%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL510+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 11:52:39 AM UTC 2026
% Result : Theorem 6.60s 2.01s
% Output : Refutation 8.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 18
% Syntax : Number of formulae : 134 ( 66 unt; 0 def)
% Number of atoms : 226 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 168 ( 76 ~; 71 |; 2 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 209 ( 207 !; 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/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
fof(f18,axiom,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
or_2,
file('/export/starexec/sandbox/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,
( kn3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f47,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f48,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
=> or_2 ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f50,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
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(f54,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f51]) ).
fof(f55,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f50]) ).
fof(f57,plain,
( or_2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f58,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(ennf_transformation,[],[f48]) ).
fof(f59,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f47]) ).
fof(f60,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(ennf_transformation,[],[f46]) ).
fof(f61,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f62,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,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)],[f57]) ).
fof(f65,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f55]) ).
fof(f66,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f56]) ).
fof(f67,plain,
( or_2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f68,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f69,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f78,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f81,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f82,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
~ or_2,
inference(cnf_transformation,[],[f45]) ).
fof(f86,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f73,f84]) ).
fof(f87,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f72,f83]) ).
fof(f88,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f71,f82]) ).
fof(f89,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(forward_subsumption_resolution,[],[f70,f80]) ).
fof(f90,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f69,f79]) ).
fof(f91,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[],[f68,f78]) ).
fof(f92,plain,
~ is_a_theorem(implies(sK1,or(sK0,sK1))),
inference(forward_subsumption_resolution,[],[f67,f85]) ).
fof(f93,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f66,f81]) ).
fof(f94,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f65,f77]) ).
fof(f95,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f88,f87]) ).
fof(f98,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[],[f95,f87]) ).
fof(f99,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f94,f91]) ).
fof(f101,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0))
| is_a_theorem(X1) ),
inference(superposition,[],[f94,f95]) ).
fof(f102,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(not(and(X1,X2)),not(and(X2,X0)))) ),
inference(resolution,[],[f89,f94]) ).
fof(f105,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),implies(not(and(X2,X0)),implies(X0,X1)))),
inference(superposition,[],[f89,f87]) ).
fof(f107,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f105,f95]) ).
fof(f109,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f102,f95]) ).
fof(f110,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f107,f95]) ).
fof(f122,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,not(X0)),or(X0,X1)))),
inference(superposition,[],[f110,f95]) ).
fof(f123,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f122,f98]) ).
fof(f124,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f123,f94]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f124,f94]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(and(X0,X1)))
| is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f101,f109]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f132,f87]) ).
fof(f136,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(X1,X1),X0))
| is_a_theorem(not(and(not(X0),X1))) ),
inference(resolution,[],[f135,f91]) ).
fof(f150,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f136,f90]) ).
fof(f155,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(and(X0,X1))) ),
inference(resolution,[],[f150,f132]) ).
fof(f157,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[],[f150,f87]) ).
fof(f158,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f157,f95]) ).
fof(f161,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(superposition,[],[f155,f95]) ).
fof(f162,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f161,f87]) ).
fof(f165,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,X1),and(X2,X0)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f162,f109]) ).
fof(f166,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f162,f158]) ).
fof(f170,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f166,f94]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X2)) ),
inference(resolution,[],[f165,f94]) ).
fof(f180,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f177,f99]) ).
fof(f205,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f126,f158]) ).
fof(f210,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(not(X0)) ),
inference(resolution,[],[f205,f101]) ).
fof(f269,plain,
! [X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f210,f90]) ).
fof(f278,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f269,f87]) ).
fof(f284,plain,
! [X0,X1] :
( is_a_theorem(not(and(X1,X0)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f278,f155]) ).
fof(f298,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f284,f87]) ).
fof(f299,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f298,f170]) ).
fof(f303,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f299,f180]) ).
fof(f312,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[],[f303,f86]) ).
fof(f313,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f312,f91]) ).
fof(f314,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f312,f166]) ).
fof(f327,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(forward_demodulation,[],[f314,f95]) ).
fof(f328,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f313,f90]) ).
fof(f330,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f327,f158]) ).
fof(f331,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f328,f93]) ).
fof(f343,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(superposition,[],[f90,f331]) ).
fof(f346,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,X0),or(X0,implies(X0,X1)))),
inference(superposition,[],[f110,f331]) ).
fof(f398,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f330,f93]) ).
fof(f400,plain,
! [X0,X1] : and(X0,not(X1)) = not(implies(X0,X1)),
inference(superposition,[],[f398,f87]) ).
fof(f405,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X1,X0)),
inference(superposition,[],[f87,f398]) ).
fof(f406,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(superposition,[],[f95,f398]) ).
fof(f426,plain,
! [X0] : not(X0) = implies(X0,not(X0)),
inference(superposition,[],[f405,f331]) ).
fof(f594,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X1)),X0)),
inference(superposition,[],[f90,f400]) ).
fof(f625,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0)),
inference(forward_demodulation,[],[f594,f95]) ).
fof(f666,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(resolution,[],[f625,f162]) ).
fof(f669,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(forward_demodulation,[],[f666,f95]) ).
