%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV174+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 01:08:18 PM UTC 2026
% Result : Theorem 0.67s 1.02s
% Output : Refutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of formulae : 194 ( 23 unt; 13 def)
% Number of atoms : 647 ( 110 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 800 ( 347 ~; 364 |; 59 &)
% ( 13 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 13 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-3 aty)
% Number of variables : 104 ( 0 sgn 98 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( ( gt(X0,X1)
& gt(X1,X2) )
=> gt(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_gt) ).
fof(f4,axiom,
! [X0] : leq(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_leq) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X0,X1)
& leq(X1,X2) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
fof(f9,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& X0 != X1 )
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f53,conjecture,
( ( leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,pred(pv10)) )
=> ! [X1] :
( ( leq(n0,X1)
& leq(X1,n4) )
=> a_select3(q_init,X0,X1) = init ) )
& ! [X2] :
( ( leq(n0,X2)
& leq(X2,n4) )
=> a_select3(center_init,X2,n0) = init ) )
=> ! [X3,X4] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n135299)
& leq(X4,n4) )
=> ( gt(pv10,X3)
=> a_select3(q_init,X3,X4) = init ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0046) ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,pred(pv10)) )
=> ! [X1] :
( ( leq(n0,X1)
& leq(X1,n4) )
=> a_select3(q_init,X0,X1) = init ) )
& ! [X2] :
( ( leq(n0,X2)
& leq(X2,n4) )
=> a_select3(center_init,X2,n0) = init ) )
=> ! [X3,X4] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n135299)
& leq(X4,n4) )
=> ( gt(pv10,X3)
=> a_select3(q_init,X3,X4) = init ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f83,axiom,
! [X0] :
( ( leq(n0,X0)
& leq(X0,n4) )
=> ( X0 = n0
| X0 = n1
| X0 = n2
| X0 = n3
| X0 = n4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_4) ).
fof(f89,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
fof(f94,plain,
( ? [X3,X4] :
( init != a_select3(q_init,X3,X4)
& gt(pv10,X3)
& leq(n0,X3)
& leq(n0,X4)
& leq(X3,n135299)
& leq(X4,n4) )
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( ! [X1] :
( a_select3(q_init,X0,X1) = init
| ~ leq(n0,X1)
| ~ leq(X1,n4) )
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
& ! [X2] :
( a_select3(center_init,X2,n0) = init
| ~ leq(n0,X2)
| ~ leq(X2,n4) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ? [X3,X4] :
( init != a_select3(q_init,X3,X4)
& gt(pv10,X3)
& leq(n0,X3)
& leq(n0,X4)
& leq(X3,n135299)
& leq(X4,n4) )
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X0] :
( ! [X1] :
( a_select3(q_init,X0,X1) = init
| ~ leq(n0,X1)
| ~ leq(X1,n4) )
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
& ! [X2] :
( a_select3(center_init,X2,n0) = init
| ~ leq(n0,X2)
| ~ leq(X2,n4) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( gt(X0,X2)
| ~ gt(X0,X1)
| ~ gt(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f97,plain,
! [X0,X1,X2] :
( gt(X0,X2)
| ~ gt(X0,X1)
| ~ gt(X1,X2) ),
inference(flattening,[],[f96]) ).
fof(f100,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f101,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f103,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f104,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0] :
( X0 = n0
| X0 = n1
| X0 = n2
| X0 = n3
| X0 = n4
| ~ leq(n0,X0)
| ~ leq(X0,n4) ),
inference(ennf_transformation,[],[f83]) ).
fof(f106,plain,
! [X0] :
( X0 = n0
| X0 = n1
| X0 = n2
| X0 = n3
| X0 = n4
| ~ leq(n0,X0)
| ~ leq(X0,n4) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
( ? [X0,X1] :
( a_select3(q_init,X0,X1) != init
& gt(pv10,X0)
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,n135299)
& leq(X1,n4) )
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X2] :
( ! [X3] :
( init = a_select3(q_init,X2,X3)
| ~ leq(n0,X3)
| ~ leq(X3,n4) )
| ~ leq(n0,X2)
| ~ leq(X2,pred(pv10)) )
& ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(n0,X4)
| ~ leq(X4,n4) ) ),
inference(rectify,[],[f95]) ).
