%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL470+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 11:52:33 AM UTC 2026
% Result : Theorem 16.65s 3.45s
% Output : Refutation 17.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 17
% Syntax : Number of formulae : 114 ( 38 unt; 3 def)
% Number of atoms : 232 ( 9 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 225 ( 107 ~; 99 |; 2 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 213 ( 0 sgn 211 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2) ).
fof(f19,axiom,
( cn1
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn1) ).
fof(f20,axiom,
( cn2
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn2) ).
fof(f21,axiom,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_modus_ponens) ).
fof(f36,axiom,
cn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn1) ).
fof(f37,axiom,
cn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn2) ).
fof(f38,axiom,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f43,conjecture,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f44,negated_conjecture,
~ or_2,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ or_2,
inference(flattening,[],[f44]) ).
fof(f46,plain,
( cn3
=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f47,plain,
( cn2
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f48,plain,
( cn1
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
=> or_2 ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f51,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f55,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f51]) ).
fof(f56,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f55]) ).
fof(f58,plain,
( or_2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f59,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(ennf_transformation,[],[f48]) ).
fof(f60,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(ennf_transformation,[],[f47]) ).
fof(f61,plain,
( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(ennf_transformation,[],[f46]) ).
fof(f62,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f63,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
( or_2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f58]) ).
fof(f66,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f56]) ).
fof(f68,plain,
( or_2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f69,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(cnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
! [X0] :
( is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(cnf_transformation,[],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f78,plain,
cn1,
inference(cnf_transformation,[],[f36]) ).
fof(f79,plain,
cn2,
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
cn3,
inference(cnf_transformation,[],[f38]) ).
fof(f82,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f85,plain,
~ or_2,
inference(cnf_transformation,[],[f45]) ).
fof(f87,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f73,f83]) ).
fof(f88,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f72,f82]) ).
fof(f89,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(forward_subsumption_resolution,[],[f71,f80]) ).
fof(f90,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(forward_subsumption_resolution,[],[f70,f79]) ).
fof(f91,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(forward_subsumption_resolution,[],[f69,f78]) ).
fof(f92,plain,
~ is_a_theorem(implies(sK1,or(sK0,sK1))),
inference(forward_subsumption_resolution,[],[f68,f85]) ).
fof(f94,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f66,f77]) ).
fof(f95,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f88,f87]) ).
fof(f96,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(superposition,[],[f90,f95]) ).
fof(f104,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,not(X0)),implies(or(X0,X1),implies(X2,X1)))),
inference(superposition,[],[f91,f95]) ).
fof(f105,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X0),X2),implies(implies(X2,X1),or(X0,X1)))),
inference(superposition,[],[f91,f95]) ).
fof(f106,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X2),implies(implies(X2,X1),or(X0,X1)))),
inference(forward_demodulation,[],[f105,f95]) ).
fof(f109,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(superposition,[],[f89,f95]) ).
fof(f112,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f94,f91]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f112,f94]) ).
fof(f123,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,or(X1,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f118,f96]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X2,X3),implies(X1,X3))))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f118,f91]) ).
fof(f125,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| is_a_theorem(implies(X0,implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(resolution,[],[f118,f112]) ).
fof(f127,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f118,f109]) ).
fof(f134,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f127,f96]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X2,X3),or(X1,X3))))
| ~ is_a_theorem(implies(X0,or(X1,X2))) ),
inference(resolution,[],[f106,f118]) ).
fof(f178,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(implies(X0,not(X1)),implies(X2,implies(X0,X3))))
| ~ is_a_theorem(implies(X2,or(X1,X3))) ),
inference(resolution,[],[f104,f125]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(or(X2,X3),implies(X1,X3))))
| ~ is_a_theorem(implies(X0,implies(X1,not(X2)))) ),
inference(resolution,[],[f104,f118]) ).
fof(f209,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(X2,X3),or(X1,X3))) ),
inference(resolution,[],[f155,f94]) ).
fof(f265,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,not(X2))))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(or(X2,X3),implies(X1,X3))) ),
inference(resolution,[],[f179,f94]) ).
fof(f532,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(or(X1,X2),implies(not(X0),X2))) ),
inference(resolution,[],[f265,f90]) ).
fof(f547,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X1,X2),or(X0,X2)))
| ~ is_a_theorem(X0) ),
inference(forward_demodulation,[],[f532,f95]) ).
fof(f548,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X1,X0),X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f547,f127]) ).
fof(f560,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,or(X2,X0)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f548,f118]) ).
fof(f576,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f560,f96]) ).
fof(f627,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X3,X0))
| is_a_theorem(implies(X2,implies(X3,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f576,f125]) ).