fof(f905,plain,
! [X0] : is_a_theorem(implies(or(not(X0),X0),or(X0,not(X0)))),
inference(superposition,[],[f346,f426]) ).
fof(f910,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),or(X0,not(X0)))),
inference(forward_demodulation,[],[f905,f406]) ).
fof(f923,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),or(not(X0),not(not(X0))))),
inference(superposition,[],[f910,f95]) ).
fof(f935,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,not(not(X0))))),
inference(forward_demodulation,[],[f923,f406]) ).
fof(f944,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,X0))),
inference(forward_demodulation,[],[f935,f398]) ).
fof(f949,plain,
! [X0] :
( ~ is_a_theorem(implies(implies(X0,X0),or(X0,not(X0))))
| is_a_theorem(equiv(implies(X0,X0),or(X0,not(X0)))) ),
inference(resolution,[],[f944,f312]) ).
fof(f970,plain,
! [X0] : is_a_theorem(equiv(implies(X0,X0),or(X0,not(X0)))),
inference(forward_subsumption_resolution,[],[f949,f910]) ).
fof(f984,plain,
! [X0] : implies(X0,X0) = or(X0,not(X0)),
inference(resolution,[],[f970,f93]) ).
fof(f1031,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(implies(not(X0),X1),or(X1,X0)))),
inference(superposition,[],[f123,f984]) ).
fof(f1048,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(or(X0,X1),or(X1,X0)))),
inference(forward_demodulation,[],[f1031,f95]) ).
fof(f1216,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[],[f1048,f94]) ).
fof(f1234,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1216,f343]) ).
fof(f1247,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| is_a_theorem(equiv(or(X0,X1),or(X1,X0))) ),
inference(resolution,[],[f1234,f312]) ).
fof(f1265,plain,
! [X0,X1] : is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1247,f1234]) ).
fof(f1268,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(resolution,[],[f1265,f93]) ).
fof(f1347,plain,
~ is_a_theorem(implies(sK1,or(sK1,sK0))),
inference(superposition,[],[f92,f1268]) ).
fof(f1348,plain,
$false,
inference(forward_subsumption_resolution,[],[f1347,f669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL510+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 15:54:15 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 6.60/2.01 % (2209852)Detected formulas, will run a generic FOF schedule.
% 6.60/2.01 % (2209861)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=272140185:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.60/2.01 % (2209861)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209861)------------------------------
% 6.60/2.01 % (2209861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209861)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209861)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209861)Time elapsed: 0.0000 s
% 6.60/2.01 % (2209861)Peak memory usage: 86 MB
% 6.60/2.01 % (2209858)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=3808178104:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.60/2.01 % (2209857)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=3493510256:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.60/2.01 % (2209860)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=449462347:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.60/2.01 % (2209859)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=2908885427:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.60/2.01 % (2209860)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209860)------------------------------
% 6.60/2.01 % (2209860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209860)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209860)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209860)Time elapsed: 0.001 s
% 6.60/2.01 % (2209860)Peak memory usage: 86 MB
% 6.60/2.01 % (2209862)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2048838397:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.60/2.01 % (2209863)dis-21_1_sil=8000:lcm=predicate:random_seed=3602514271: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)
% 6.60/2.01 % (2209863)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209863)------------------------------
% 6.60/2.01 % (2209863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209863)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209863)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209863)Time elapsed: 0.002 s
% 6.60/2.01 % (2209863)Peak memory usage: 88 MB
% 6.60/2.01 % (2209863)Instructions burned: 1 (million)
% 6.60/2.01 % (2209862)Instruction limit reached!
% 6.60/2.01 % (2209862)------------------------------
% 6.60/2.01 % (2209862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209862)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209862)Termination reason: Instruction limit
% 6.60/2.01 % (2209862)Termination phase: Saturation
% 6.60/2.01 % (2209862)Time elapsed: 0.096 s
% 6.60/2.01 % (2209862)Peak memory usage: 90 MB
% 6.60/2.01 % (2209862)Instructions burned: 140 (million)
% 6.60/2.01 % (2209861)------------------------------
% 6.60/2.01 % (2209861)------------------------------
% 6.60/2.01 % (2209872)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1532480871:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.60/2.01 % (2209872)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209872)------------------------------
% 6.60/2.01 % (2209872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209872)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209872)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209872)Time elapsed: 0.0000 s
% 6.60/2.01 % (2209872)Peak memory usage: 87 MB
% 6.60/2.01 % (2209871)lrs+10_1_sil=8000:sp=occurrence:random_seed=2929587804:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.60/2.01 % (2209871)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209871)------------------------------
% 6.60/2.01 % (2209871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209871)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209871)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209871)Time elapsed: 0.001 s
% 6.60/2.01 % (2209871)Peak memory usage: 87 MB
% 6.60/2.01 % (2209863)------------------------------
% 6.60/2.01 % (2209863)------------------------------
% 6.60/2.01 % (2209860)------------------------------
% 6.60/2.01 % (2209860)------------------------------
% 6.60/2.01 % (2209872)------------------------------
% 6.60/2.01 % (2209872)------------------------------
% 6.60/2.01 % (2209875)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3299060424:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 6.60/2.01 % (2209876)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=2549145204:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.60/2.01 % (2209875)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209875)------------------------------
% 6.60/2.01 % (2209875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209875)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209875)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209875)Time elapsed: 0.001 s
% 6.60/2.01 % (2209875)Peak memory usage: 87 MB
% 6.60/2.01 % (2209877)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1311506915:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 6.60/2.01 % (2209877)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209877)------------------------------
% 6.60/2.01 % (2209877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209877)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209877)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209877)Time elapsed: 0.0000 s
% 6.60/2.01 % (2209877)Peak memory usage: 86 MB
% 6.60/2.01 % (2209871)------------------------------
% 6.60/2.01 % (2209871)------------------------------
% 6.60/2.01 % (2209876)Instruction limit reached!
