%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL513+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 : n019.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 11:52:49 AM UTC 2026
% Result : Theorem 11.91s 2.97s
% Output : Refutation 14.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 18
% Syntax : Number of formulae : 138 ( 70 unt; 0 def)
% Number of atoms : 230 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 167 ( 75 ~; 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 : 222 ( 220 !; 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(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_2) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',kn3) ).
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(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
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(f42,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
equivalence_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f44,negated_conjecture,
~ equivalence_2,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ equivalence_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(equiv(X0,X1),implies(X1,X0)))
=> equivalence_2 ),
inference(unused_predicate_definition_removal,[],[f14]) ).
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,
( equivalence_2
| ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
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,
( equivalence_2
| ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))) ),
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,
( equivalence_2
| ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))) ),
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,
~ equivalence_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(equiv(sK0,sK1),implies(sK1,sK0))),
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(f99,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[],[f95,f87]) ).
fof(f105,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f94,f91]) ).
fof(f109,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0))
| is_a_theorem(X1) ),
inference(superposition,[],[f94,f95]) ).
fof(f110,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(f115,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(f116,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X0),or(and(X0,X1),not(and(X1,X2))))),
inference(superposition,[],[f89,f95]) ).
fof(f117,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f115,f95]) ).
fof(f121,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f110,f95]) ).
fof(f122,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f117,f95]) ).
fof(f126,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,not(X0)),or(X0,X1)))),
inference(superposition,[],[f122,f95]) ).
fof(f127,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f126,f99]) ).
fof(f128,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f127,f94]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f128,f94]) ).
fof(f165,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,[],[f109,f121]) ).
fof(f170,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,[],[f165,f87]) ).
fof(f171,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(X1,X1),X0))
| is_a_theorem(not(and(not(X0),X1))) ),
inference(resolution,[],[f170,f91]) ).
fof(f192,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f171,f90]) ).
fof(f197,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(and(X0,X1))) ),
inference(resolution,[],[f192,f165]) ).
fof(f199,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[],[f192,f87]) ).
fof(f200,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f199,f95]) ).
fof(f202,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f200,f141]) ).
fof(f206,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(superposition,[],[f197,f95]) ).
fof(f207,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f206,f87]) ).
fof(f208,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,X1),and(X2,X0)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f207,f121]) ).
fof(f209,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f207,f200]) ).
fof(f214,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f209,f94]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X2)) ),
inference(resolution,[],[f208,f94]) ).
fof(f224,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f221,f105]) ).
fof(f241,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(not(X0)) ),
inference(resolution,[],[f202,f109]) ).
fof(f292,plain,
! [X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f241,f90]) ).
fof(f301,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f292,f87]) ).
fof(f307,plain,
! [X0,X1] :
( is_a_theorem(not(and(X1,X0)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f301,f197]) ).
fof(f319,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f307,f87]) ).
fof(f320,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f319,f214]) ).
fof(f324,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f320,f224]) ).
fof(f337,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[],[f324,f86]) ).
fof(f338,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f337,f91]) ).
fof(f339,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f337,f209]) ).
fof(f356,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(forward_demodulation,[],[f339,f95]) ).
fof(f357,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f338,f90]) ).
fof(f359,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f356,f200]) ).
fof(f360,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f357,f93]) ).
fof(f372,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(superposition,[],[f90,f360]) ).
fof(f373,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,not(and(X0,X1))))),
inference(superposition,[],[f116,f360]) ).
fof(f444,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),or(X0,not(X0)))),
inference(superposition,[],[f373,f360]) ).
fof(f452,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f359,f93]) ).
fof(f454,plain,
! [X0,X1] : and(X0,not(X1)) = not(implies(X0,X1)),
inference(superposition,[],[f452,f87]) ).
fof(f459,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X1,X0)),
inference(superposition,[],[f87,f452]) ).
fof(f460,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(superposition,[],[f95,f452]) ).
fof(f480,plain,
! [X0,X1] : not(equiv(X0,X1)) = implies(implies(X0,X1),not(implies(X1,X0))),
inference(superposition,[],[f459,f86]) ).