fof(f730,plain,
! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(implies(X2,X4),or(X1,X4)),X3))
| is_a_theorem(implies(X0,implies(or(X1,X2),X3))) ),
inference(resolution,[],[f627,f106]) ).
fof(f1082,definition,
( spl2_3
<=> ! [X3] : ~ is_a_theorem(X3) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f1083,plain,
( ! [X3] : ~ is_a_theorem(X3)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f1243,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(or(X1,X2),X3)))
| ~ is_a_theorem(X3) ),
inference(resolution,[],[f730,f576]) ).
fof(f1262,plain,
! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(X2,or(X3,X4)))
| is_a_theorem(implies(X1,implies(X2,X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f1243,f125]) ).
fof(f1299,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f1083,f134]) ).
fof(f1350,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f1299]) ).
fof(f1372,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(X2) ),
inference(resolution,[],[f1262,f96]) ).
fof(f1402,definition,
( spl2_17
<=> ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(X2) ) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f1403,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(X2) )
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f1402]) ).
fof(f1406,plain,
spl2_17,
inference(avatar_split_clause,[],[f1372,f1402]) ).
fof(f1467,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X2,or(X0,X1)))
| ~ is_a_theorem(X1) )
| ~ spl2_17 ),
inference(superposition,[],[f1403,f95]) ).
fof(f1498,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X0,X2),or(X3,X2))) )
| ~ spl2_17 ),
inference(resolution,[],[f1467,f209]) ).
fof(f1534,definition,
( spl2_27
<=> ! [X2,X0,X3] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(X0,X2),or(X3,X2))) ) ),
introduced(definition,[new_symbols(definition,[spl2_27])],[avatar_definition]) ).
fof(f1535,plain,
( ! [X2,X3,X0] :
( is_a_theorem(implies(implies(X0,X2),or(X3,X2)))
| ~ is_a_theorem(X0) )
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f1534]) ).
fof(f1536,plain,
( spl2_3
| spl2_27
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f1498,f1402,f1534,f1082]) ).
fof(f1543,plain,
( ! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) )
| ~ spl2_27 ),
inference(resolution,[],[f1535,f127]) ).
fof(f1567,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,X2)) )
| ~ spl2_27 ),
inference(resolution,[],[f1543,f118]) ).
fof(f1625,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X2,implies(X3,X0)))
| is_a_theorem(implies(X2,implies(X3,X1)))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl2_27 ),
inference(resolution,[],[f1567,f124]) ).
fof(f2112,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(X0,X4),X3))
| is_a_theorem(implies(implies(X0,not(X1)),implies(X2,X3)))
| ~ is_a_theorem(implies(X2,or(X1,X4))) )
| ~ spl2_27 ),
inference(resolution,[],[f1625,f178]) ).
fof(f2490,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X2,X0)))
| ~ is_a_theorem(implies(X2,or(X1,X0))) )
| ~ spl2_27 ),
inference(resolution,[],[f2112,f89]) ).
fof(f2529,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,not(X1)),implies(X2,X0)))
| ~ is_a_theorem(implies(X2,or(X1,X0))) )
| ~ spl2_27 ),
inference(forward_demodulation,[],[f2490,f95]) ).
fof(f2530,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| is_a_theorem(implies(or(X2,not(X1)),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X0)) )
| ~ spl2_27 ),
inference(resolution,[],[f2529,f125]) ).
fof(f2562,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(or(X0,not(X1)),implies(X2,X0))) )
| ~ spl2_27 ),
inference(resolution,[],[f2530,f123]) ).
fof(f2947,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X1)))
| is_a_theorem(implies(or(X2,not(X1)),implies(X0,X2))) )
| ~ spl2_27 ),
inference(resolution,[],[f2562,f109]) ).
fof(f3053,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0)))
| ~ spl2_27 ),
inference(resolution,[],[f2947,f96]) ).
fof(f3097,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,not(X2))))
| is_a_theorem(implies(X0,implies(X2,X1))) )
| ~ spl2_27 ),
inference(resolution,[],[f3053,f118]) ).
fof(f3117,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ spl2_27 ),
inference(resolution,[],[f3097,f96]) ).
fof(f3184,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ spl2_27 ),
inference(superposition,[],[f3117,f95]) ).
fof(f3186,plain,
( $false
| ~ spl2_27 ),
inference(resolution,[],[f3184,f92]) ).
fof(f3229,plain,
~ spl2_27,
inference(avatar_contradiction_clause,[],[f3186]) ).
cnf(s25,plain,
~ spl2_3,
inference(sat_conversion,[],[f1350]) ).
cnf(s29,plain,
spl2_17,
inference(sat_conversion,[],[f1406]) ).
cnf(s39,plain,
( spl2_3
| ~ spl2_17
| spl2_27 ),
inference(sat_conversion,[],[f1536]) ).
cnf(s70,plain,
~ spl2_27,
inference(sat_conversion,[],[f3229]) ).
cnf(s71,plain,
( spl2_3
| ~ spl2_17 ),
inference(rat,[],[s39,s70]) ).
cnf(s72,plain,
spl2_3,
inference(rat,[],[s71,s29]) ).
cnf(s73,plain,
$false,
inference(rat,[],[s25,s72]) ).
fof(f3231,plain,
$false,
inference(avatar_sat_refutation,[],[s73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL470+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n001.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 15:54:01 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 Running first-order theorem proving
% 0.23/0.48 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
% 16.65/3.45 % (3746619)Detected formulas, will run a generic FOF schedule.