fof(f108,plain,
( init != a_select3(q_init,sK0,sK1)
& gt(pv10,sK0)
& leq(n0,sK0)
& leq(n0,sK1)
& leq(sK0,n135299)
& leq(sK1,n4)
& leq(n0,pv10)
& leq(pv10,n135299)
& ! [X2] :
( ! [X3] :
( init = a_select3(q_init,X2,X3)
| ~ leq(n0,X3)
| ~ leq(X3,n4) )
| ~ leq(n0,X2)
| ~ leq(X2,pred(pv10)) )
& ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(n0,X4)
| ~ leq(X4,n4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f110,plain,
! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(n0,X4)
| ~ leq(X4,n4) ),
inference(cnf_transformation,[],[f108]) ).
fof(f111,plain,
! [X2,X3] :
( init = a_select3(q_init,X2,X3)
| ~ leq(n0,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X2)
| ~ leq(X2,pred(pv10)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f114,plain,
leq(sK1,n4),
inference(cnf_transformation,[],[f108]) ).
fof(f116,plain,
leq(n0,sK1),
inference(cnf_transformation,[],[f108]) ).
fof(f117,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f118,plain,
gt(pv10,sK0),
inference(cnf_transformation,[],[f108]) ).
fof(f119,plain,
init != a_select3(q_init,sK0,sK1),
inference(cnf_transformation,[],[f108]) ).
fof(f123,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f128,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| gt(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f129,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f131,plain,
! [X0] : leq(X0,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f132,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(cnf_transformation,[],[f89]) ).
fof(f133,plain,
! [X0] :
( ~ leq(n0,X0)
| n1 = X0
| n2 = X0
| n3 = X0
| n4 = X0
| n0 = X0
| ~ leq(X0,n4) ),
inference(cnf_transformation,[],[f106]) ).
fof(f145,definition,
~ sP2(init),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f146,plain,
sP2(a_select3(q_init,sK0,sK1)),
inference(inequality_splitting,[],[f119,f145]) ).
fof(f147,plain,
! [X4] :
( ~ leq(X4,succ(succ(succ(succ(n0)))))
| init = a_select3(center_init,X4,n0)
| ~ leq(n0,X4) ),
inference(forward_demodulation,[],[f110,f132]) ).
fof(f148,plain,
! [X2,X3] :
( ~ leq(X3,succ(succ(succ(succ(n0)))))
| init = a_select3(q_init,X2,X3)
| ~ leq(n0,X3)
| ~ leq(n0,X2)
| ~ leq(X2,pred(pv10)) ),
inference(forward_demodulation,[],[f111,f132]) ).
fof(f149,plain,
leq(sK1,succ(succ(succ(succ(n0))))),
inference(forward_demodulation,[],[f114,f132]) ).
fof(f213,plain,
( n1 = sK1
| n2 = sK1
| n3 = sK1
| n4 = sK1
| n0 = sK1
| ~ leq(sK1,n4) ),
inference(resolution,[],[f116,f133]) ).
fof(f216,plain,
( gt(sK1,n0)
| n0 = sK1 ),
inference(resolution,[],[f116,f128]) ).
fof(f218,definition,
( spl3_13
<=> n0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f220,plain,
( n0 = sK1
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f222,definition,
( spl3_14
<=> gt(sK1,n0) ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f224,plain,
( gt(sK1,n0)
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,plain,
( spl3_13
| spl3_14 ),
inference(avatar_split_clause,[],[f216,f222,f218]) ).
fof(f231,plain,
( succ(succ(succ(succ(n0)))) = sK1
| n1 = sK1
| n2 = sK1
| n3 = sK1
| n0 = sK1
| ~ leq(sK1,n4) ),
inference(forward_demodulation,[],[f213,f132]) ).
fof(f232,plain,
( ~ leq(sK1,succ(succ(succ(succ(n0)))))
| succ(succ(succ(succ(n0)))) = sK1
| n1 = sK1
| n2 = sK1
| n3 = sK1
| n0 = sK1 ),
inference(forward_demodulation,[],[f231,f132]) ).
fof(f233,plain,
( succ(succ(succ(succ(n0)))) = sK1
| n1 = sK1
| n2 = sK1
| n3 = sK1
| n0 = sK1 ),
inference(forward_subsumption_resolution,[],[f232,f149]) ).