fof(f716,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X1)),X0)),
inference(superposition,[],[f90,f454]) ).
fof(f753,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0)),
inference(forward_demodulation,[],[f716,f95]) ).
fof(f796,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(resolution,[],[f753,f207]) ).
fof(f799,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(forward_demodulation,[],[f796,f95]) ).
fof(f1380,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),or(not(X0),not(not(X0))))),
inference(superposition,[],[f444,f95]) ).
fof(f1390,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,not(not(X0))))),
inference(forward_demodulation,[],[f1380,f460]) ).
fof(f1397,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,X0))),
inference(forward_demodulation,[],[f1390,f452]) ).
fof(f1403,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,[],[f1397,f337]) ).
fof(f1421,plain,
! [X0] : is_a_theorem(equiv(implies(X0,X0),or(X0,not(X0)))),
inference(forward_subsumption_resolution,[],[f1403,f444]) ).
fof(f1433,plain,
! [X0] : implies(X0,X0) = or(X0,not(X0)),
inference(resolution,[],[f1421,f93]) ).
fof(f1479,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(implies(not(X0),X1),or(X1,X0)))),
inference(superposition,[],[f127,f1433]) ).
fof(f1499,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(or(X0,X1),or(X1,X0)))),
inference(forward_demodulation,[],[f1479,f95]) ).
fof(f1594,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[],[f1499,f94]) ).
fof(f1612,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1594,f372]) ).
fof(f1625,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,[],[f1612,f337]) ).
fof(f1643,plain,
! [X0,X1] : is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1625,f1612]) ).
fof(f1645,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(resolution,[],[f1643,f93]) ).
fof(f1727,plain,
! [X0,X1] : implies(X1,X0) = or(X0,not(X1)),
inference(superposition,[],[f460,f1645]) ).
fof(f1787,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X1))),
inference(superposition,[],[f799,f1727]) ).
fof(f1854,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X1,X0)),not(equiv(X0,X1)))),
inference(superposition,[],[f1787,f480]) ).
fof(f1857,plain,
! [X0,X1] : is_a_theorem(or(implies(X1,X0),not(equiv(X0,X1)))),
inference(forward_demodulation,[],[f1854,f95]) ).
fof(f1863,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(forward_demodulation,[],[f1857,f1727]) ).
fof(f1869,plain,
$false,
inference(resolution,[],[f1863,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL513+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 15:55:03 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 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
% 11.91/2.97 % (3233267)Detected formulas, will run a generic FOF schedule.
% 11.91/2.97 % (3233276)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2357464429:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.91/2.97 % (3233278)dis-21_1_sil=8000:lcm=predicate:random_seed=2697038642: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)
% 11.91/2.97 % (3233276)Refutation not found, incomplete strategy
% 11.91/2.97 % (3233276)------------------------------
% 11.91/2.97 % (3233276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233276)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233276)Termination reason: Refutation not found, incomplete strategy
% 11.91/2.97 % (3233276)Time elapsed: 0.001 s
% 11.91/2.97 % (3233276)Peak memory usage: 86 MB
% 11.91/2.97 % (3233278)Refutation not found, incomplete strategy
% 11.91/2.97 % (3233278)------------------------------
% 11.91/2.97 % (3233278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233278)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233278)Termination reason: Refutation not found, incomplete strategy
% 11.91/2.97 % (3233278)Time elapsed: 0.002 s
% 11.91/2.97 % (3233278)Peak memory usage: 88 MB
% 11.91/2.97 % (3233278)Instructions burned: 1 (million)
% 11.91/2.97 % (3233272)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=930386322:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.91/2.97 % (3233273)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=1512206671:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.91/2.97 % (3233275)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=110687949:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.91/2.97 % (3233274)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=3168474083:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.91/2.97 % (3233275)Refutation not found, incomplete strategy
% 11.91/2.97 % (3233275)------------------------------
% 11.91/2.97 % (3233275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233275)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233275)Termination reason: Refutation not found, incomplete strategy
% 11.91/2.97 % (3233275)Time elapsed: 0.001 s
% 11.91/2.97 % (3233275)Peak memory usage: 86 MB
% 11.91/2.97 % (3233277)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2424210354:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.91/2.97 % (3233276)------------------------------
% 11.91/2.97 % (3233276)------------------------------
% 11.91/2.97 % (3233277)Instruction limit reached!