% 16.65/3.45 % (3746627)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=929901842:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 16.65/3.45 % (3746626)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=384651530:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 16.65/3.45 % (3746630)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=548154996:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 16.65/3.45 % (3746629)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2126747901:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 16.65/3.45 % (3746631)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=332008188:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 16.65/3.45 % (3746628)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=4109794756:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 16.65/3.45 % (3746632)dis-21_1_sil=8000:lcm=predicate:random_seed=1563635707: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)
% 16.65/3.45 % (3746630)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746630)------------------------------
% 16.65/3.45 % (3746630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746629)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746629)------------------------------
% 16.65/3.45 % (3746629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746630)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746630)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746630)Time elapsed: 0.001 s
% 16.65/3.45 % (3746630)Peak memory usage: 86 MB
% 16.65/3.45 % (3746629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746629)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746629)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746629)Time elapsed: 0.001 s
% 16.65/3.45 % (3746629)Peak memory usage: 87 MB
% 16.65/3.45 % (3746632)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746632)------------------------------
% 16.65/3.45 % (3746632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746632)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746632)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746632)Time elapsed: 0.003 s
% 16.65/3.45 % (3746632)Peak memory usage: 88 MB
% 16.65/3.45 % (3746632)Instructions burned: 1 (million)
% 16.65/3.45 % (3746631)Instruction limit reached!
% 16.65/3.45 % (3746631)------------------------------
% 16.65/3.45 % (3746631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746631)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746631)Termination reason: Instruction limit
% 16.65/3.45 % (3746631)Termination phase: Saturation
% 16.65/3.45 % (3746631)Time elapsed: 0.151 s
% 16.65/3.45 % (3746631)Peak memory usage: 90 MB
% 16.65/3.45 % (3746631)Instructions burned: 139 (million)
% 16.65/3.45 % (3746640)lrs+10_1_sil=8000:sp=occurrence:random_seed=2601475630:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 16.65/3.45 % (3746640)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746640)------------------------------
% 16.65/3.45 % (3746640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746640)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746640)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746640)Time elapsed: 0.001 s
% 16.65/3.45 % (3746640)Peak memory usage: 87 MB
% 16.65/3.45 % (3746629)------------------------------
% 16.65/3.45 % (3746629)------------------------------
% 16.65/3.45 % (3746632)------------------------------
% 16.65/3.45 % (3746632)------------------------------
% 16.65/3.45 % (3746630)------------------------------
% 16.65/3.45 % (3746630)------------------------------
% 16.65/3.45 % (3746642)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3151123412:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 16.65/3.45 % (3746642)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746642)------------------------------
% 16.65/3.45 % (3746642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746642)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746642)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746642)Time elapsed: 0.001 s
% 16.65/3.45 % (3746642)Peak memory usage: 87 MB
% 16.65/3.45 % (3746644)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1014270906:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 16.65/3.45 % (3746643)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2957973224:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 16.65/3.45 % (3746643)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746643)------------------------------
% 16.65/3.45 % (3746643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746643)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746643)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746643)Time elapsed: 0.001 s
% 16.65/3.45 % (3746643)Peak memory usage: 87 MB
% 16.65/3.45 % (3746640)------------------------------
% 16.65/3.45 % (3746640)------------------------------
% 16.65/3.45 % (3746628)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746628)------------------------------
% 16.65/3.45 % (3746628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746628)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746628)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746628)Time elapsed: 0.911 s
% 16.65/3.45 % (3746628)Peak memory usage: 126 MB
% 16.65/3.45 % (3746628)Instructions burned: 828 (million)
% 16.65/3.45 % (3746644)Instruction limit reached!