fof(f235,definition,
( spl3_16
<=> n3 = sK1 ),
introduced(definition,[new_symbols(definition,[spl3_16])],[avatar_definition]) ).
fof(f237,plain,
( n3 = sK1
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f239,definition,
( spl3_17
<=> n2 = sK1 ),
introduced(definition,[new_symbols(definition,[spl3_17])],[avatar_definition]) ).
fof(f241,plain,
( n2 = sK1
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f243,definition,
( spl3_18
<=> n1 = sK1 ),
introduced(definition,[new_symbols(definition,[spl3_18])],[avatar_definition]) ).
fof(f245,plain,
( n1 = sK1
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f247,definition,
( spl3_19
<=> succ(succ(succ(succ(n0)))) = sK1 ),
introduced(definition,[new_symbols(definition,[spl3_19])],[avatar_definition]) ).
fof(f248,plain,
( succ(succ(succ(succ(n0)))) != sK1
| spl3_19 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f249,plain,
( succ(succ(succ(succ(n0)))) = sK1
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f250,plain,
( spl3_13
| spl3_16
| spl3_17
| spl3_18
| spl3_19 ),
inference(avatar_split_clause,[],[f233,f247,f243,f239,f235,f218]) ).
fof(f347,plain,
! [X0] :
( ~ leq(X0,sK1)
| leq(X0,succ(succ(succ(succ(n0))))) ),
inference(resolution,[],[f149,f130]) ).
fof(f348,plain,
( gt(succ(succ(succ(succ(n0)))),sK1)
| succ(succ(succ(succ(n0)))) = sK1 ),
inference(resolution,[],[f149,f128]) ).
fof(f353,definition,
( spl3_35
<=> gt(succ(succ(succ(succ(n0)))),n0) ),
introduced(definition,[new_symbols(definition,[spl3_35])],[avatar_definition]) ).
fof(f354,plain,
( ~ gt(succ(succ(succ(succ(n0)))),n0)
| spl3_35 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f355,plain,
( gt(succ(succ(succ(succ(n0)))),n0)
| ~ spl3_35 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f361,plain,
( gt(succ(succ(succ(succ(n0)))),n3)
| succ(succ(succ(succ(n0)))) = sK1
| ~ spl3_16 ),
inference(forward_demodulation,[],[f348,f237]) ).
fof(f363,plain,
( n3 = succ(succ(succ(succ(n0))))
| gt(succ(succ(succ(succ(n0)))),n3)
| ~ spl3_16 ),
inference(forward_demodulation,[],[f361,f237]) ).
fof(f365,definition,
( spl3_37
<=> gt(succ(succ(succ(succ(n0)))),n3) ),
introduced(definition,[new_symbols(definition,[spl3_37])],[avatar_definition]) ).
fof(f367,plain,
( gt(succ(succ(succ(succ(n0)))),n3)
| ~ spl3_37 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f369,definition,
( spl3_38
<=> n3 = succ(succ(succ(succ(n0)))) ),
introduced(definition,[new_symbols(definition,[spl3_38])],[avatar_definition]) ).
fof(f372,plain,
( spl3_37
| spl3_38
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f363,f235,f369,f365]) ).
fof(f398,plain,
( init = a_select3(center_init,succ(succ(succ(succ(n0)))),n0)
| ~ leq(n0,succ(succ(succ(succ(n0))))) ),
inference(resolution,[],[f147,f131]) ).
fof(f399,plain,
( init = a_select3(center_init,sK1,n0)
| ~ leq(n0,sK1) ),
inference(resolution,[],[f147,f149]) ).
fof(f400,plain,
init = a_select3(center_init,sK1,n0),
inference(forward_subsumption_resolution,[],[f399,f116]) ).
fof(f402,definition,
( spl3_43
<=> leq(n0,succ(succ(succ(succ(n0))))) ),
introduced(definition,[new_symbols(definition,[spl3_43])],[avatar_definition]) ).
fof(f403,plain,
( leq(n0,succ(succ(succ(succ(n0)))))
| ~ spl3_43 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f404,plain,
( ~ leq(n0,succ(succ(succ(succ(n0)))))
| spl3_43 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f406,definition,
( spl3_44
<=> init = a_select3(center_init,succ(succ(succ(succ(n0)))),n0) ),
introduced(definition,[new_symbols(definition,[spl3_44])],[avatar_definition]) ).