% 11.91/2.97 % (3233277)------------------------------
% 11.91/2.97 % (3233277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233277)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233277)Termination reason: Instruction limit
% 11.91/2.97 % (3233277)Termination phase: Saturation
% 11.91/2.97 % (3233277)Time elapsed: 0.153 s
% 11.91/2.97 % (3233277)Peak memory usage: 90 MB
% 11.91/2.97 % (3233277)Instructions burned: 139 (million)
% 11.91/2.97 % (3233278)------------------------------
% 11.91/2.97 % (3233278)------------------------------
% 11.91/2.97 % (3233286)lrs+10_1_sil=8000:sp=occurrence:random_seed=3072151238:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 11.91/2.97 % (3233286)Refutation not found, incomplete strategy
% 11.91/2.97 % (3233286)------------------------------
% 11.91/2.97 % (3233286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233286)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233286)Termination reason: Refutation not found, incomplete strategy
% 11.91/2.97 % (3233286)Time elapsed: 0.001 s
% 11.91/2.97 % (3233286)Peak memory usage: 88 MB
% 11.91/2.97 % (3233275)------------------------------
% 11.91/2.97 % (3233275)------------------------------
% 11.91/2.97 % (3233287)lrs+10_1_sil=32000:urr=on:br=off:random_seed=475416725:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 11.91/2.97 % (3233287)Refutation not found, incomplete strategy
% 11.91/2.97 % (3233287)------------------------------
% 11.91/2.97 % (3233287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233287)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233287)Termination reason: Refutation not found, incomplete strategy
% 11.91/2.97 % (3233287)Time elapsed: 0.002 s
% 11.91/2.97 % (3233287)Peak memory usage: 87 MB
% 11.91/2.97 % (3233288)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1475093683:i=325:sd=1:ss=axioms:sgt=32_2994 on theBenchmark for (2994ds/325Mi)
% 11.91/2.97 % (3233288)Refutation not found, incomplete strategy
% 11.91/2.97 % (3233288)------------------------------
% 11.91/2.97 % (3233288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233288)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233288)Termination reason: Refutation not found, incomplete strategy
% 11.91/2.97 % (3233288)Time elapsed: 0.001 s
% 11.91/2.97 % (3233288)Peak memory usage: 87 MB
% 11.91/2.97 % (3233286)------------------------------
% 11.91/2.97 % (3233286)------------------------------
% 11.91/2.97 % (3233290)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=2580248344:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 11.91/2.97 % (3233293)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3134821131:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 11.91/2.97 % (3233293)Refutation not found, incomplete strategy
% 11.91/2.97 % (3233293)------------------------------
% 11.91/2.97 % (3233293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233293)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233293)Termination reason: Refutation not found, incomplete strategy
% 11.91/2.97 % (3233293)Time elapsed: 0.001 s
% 11.91/2.97 % (3233293)Peak memory usage: 86 MB
% 11.91/2.97 % (3233287)------------------------------
% 11.91/2.97 % (3233287)------------------------------
% 11.91/2.97 % (3233274)Refutation not found, incomplete strategy
% 11.91/2.97 % (3233274)------------------------------
% 11.91/2.97 % (3233274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233274)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233274)Termination reason: Refutation not found, incomplete strategy
% 11.91/2.97 % (3233274)Time elapsed: 0.902 s
% 11.91/2.97 % (3233274)Peak memory usage: 126 MB
% 11.91/2.97 % (3233274)Instructions burned: 828 (million)
% 11.91/2.97 % (3233288)------------------------------
% 11.91/2.97 % (3233288)------------------------------
% 11.91/2.97 % (3233290)Instruction limit reached!
