~ spl9_4
| ~ spl9_27 ),
inference(forward_demodulation,[],[f251,f415]) ).
fof(f799,plain,
( $false
| ~ spl9_4
| ~ spl9_27 ),
inference(forward_subsumption_resolution,[],[f796,f208]) ).
fof(f800,plain,
( ~ spl9_4
| ~ spl9_27 ),
inference(avatar_contradiction_clause,[],[f799]) ).
fof(f801,plain,
( sP8(n0)
| ~ spl9_1
| ~ spl9_11 ),
inference(forward_demodulation,[],[f238,f304]) ).
fof(f807,plain,
( $false
| ~ spl9_1
| ~ spl9_9
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f801,f607]) ).
fof(f808,plain,
( ~ spl9_1
| ~ spl9_9
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f807]) ).
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(s7,plain,
( spl9_11
| ~ spl9_13 ),
inference(sat_conversion,[],[f314]) ).
cnf(s16,plain,
( spl9_24
| spl9_27
| spl9_29 ),
inference(sat_conversion,[],[f433]) ).
cnf(s21,plain,
spl9_9,
inference(sat_conversion,[],[f513]) ).
cnf(s31,plain,
( ~ spl9_9
| spl9_13 ),
inference(sat_conversion,[],[f642]) ).
cnf(s32,plain,
( ~ spl9_5
| ~ spl9_9
| ~ spl9_11 ),
inference(sat_conversion,[],[f654]) ).
cnf(s33,plain,
( ~ spl9_3
| ~ spl9_9
| ~ spl9_11 ),
inference(sat_conversion,[],[f656]) ).
cnf(s43,plain,
( ~ spl9_2
| ~ spl9_29 ),
inference(sat_conversion,[],[f779]) ).
cnf(s46,plain,
( ~ spl9_6
| ~ spl9_24 ),
inference(sat_conversion,[],[f791]) ).
cnf(s48,plain,
( ~ spl9_4
| ~ spl9_27 ),
inference(sat_conversion,[],[f800]) ).
cnf(s50,plain,
( ~ spl9_1
| ~ spl9_9
| ~ spl9_11 ),
inference(sat_conversion,[],[f808]) ).
cnf(s51,plain,
spl9_13,
inference(rat,[],[s31,s21]) ).
cnf(s53,plain,
spl9_11,
inference(rat,[],[s7,s51]) ).
cnf(s54,plain,
~ spl9_1,
inference(rat,[],[s50,s21,s53]) ).
cnf(s55,plain,
~ spl9_3,
inference(rat,[],[s33,s21,s53]) ).
cnf(s56,plain,
~ spl9_5,
inference(rat,[],[s32,s21,s53]) ).
cnf(s57,plain,
spl9_6,
inference(rat,[],[s3,s56]) ).
cnf(s58,plain,
~ spl9_24,
inference(rat,[],[s46,s57]) ).
cnf(s61,plain,
spl9_4,
inference(rat,[],[s2,s55]) ).
cnf(s62,plain,
~ spl9_27,
inference(rat,[],[s48,s61]) ).
cnf(s63,plain,
spl9_29,
inference(rat,[],[s16,s58,s62]) ).
cnf(s65,plain,
~ spl9_2,
inference(rat,[],[s43,s63]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s1,s65,s54]) ).
fof(f809,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV197+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n011.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 10:08:31 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 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
% 0.63/0.92 % (3297082)Detected formulas, will run a generic FOF schedule.
% 0.63/0.92 % (3297090)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2224728152:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.63/0.92 % (3297090)First to succeed.
% 0.63/0.92 % (3297090)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3297082"
% 0.63/0.92 % (3297091)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1338858180:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.63/0.92 % (3297089)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=2311389645:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.63/0.92 % (3297092)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1955569141:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.63/0.92 % (3297088)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=74446358:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.63/0.92 % (3297087)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=954661753:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.63/0.92 % (3297091)Also succeeded, but the first one will report.
% 0.63/0.92 % (3297092)Also succeeded, but the first one will report.
% 0.63/0.92 % (3297093)dis-21_1_sil=8000:lcm=predicate:random_seed=4075513260: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)
% 0.63/0.92 % (3297093)Also succeeded, but the first one will report.
% 0.63/0.92 % (3297090)Refutation found. Thanks to Tanya!
% 0.63/0.92 % SZS status Theorem for theBenchmark
% 0.63/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.12 % (3297090)------------------------------
% 2.56/1.12 % (3297090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.12 % (3297090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.12 % (3297090)CaDiCaL version: 2.1.3
% 2.56/1.12 % (3297090)Termination reason: Refutation
% 2.56/1.12 % (3297090)Time elapsed: 0.008 s
% 2.56/1.12 % (3297090)Peak memory usage: 90 MB
% 2.56/1.12 % (3297090)Instructions burned: 22 (million)
% 2.56/1.12 % (3297090)------------------------------
% 2.56/1.12 % (3297090)------------------------------
% 2.56/1.12 % (3297082)Success in time 0.282 s
% 2.56/1.12 % Vampire exiting
%------------------------------------------------------------------------------