fof(f408,plain,
( init = a_select3(center_init,succ(succ(succ(succ(n0)))),n0)
| ~ spl3_44 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f409,plain,
( ~ spl3_43
| spl3_44 ),
inference(avatar_split_clause,[],[f398,f406,f402]) ).
fof(f410,plain,
( init = a_select3(center_init,succ(succ(succ(succ(n0)))),n0)
| ~ spl3_19 ),
inference(forward_demodulation,[],[f400,f249]) ).
fof(f411,plain,
( spl3_44
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f410,f247,f406]) ).
fof(f420,plain,
! [X0] :
( init = a_select3(q_init,X0,sK1)
| ~ leq(n0,sK1)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) ),
inference(resolution,[],[f148,f149]) ).
fof(f421,plain,
! [X0] :
( init = a_select3(q_init,X0,sK1)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) ),
inference(forward_subsumption_resolution,[],[f420,f116]) ).
fof(f427,plain,
( leq(n0,succ(succ(succ(succ(n0)))))
| ~ spl3_13 ),
inference(superposition,[],[f149,f220]) ).
fof(f431,plain,
( $false
| ~ spl3_13
| spl3_43 ),
inference(forward_subsumption_resolution,[],[f427,f404]) ).
fof(f432,plain,
( ~ spl3_13
| spl3_43 ),
inference(avatar_contradiction_clause,[],[f431]) ).
fof(f433,plain,
( n3 != succ(succ(succ(succ(n0))))
| ~ spl3_16
| spl3_19 ),
inference(forward_demodulation,[],[f248,f237]) ).
fof(f438,plain,
( ~ spl3_38
| ~ spl3_16
| spl3_19 ),
inference(avatar_split_clause,[],[f433,f247,f235,f369]) ).
fof(f441,plain,
( ! [X0] :
( ~ gt(X0,sK1)
| gt(X0,n0) )
| ~ spl3_14 ),
inference(resolution,[],[f224,f125]) ).
fof(f442,plain,
( ! [X0] :
( ~ gt(X0,n3)
| gt(X0,n0) )
| ~ spl3_14
| ~ spl3_16 ),
inference(forward_demodulation,[],[f441,f237]) ).
fof(f484,plain,
( leq(n0,succ(succ(succ(succ(n0)))))
| ~ spl3_35 ),
inference(resolution,[],[f355,f129]) ).
fof(f495,plain,
( gt(succ(succ(succ(succ(n0)))),n0)
| ~ spl3_14
| ~ spl3_16
| ~ spl3_37 ),
inference(resolution,[],[f367,f442]) ).
fof(f498,plain,
( $false
| ~ spl3_14
| ~ spl3_16
| spl3_35
| ~ spl3_37 ),
inference(forward_subsumption_resolution,[],[f495,f354]) ).
fof(f499,plain,
( ~ spl3_14
| ~ spl3_16
| spl3_35
| ~ spl3_37 ),
inference(avatar_contradiction_clause,[],[f498]) ).
fof(f502,plain,
( ! [X0] :
( leq(X0,succ(succ(succ(succ(n0)))))
| ~ leq(X0,n2) )
| ~ spl3_17 ),
inference(forward_demodulation,[],[f347,f241]) ).
fof(f509,plain,
( leq(n0,n2)
| ~ spl3_17 ),
inference(superposition,[],[f116,f241]) ).
fof(f531,plain,
( ~ leq(n0,n2)
| ~ spl3_17
| spl3_43 ),
inference(resolution,[],[f502,f404]) ).
fof(f537,plain,
( $false
| ~ spl3_17
| spl3_43 ),
inference(forward_subsumption_resolution,[],[f531,f509]) ).
fof(f538,plain,
( ~ spl3_17
| spl3_43 ),
inference(avatar_contradiction_clause,[],[f537]) ).
fof(f544,plain,
( ! [X0] :
( leq(X0,succ(succ(succ(succ(n0)))))
| ~ leq(X0,n1) )
| ~ spl3_18 ),
inference(forward_demodulation,[],[f347,f245]) ).
fof(f551,plain,
( leq(n0,n1)
| ~ spl3_18 ),
inference(superposition,[],[f116,f245]) ).