% 6.60/2.01 % (2209876)------------------------------
% 6.60/2.01 % (2209876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209876)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209876)Termination reason: Instruction limit
% 6.60/2.01 % (2209876)Termination phase: Saturation
% 6.60/2.01 % (2209876)Time elapsed: 0.163 s
% 6.60/2.01 % (2209876)Peak memory usage: 92 MB
% 6.60/2.01 % (2209876)Instructions burned: 248 (million)
% 6.60/2.01 % (2209859)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209859)------------------------------
% 6.60/2.01 % (2209859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209859)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209859)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209859)Time elapsed: 0.561 s
% 6.60/2.01 % (2209859)Peak memory usage: 127 MB
% 6.60/2.01 % (2209859)Instructions burned: 829 (million)
% 6.60/2.01 % (2209877)------------------------------
% 6.60/2.01 % (2209877)------------------------------
% 6.60/2.01 % (2209881)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4243286865:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 6.60/2.01 % (2209875)------------------------------
% 6.60/2.01 % (2209875)------------------------------
% 6.60/2.01 % (2209882)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=389596716:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 6.60/2.01 % (2209882)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209882)------------------------------
% 6.60/2.01 % (2209882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209882)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209882)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209882)Time elapsed: 0.001 s
% 6.60/2.01 % (2209882)Peak memory usage: 88 MB
% 6.60/2.01 % (2209883)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3793793927:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.60/2.01 % (2209883)Instruction limit reached!
% 6.60/2.01 % (2209883)------------------------------
% 6.60/2.01 % (2209883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209883)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209883)Termination reason: Instruction limit
% 6.60/2.01 % (2209883)Termination phase: Saturation
% 6.60/2.01 % (2209883)Time elapsed: 0.037 s
% 6.60/2.01 % (2209883)Peak memory usage: 89 MB
% 6.60/2.01 % (2209883)Instructions burned: 127 (million)
% 6.60/2.01 % (2209857)First to succeed.
% 6.60/2.01 % (2209857)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2209852"
% 6.60/2.01 % (2209885)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=39034288:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.60/2.01 % (2209885)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209885)------------------------------
% 6.60/2.01 % (2209885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209885)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209885)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209885)Time elapsed: 0.001 s
% 6.60/2.01 % (2209885)Peak memory usage: 87 MB
% 6.60/2.01 % (2209859)------------------------------
% 6.60/2.01 % (2209859)------------------------------
% 6.60/2.01 % (2209888)lrs+10_1_sil=8000:sp=occurrence:random_seed=2184026466:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.60/2.01 % (2209882)------------------------------
% 6.60/2.01 % (2209882)------------------------------
% 6.60/2.01 % (2209891)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2111554535:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 6.60/2.01 % (2209891)Refutation not found, incomplete strategy
% 6.60/2.01 % (2209891)------------------------------
% 6.60/2.01 % (2209891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.60/2.01 % (2209891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.60/2.01 % (2209891)CaDiCaL version: 2.1.3
% 6.60/2.01 % (2209891)Termination reason: Refutation not found, incomplete strategy
% 6.60/2.01 % (2209891)Time elapsed: 0.001 s
% 6.60/2.01 % (2209891)Peak memory usage: 88 MB
% 6.60/2.01 % (2209857)Refutation found. Thanks to Tanya!
% 6.60/2.01 % SZS status Theorem for theBenchmark
% 6.60/2.01 % SZS output start Proof for theBenchmark
% See solution above
% 8.76/2.11 % (2209857)------------------------------
% 8.76/2.11 % (2209857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.76/2.11 % (2209857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.76/2.11 % (2209857)CaDiCaL version: 2.1.3
% 8.76/2.11 % (2209857)Termination reason: Refutation
% 8.76/2.11 % (2209857)Time elapsed: 0.766 s
% 8.76/2.11 % (2209857)Peak memory usage: 130 MB
% 8.76/2.11 % (2209857)Instructions burned: 1118 (million)
% 8.76/2.11 % (2209857)------------------------------
% 8.76/2.11 % (2209857)------------------------------
% 8.76/2.11 % (2209852)Success in time 1.177 s
% 8.76/2.11 % Vampire exiting
%------------------------------------------------------------------------------