% 11.91/2.97 % (3233290)------------------------------
% 11.91/2.97 % (3233290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233290)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233290)Termination reason: Instruction limit
% 11.91/2.97 % (3233290)Termination phase: Saturation
% 11.91/2.97 % (3233290)Time elapsed: 0.256 s
% 11.91/2.97 % (3233290)Peak memory usage: 92 MB
% 11.91/2.97 % (3233290)Instructions burned: 249 (million)
% 11.91/2.97 % (3233293)------------------------------
% 11.91/2.97 % (3233293)------------------------------
% 11.91/2.97 % (3233296)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3735268903:i=2350_2988 on theBenchmark for (2988ds/2350Mi)
% 11.91/2.97 % (3233272)First to succeed.
% 11.91/2.97 % (3233272)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3233267"
% 11.91/2.97 % (3233297)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2648256764:cts=off:i=113:fsr=off:ss=included:sgt=4_2987 on theBenchmark for (2987ds/113Mi)
% 11.91/2.97 % (3233298)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1012812305:i=127:av=off:fsr=off:sup=off_2987 on theBenchmark for (2987ds/127Mi)
% 11.91/2.97 % (3233297)Refutation not found, incomplete strategy
% 11.91/2.97 % (3233297)------------------------------
% 11.91/2.97 % (3233297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233297)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233297)Termination reason: Refutation not found, incomplete strategy
% 11.91/2.97 % (3233297)Time elapsed: 0.002 s
% 11.91/2.97 % (3233297)Peak memory usage: 87 MB
% 11.91/2.97 % (3233274)------------------------------
% 11.91/2.97 % (3233274)------------------------------
% 11.91/2.97 % (3233299)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2742246218:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2986 on theBenchmark for (2986ds/114Mi)
% 11.91/2.97 % (3233299)Refutation not found, incomplete strategy
% 11.91/2.97 % (3233299)------------------------------
% 11.91/2.97 % (3233299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233299)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233299)Termination reason: Refutation not found, incomplete strategy
% 11.91/2.97 % (3233299)Time elapsed: 0.001 s
% 11.91/2.97 % (3233299)Peak memory usage: 87 MB
% 11.91/2.97 % (3233298)Instruction limit reached!
% 11.91/2.97 % (3233298)------------------------------
% 11.91/2.97 % (3233298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.91/2.97 % (3233298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.91/2.97 % (3233298)CaDiCaL version: 2.1.3
% 11.91/2.97 % (3233298)Termination reason: Instruction limit
% 11.91/2.97 % (3233298)Termination phase: Saturation
% 11.91/2.97 % (3233298)Time elapsed: 0.118 s
% 11.91/2.97 % (3233298)Peak memory usage: 88 MB
% 11.91/2.97 % (3233298)Instructions burned: 128 (million)
% 11.91/2.97 % (3233299)------------------------------
% 11.91/2.97 % (3233299)------------------------------
% 11.91/2.97 % (3233304)lrs+10_1_sil=8000:sp=occurrence:random_seed=3309340577:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2984 on theBenchmark for (2984ds/907Mi)
% 11.91/2.97 % (3233272)Refutation found. Thanks to Tanya!
% 11.91/2.97 % SZS status Theorem for theBenchmark
% 11.91/2.97 % SZS output start Proof for theBenchmark
% See solution above
% 14.34/3.23 % (3233272)------------------------------
% 14.34/3.23 % (3233272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.34/3.23 % (3233272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.34/3.23 % (3233272)CaDiCaL version: 2.1.3
% 14.34/3.23 % (3233272)Termination reason: Refutation
% 14.34/3.23 % (3233272)Time elapsed: 1.262 s
% 14.34/3.23 % (3233272)Peak memory usage: 130 MB
% 14.34/3.23 % (3233272)Instructions burned: 1178 (million)
% 14.34/3.23 % (3233272)------------------------------
% 14.34/3.23 % (3233272)------------------------------
% 14.34/3.23 % (3233267)Success in time 1.913 s
% 14.34/3.23 % Vampire exiting
%------------------------------------------------------------------------------