fof(f573,plain,
( ~ leq(n0,n1)
| ~ spl3_18
| spl3_43 ),
inference(resolution,[],[f544,f404]) ).
fof(f579,plain,
( $false
| ~ spl3_18
| spl3_43 ),
inference(forward_subsumption_resolution,[],[f573,f551]) ).
fof(f580,plain,
( ~ spl3_18
| spl3_43 ),
inference(avatar_contradiction_clause,[],[f579]) ).
fof(f584,plain,
( spl3_43
| ~ spl3_35 ),
inference(avatar_split_clause,[],[f484,f353,f402]) ).
fof(f590,plain,
( ! [X0] :
( init = a_select3(q_init,X0,n0)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_13 ),
inference(forward_demodulation,[],[f421,f220]) ).
fof(f594,plain,
( ! [X0] :
( a_select3(center_init,succ(succ(succ(succ(n0)))),n0) = a_select3(q_init,X0,n0)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_13
| ~ spl3_44 ),
inference(forward_demodulation,[],[f590,f408]) ).
fof(f596,plain,
( sP2(a_select3(q_init,sK0,n0))
| ~ spl3_13 ),
inference(superposition,[],[f146,f220]) ).
fof(f623,plain,
( ~ sP2(a_select3(center_init,succ(succ(succ(succ(n0)))),n0))
| ~ spl3_44 ),
inference(superposition,[],[f145,f408]) ).
fof(f667,plain,
( sP2(a_select3(center_init,succ(succ(succ(succ(n0)))),n0))
| ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10))
| ~ spl3_13
| ~ spl3_44 ),
inference(superposition,[],[f596,f594]) ).
fof(f668,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10))
| ~ spl3_13
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f667,f623]) ).
fof(f669,plain,
( ~ leq(sK0,pred(pv10))
| ~ spl3_13
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f668,f117]) ).
fof(f670,plain,
( ~ gt(pv10,sK0)
| ~ spl3_13
| ~ spl3_44 ),
inference(resolution,[],[f669,f123]) ).
fof(f671,plain,
( $false
| ~ spl3_13
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f670,f118]) ).
fof(f672,plain,
( ~ spl3_13
| ~ spl3_44 ),
inference(avatar_contradiction_clause,[],[f671]) ).
fof(f676,plain,
( ! [X0] :
( init = a_select3(q_init,X0,succ(succ(succ(succ(n0)))))
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_19 ),
inference(forward_demodulation,[],[f421,f249]) ).
fof(f697,plain,
( sP2(a_select3(q_init,sK0,succ(succ(succ(succ(n0))))))
| ~ spl3_19 ),
inference(superposition,[],[f146,f249]) ).
fof(f745,definition,
( spl3_47
<=> leq(sK0,pred(pv10)) ),
introduced(definition,[new_symbols(definition,[spl3_47])],[avatar_definition]) ).
fof(f746,plain,
( leq(sK0,pred(pv10))
| ~ spl3_47 ),
inference(avatar_component_clause,[],[f745]) ).
fof(f747,plain,
( ~ leq(sK0,pred(pv10))
| spl3_47 ),
inference(avatar_component_clause,[],[f745]) ).
fof(f766,plain,
( ~ gt(pv10,sK0)
| spl3_47 ),
inference(resolution,[],[f747,f123]) ).
fof(f767,plain,
( $false
| spl3_47 ),
inference(forward_subsumption_resolution,[],[f766,f118]) ).
fof(f768,plain,
spl3_47,
inference(avatar_contradiction_clause,[],[f767]) ).
fof(f874,plain,
( ! [X0] :
( a_select3(center_init,succ(succ(succ(succ(n0)))),n0) = a_select3(q_init,X0,succ(succ(succ(succ(n0)))))
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_19
| ~ spl3_44 ),
inference(forward_demodulation,[],[f676,f408]) ).
fof(f968,plain,
( init = a_select3(center_init,n0,n0)
| ~ leq(n0,n0)
| ~ spl3_43 ),
inference(resolution,[],[f403,f147]) ).
fof(f973,plain,
( init = a_select3(center_init,n0,n0)
| ~ spl3_43 ),
inference(forward_subsumption_resolution,[],[f968,f131]) ).
fof(f1085,plain,
( a_select3(center_init,succ(succ(succ(succ(n0)))),n0) = a_select3(center_init,n0,n0)
| ~ spl3_43
| ~ spl3_44 ),
inference(superposition,[],[f408,f973]) ).