% 16.65/3.45 % (3746644)------------------------------
% 16.65/3.45 % (3746644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746644)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746644)Termination reason: Instruction limit
% 16.65/3.45 % (3746644)Termination phase: Saturation
% 16.65/3.45 % (3746644)Time elapsed: 0.248 s
% 16.65/3.45 % (3746644)Peak memory usage: 92 MB
% 16.65/3.45 % (3746644)Instructions burned: 248 (million)
% 16.65/3.45 % (3746642)------------------------------
% 16.65/3.45 % (3746642)------------------------------
% 16.65/3.45 % (3746648)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1877544334:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2989 on theBenchmark for (2989ds/294Mi)
% 16.65/3.45 % (3746648)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746648)------------------------------
% 16.65/3.45 % (3746648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746648)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746648)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746648)Time elapsed: 0.001 s
% 16.65/3.45 % (3746648)Peak memory usage: 87 MB
% 16.65/3.45 % (3746643)------------------------------
% 16.65/3.45 % (3746643)------------------------------
% 16.65/3.45 % (3746649)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2622827936:i=2350_2987 on theBenchmark for (2987ds/2350Mi)
% 16.65/3.45 % (3746650)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=512425418:cts=off:i=113:fsr=off:ss=included:sgt=4_2987 on theBenchmark for (2987ds/113Mi)
% 16.65/3.45 % (3746650)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746650)------------------------------
% 16.65/3.45 % (3746650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746650)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746650)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746650)Time elapsed: 0.002 s
% 16.65/3.45 % (3746650)Peak memory usage: 88 MB
% 16.65/3.45 % (3746628)------------------------------
% 16.65/3.45 % (3746628)------------------------------
% 16.65/3.45 % (3746652)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3082291048:i=127:av=off:fsr=off:sup=off_2986 on theBenchmark for (2986ds/127Mi)
% 16.65/3.45 % (3746648)------------------------------
% 16.65/3.45 % (3746648)------------------------------
% 16.65/3.45 % (3746652)Instruction limit reached!
% 16.65/3.45 % (3746652)------------------------------
% 16.65/3.45 % (3746652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746652)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746652)Termination reason: Instruction limit
% 16.65/3.45 % (3746652)Termination phase: Saturation
% 16.65/3.45 % (3746652)Time elapsed: 0.123 s
% 16.65/3.45 % (3746652)Peak memory usage: 89 MB
% 16.65/3.45 % (3746652)Instructions burned: 127 (million)
% 16.65/3.45 % (3746626)First to succeed.
% 16.65/3.45 % (3746626)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3746619"
% 16.65/3.45 % (3746655)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1902024874:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2983 on theBenchmark for (2983ds/114Mi)
% 16.65/3.45 % (3746655)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746655)------------------------------
% 16.65/3.45 % (3746655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746655)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746655)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746655)Time elapsed: 0.002 s
% 16.65/3.45 % (3746655)Peak memory usage: 87 MB
% 16.65/3.45 % (3746650)------------------------------
% 16.65/3.45 % (3746650)------------------------------
% 16.65/3.45 % (3746657)lrs+10_1_sil=8000:sp=occurrence:random_seed=3170245695:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2982 on theBenchmark for (2982ds/907Mi)
% 16.65/3.45 % (3746658)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2391909919:i=437:sd=1:aac=none:ss=included_2982 on theBenchmark for (2982ds/437Mi)
% 16.65/3.45 % (3746658)Refutation not found, incomplete strategy
% 16.65/3.45 % (3746658)------------------------------
% 16.65/3.45 % (3746658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.65/3.45 % (3746658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.65/3.45 % (3746658)CaDiCaL version: 2.1.3
% 16.65/3.45 % (3746658)Termination reason: Refutation not found, incomplete strategy
% 16.65/3.45 % (3746658)Time elapsed: 0.002 s
% 16.65/3.45 % (3746658)Peak memory usage: 88 MB
% 16.65/3.45 % (3746660)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=372094669:i=5202:ss=axioms:sgt=16_2980 on theBenchmark for (2980ds/5202Mi)
% 16.65/3.45 % (3746655)------------------------------
% 16.65/3.45 % (3746655)------------------------------
% 16.65/3.45 % (3746626)Refutation found. Thanks to Tanya!
% 16.65/3.45 % SZS status Theorem for theBenchmark
% 16.65/3.45 % SZS output start Proof for theBenchmark
% See solution above
% 17.45/3.70 % (3746626)------------------------------
% 17.45/3.70 % (3746626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.45/3.70 % (3746626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.45/3.70 % (3746626)CaDiCaL version: 2.1.3
% 17.45/3.70 % (3746626)Termination reason: Refutation
% 17.45/3.70 % (3746626)Time elapsed: 1.733 s
% 17.45/3.70 % (3746626)Peak memory usage: 135 MB
% 17.45/3.70 % (3746626)Instructions burned: 1626 (million)
% 17.45/3.70 % (3746626)------------------------------
% 17.45/3.70 % (3746626)------------------------------
% 17.45/3.70 % (3746619)Success in time 2.384 s
% 17.45/3.70 % Vampire exiting
%------------------------------------------------------------------------------