fof(f1086,plain,
( ~ sP2(a_select3(center_init,n0,n0))
| ~ spl3_43 ),
inference(superposition,[],[f145,f973]) ).
fof(f1304,plain,
( sP2(a_select3(center_init,succ(succ(succ(succ(n0)))),n0))
| ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10))
| ~ spl3_19
| ~ spl3_44 ),
inference(superposition,[],[f697,f874]) ).
fof(f1305,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10))
| ~ spl3_19
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f1304,f623]) ).
fof(f1306,plain,
( ~ leq(sK0,pred(pv10))
| ~ spl3_19
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f1305,f117]) ).
fof(f1307,plain,
( $false
| ~ spl3_19
| ~ spl3_44
| ~ spl3_47 ),
inference(forward_subsumption_resolution,[],[f1306,f746]) ).
fof(f1308,plain,
( ~ spl3_19
| ~ spl3_44
| ~ spl3_47 ),
inference(avatar_contradiction_clause,[],[f1307]) ).
fof(f1319,plain,
( ! [X0] :
( init = a_select3(q_init,X0,n3)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_16 ),
inference(forward_demodulation,[],[f421,f237]) ).
fof(f1323,plain,
( ! [X0] :
( a_select3(center_init,succ(succ(succ(succ(n0)))),n0) = a_select3(q_init,X0,n3)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_16
| ~ spl3_44 ),
inference(forward_demodulation,[],[f1319,f408]) ).
fof(f1324,plain,
( ! [X0] :
( a_select3(center_init,n0,n0) = a_select3(q_init,X0,n3)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_16
| ~ spl3_43
| ~ spl3_44 ),
inference(forward_demodulation,[],[f1323,f1085]) ).
fof(f1330,plain,
( sP2(a_select3(q_init,sK0,n3))
| ~ spl3_16 ),
inference(superposition,[],[f146,f237]) ).
fof(f1352,plain,
( sP2(a_select3(center_init,n0,n0))
| ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10))
| ~ spl3_16
| ~ spl3_43
| ~ spl3_44 ),
inference(superposition,[],[f1330,f1324]) ).
fof(f1355,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10))
| ~ spl3_16
| ~ spl3_43
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f1352,f1086]) ).
fof(f1357,plain,
( ~ leq(sK0,pred(pv10))
| ~ spl3_16
| ~ spl3_43
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f1355,f117]) ).
fof(f1360,plain,
( $false
| ~ spl3_16
| ~ spl3_43
| ~ spl3_44
| ~ spl3_47 ),
inference(forward_subsumption_resolution,[],[f1357,f746]) ).
fof(f1361,plain,
( ~ spl3_16
| ~ spl3_43
| ~ spl3_44
| ~ spl3_47 ),
inference(avatar_contradiction_clause,[],[f1360]) ).
fof(f1368,plain,
( ! [X0] :
( init = a_select3(q_init,X0,n1)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_18 ),
inference(forward_demodulation,[],[f421,f245]) ).
fof(f1370,plain,
( ! [X0] :
( a_select3(center_init,succ(succ(succ(succ(n0)))),n0) = a_select3(q_init,X0,n1)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_18
| ~ spl3_44 ),
inference(forward_demodulation,[],[f1368,f408]) ).
fof(f1371,plain,
( ! [X0] :
( a_select3(center_init,n0,n0) = a_select3(q_init,X0,n1)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_18
| ~ spl3_43
| ~ spl3_44 ),
inference(forward_demodulation,[],[f1370,f1085]) ).
fof(f1376,plain,
( sP2(a_select3(q_init,sK0,n1))
| ~ spl3_18 ),
inference(superposition,[],[f146,f245]) ).
fof(f1390,plain,
( sP2(a_select3(center_init,n0,n0))
| ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10))
| ~ spl3_18
| ~ spl3_43
| ~ spl3_44 ),
inference(superposition,[],[f1376,f1371]) ).
fof(f1391,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10))
| ~ spl3_18
| ~ spl3_43
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f1390,f1086]) ).
fof(f1392,plain,
( ~ leq(sK0,pred(pv10))
| ~ spl3_18
| ~ spl3_43
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f1391,f117]) ).
fof(f1393,plain,
( $false
| ~ spl3_18
| ~ spl3_43
| ~ spl3_44
| ~ spl3_47 ),
inference(forward_subsumption_resolution,[],[f1392,f746]) ).
fof(f1394,plain,
( ~ spl3_18
| ~ spl3_43
| ~ spl3_44
| ~ spl3_47 ),
inference(avatar_contradiction_clause,[],[f1393]) ).
fof(f1402,plain,
( ! [X0] :
( init = a_select3(q_init,X0,n2)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_17 ),
inference(forward_demodulation,[],[f421,f241]) ).
fof(f1404,plain,
( ! [X0] :
( a_select3(center_init,succ(succ(succ(succ(n0)))),n0) = a_select3(q_init,X0,n2)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_17
| ~ spl3_44 ),
inference(forward_demodulation,[],[f1402,f408]) ).
fof(f1405,plain,
( ! [X0] :
( a_select3(center_init,n0,n0) = a_select3(q_init,X0,n2)
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv10)) )
| ~ spl3_17
| ~ spl3_43
| ~ spl3_44 ),
inference(forward_demodulation,[],[f1404,f1085]) ).
fof(f1411,plain,
( sP2(a_select3(q_init,sK0,n2))
| ~ spl3_17 ),
inference(superposition,[],[f146,f241]) ).
fof(f1433,plain,
( sP2(a_select3(center_init,n0,n0))
| ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10))
| ~ spl3_17
| ~ spl3_43
| ~ spl3_44 ),
inference(superposition,[],[f1411,f1405]) ).
fof(f1434,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,pred(pv10))
| ~ spl3_17
| ~ spl3_43
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f1433,f1086]) ).
fof(f1435,plain,
( ~ leq(sK0,pred(pv10))
| ~ spl3_17
| ~ spl3_43
| ~ spl3_44 ),
inference(forward_subsumption_resolution,[],[f1434,f117]) ).
fof(f1436,plain,
( $false
| ~ spl3_17
| ~ spl3_43
| ~ spl3_44
| ~ spl3_47 ),
inference(forward_subsumption_resolution,[],[f1435,f746]) ).
fof(f1437,plain,
( ~ spl3_17
| ~ spl3_43
| ~ spl3_44
| ~ spl3_47 ),
inference(avatar_contradiction_clause,[],[f1436]) ).
cnf(s6,plain,
( spl3_13
| spl3_14 ),
inference(sat_conversion,[],[f225]) ).
cnf(s8,plain,
( spl3_13
| spl3_16
| spl3_17
| spl3_18
| spl3_19 ),
inference(sat_conversion,[],[f250]) ).
cnf(s17,plain,
( ~ spl3_16
| spl3_37
| spl3_38 ),
inference(sat_conversion,[],[f372]) ).
cnf(s20,plain,
( ~ spl3_43
| spl3_44 ),
inference(sat_conversion,[],[f409]) ).
cnf(s21,plain,
( ~ spl3_19
| spl3_44 ),
inference(sat_conversion,[],[f411]) ).
cnf(s23,plain,
( ~ spl3_13
| spl3_43 ),
inference(sat_conversion,[],[f432]) ).
cnf(s24,plain,
( ~ spl3_16
| spl3_19
| ~ spl3_38 ),
inference(sat_conversion,[],[f438]) ).
cnf(s27,plain,
( ~ spl3_14
| ~ spl3_16
| spl3_35
| ~ spl3_37 ),
inference(sat_conversion,[],[f499]) ).
cnf(s29,plain,
( ~ spl3_17
| spl3_43 ),
inference(sat_conversion,[],[f538]) ).
cnf(s31,plain,
( ~ spl3_18
| spl3_43 ),
inference(sat_conversion,[],[f580]) ).
cnf(s32,plain,
( ~ spl3_35
| spl3_43 ),
inference(sat_conversion,[],[f584]) ).
cnf(s37,plain,
( ~ spl3_13
| ~ spl3_44 ),
inference(sat_conversion,[],[f672]) ).
cnf(s43,plain,
spl3_47,
inference(sat_conversion,[],[f768]) ).
cnf(s81,plain,
( ~ spl3_19
| ~ spl3_44
| ~ spl3_47 ),
inference(sat_conversion,[],[f1308]) ).
cnf(s87,plain,
( ~ spl3_16
| ~ spl3_43
| ~ spl3_44
| ~ spl3_47 ),
inference(sat_conversion,[],[f1361]) ).
cnf(s89,plain,
( ~ spl3_18
| ~ spl3_43
| ~ spl3_44
| ~ spl3_47 ),
inference(sat_conversion,[],[f1394]) ).
cnf(s91,plain,
( ~ spl3_17
| ~ spl3_43
| ~ spl3_44
| ~ spl3_47 ),
inference(sat_conversion,[],[f1437]) ).
cnf(s93,plain,
~ spl3_19,
inference(rat,[],[s21,s81,s43]) ).
cnf(s94,plain,
( ~ spl3_43
| ~ spl3_18 ),
inference(rat,[],[s20,s89,s43]) ).
cnf(s95,plain,
~ spl3_18,
inference(rat,[],[s94,s31]) ).
cnf(s96,plain,
( ~ spl3_43
| ~ spl3_17 ),
inference(rat,[],[s20,s91,s43]) ).
cnf(s97,plain,
~ spl3_17,
inference(rat,[],[s96,s29]) ).
cnf(s98,plain,
( ~ spl3_43
| ~ spl3_16 ),
inference(rat,[],[s20,s87,s43]) ).
cnf(s99,plain,
( ~ spl3_37
| ~ spl3_16
| ~ spl3_14 ),
inference(rat,[],[s98,s32,s27]) ).
cnf(s100,plain,
spl3_13,
inference(rat,[],[s99,s17,s24,s8,s6,s93,s97,s95]) ).
cnf(s101,plain,
~ spl3_44,
inference(rat,[],[s37,s100]) ).
cnf(s104,plain,
spl3_43,
inference(rat,[],[s23,s100]) ).
cnf(s107,plain,
$false,
inference(rat,[],[s20,s101,s104]) ).
fof(f1438,plain,
$false,
inference(avatar_sat_refutation,[],[s107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV174+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n005.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 10:07:48 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running first-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.67/1.02 % (686817)Detected formulas, will run a generic FOF schedule.
% 0.67/1.02 % (686825)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1950002917:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.67/1.02 % (686825)First to succeed.
% 0.67/1.02 % (686825)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-686817"
% 0.67/1.02 % (686828)dis-21_1_sil=8000:lcm=predicate:random_seed=2482390799: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)
% 0.67/1.02 % (686822)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=3953534340:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.67/1.02 % (686824)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=1364095274:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.67/1.02 % (686826)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3823330333:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.67/1.02 % (686823)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=3371112307:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.67/1.02 % (686827)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4026065070:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.67/1.02 % (686826)Also succeeded, but the first one will report.
% 0.67/1.02 % (686828)Also succeeded, but the first one will report.
% 0.67/1.02 % (686827)Instruction limit reached!
% 0.67/1.02 % (686827)------------------------------
% 0.67/1.02 % (686827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.67/1.02 % (686827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/1.02 % (686827)CaDiCaL version: 2.1.3
% 0.67/1.02 % (686827)Termination reason: Instruction limit
% 0.67/1.02 % (686827)Termination phase: Saturation
% 0.67/1.02 % (686827)Time elapsed: 0.110 s
% 0.67/1.02 % (686827)Peak memory usage: 90 MB
% 0.67/1.02 % (686827)Instructions burned: 139 (million)
% 0.67/1.02 % (686825)Refutation found. Thanks to Tanya!
% 0.67/1.02 % SZS status Theorem for theBenchmark
% 0.67/1.02 % SZS output start Proof for theBenchmark
% See solution above
% 2.96/1.15 % (686825)------------------------------
% 2.96/1.15 % (686825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.15 % (686825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.15 % (686825)CaDiCaL version: 2.1.3
% 2.96/1.15 % (686825)Termination reason: Refutation
% 2.96/1.15 % (686825)Time elapsed: 0.018 s
% 2.96/1.15 % (686825)Peak memory usage: 90 MB
% 2.96/1.15 % (686825)Instructions burned: 43 (million)
% 2.96/1.15 % (686825)------------------------------
% 2.96/1.15 % (686825)------------------------------
% 2.96/1.15 % (686817)Success in time 0.333 s
% 2.96/1.15 % Vampire exiting
%------------------------------------------------------------------------------