%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL503+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 11:52:38 AM UTC 2026
% Result : Theorem 8.39s 2.09s
% Output : Refutation 8.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 18
% Syntax : Number of formulae : 133 ( 65 unt; 0 def)
% Number of atoms : 225 ( 26 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 : 212 ( 210 !; 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(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
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,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f44,negated_conjecture,
~ implies_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ implies_1,
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(X0,implies(X1,X0)))
=> implies_1 ),
inference(unused_predicate_definition_removal,[],[f4]) ).
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,
( implies_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,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,
( implies_1
| ~ is_a_theorem(implies(sK0,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,
( implies_1
| ~ is_a_theorem(implies(sK0,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,
~ implies_1,
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(sK0,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(f97,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(f106,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X0),or(and(X0,X1),not(and(X1,X2))))),
inference(superposition,[],[f89,f95]) ).
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(f113,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,not(X0)),or(X0,X1)))),
inference(superposition,[],[f110,f95]) ).
fof(f114,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f113,f97]) ).
fof(f115,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f114,f94]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f115,f94]) ).
fof(f160,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(f165,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,[],[f160,f87]) ).
fof(f166,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(X1,X1),X0))
| is_a_theorem(not(and(not(X0),X1))) ),
inference(resolution,[],[f165,f91]) ).
fof(f183,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f166,f90]) ).
fof(f188,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(and(X0,X1))) ),
inference(resolution,[],[f183,f160]) ).
fof(f190,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[],[f183,f87]) ).
fof(f191,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f190,f95]) ).
fof(f193,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f191,f130]) ).
fof(f197,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(superposition,[],[f188,f95]) ).
fof(f198,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f197,f87]) ).
fof(f199,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,X1),and(X2,X0)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f198,f109]) ).
fof(f200,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f198,f191]) ).
fof(f205,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f200,f94]) ).
fof(f212,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X2)) ),
inference(resolution,[],[f199,f94]) ).
fof(f216,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f212,f99]) ).
fof(f230,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(not(X0)) ),
inference(resolution,[],[f193,f101]) ).
fof(f277,plain,
! [X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f230,f90]) ).
fof(f286,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f277,f87]) ).
fof(f292,plain,
! [X0,X1] :
( is_a_theorem(not(and(X1,X0)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f286,f188]) ).
fof(f304,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f292,f87]) ).
fof(f305,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f304,f205]) ).
fof(f309,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f305,f216]) ).
fof(f322,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[],[f309,f86]) ).
fof(f323,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f322,f91]) ).
fof(f324,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f322,f200]) ).
fof(f338,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(forward_demodulation,[],[f324,f95]) ).
fof(f339,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f323,f90]) ).
fof(f341,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f338,f191]) ).
fof(f342,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f339,f93]) ).
fof(f353,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(superposition,[],[f90,f342]) ).
fof(f354,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,not(and(X0,X1))))),
inference(superposition,[],[f106,f342]) ).
fof(f407,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f341,f93]) ).
fof(f409,plain,
! [X0,X1] : and(X0,not(X1)) = not(implies(X0,X1)),
inference(superposition,[],[f407,f87]) ).
fof(f415,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(superposition,[],[f95,f407]) ).
fof(f607,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X1)),X0)),
inference(superposition,[],[f90,f409]) ).
fof(f640,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0)),
inference(forward_demodulation,[],[f607,f95]) ).
fof(f673,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(resolution,[],[f640,f198]) ).
fof(f676,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(forward_demodulation,[],[f673,f95]) ).
fof(f755,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),or(X0,not(X0)))),
inference(superposition,[],[f354,f342]) ).
fof(f975,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),or(not(X0),not(not(X0))))),
inference(superposition,[],[f755,f95]) ).
fof(f985,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,not(not(X0))))),
inference(forward_demodulation,[],[f975,f415]) ).
fof(f992,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,X0))),
inference(forward_demodulation,[],[f985,f407]) ).
fof(f998,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,[],[f992,f322]) ).
fof(f1016,plain,
! [X0] : is_a_theorem(equiv(implies(X0,X0),or(X0,not(X0)))),
inference(forward_subsumption_resolution,[],[f998,f755]) ).
fof(f1028,plain,
! [X0] : implies(X0,X0) = or(X0,not(X0)),
inference(resolution,[],[f1016,f93]) ).
fof(f1072,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(implies(not(X0),X1),or(X1,X0)))),
inference(superposition,[],[f114,f1028]) ).
fof(f1093,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(or(X0,X1),or(X1,X0)))),
inference(forward_demodulation,[],[f1072,f95]) ).
fof(f1188,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[],[f1093,f94]) ).
fof(f1206,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1188,f353]) ).
fof(f1219,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,[],[f1206,f322]) ).
fof(f1237,plain,
! [X0,X1] : is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1219,f1206]) ).
fof(f1239,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(resolution,[],[f1237,f93]) ).
fof(f1316,plain,
! [X0,X1] : implies(X1,X0) = or(X0,not(X1)),
inference(superposition,[],[f415,f1239]) ).
fof(f1371,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X1))),
inference(superposition,[],[f676,f1316]) ).
fof(f1429,plain,
$false,
inference(resolution,[],[f1371,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL503+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 % Computer : n001.cluster.edu
% 0.09/0.40 % Model : x86_64 x86_64
% 0.09/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.40 % Memory : 8046.5625MB
% 0.09/0.40 % OS : Linux 6.8.0-71-generic
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Sun Sep 27 15:59:32 UTC 2026
% 0.09/0.41 % CPUTime :
% 0.09/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.44 Running first-order theorem proving
% 0.09/0.44 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
% 8.39/2.09 % (3748418)Detected formulas, will run a generic FOF schedule.
% 8.39/2.09 % (3748427)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3271393569:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.39/2.09 % (3748427)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748427)------------------------------
% 8.39/2.09 % (3748427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748427)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748427)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748427)Time elapsed: 0.0000 s
% 8.39/2.09 % (3748427)Peak memory usage: 87 MB
% 8.39/2.09 % (3748425)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=3519124233:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.39/2.09 % (3748426)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3862367093:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.39/2.09 % (3748429)dis-21_1_sil=8000:lcm=predicate:random_seed=3457487351: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)
% 8.39/2.09 % (3748428)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2521332813:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.39/2.09 % (3748423)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=1490304660:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.39/2.09 % (3748424)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=2934200707:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.39/2.09 % (3748426)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748426)------------------------------
% 8.39/2.09 % (3748426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748426)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748426)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748426)Time elapsed: 0.001 s
% 8.39/2.09 % (3748426)Peak memory usage: 87 MB
% 8.39/2.09 % (3748429)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748429)------------------------------
% 8.39/2.09 % (3748429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748429)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748429)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748429)Time elapsed: 0.002 s
% 8.39/2.09 % (3748429)Peak memory usage: 88 MB
% 8.39/2.09 % (3748429)Instructions burned: 1 (million)
% 8.39/2.09 % (3748428)Instruction limit reached!
% 8.39/2.09 % (3748428)------------------------------
% 8.39/2.09 % (3748428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748428)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748428)Termination reason: Instruction limit
% 8.39/2.09 % (3748428)Termination phase: Saturation
% 8.39/2.09 % (3748428)Time elapsed: 0.095 s
% 8.39/2.09 % (3748428)Peak memory usage: 90 MB
% 8.39/2.09 % (3748428)Instructions burned: 140 (million)
% 8.39/2.09 % (3748427)------------------------------
% 8.39/2.09 % (3748427)------------------------------
% 8.39/2.09 % (3748438)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2296388498:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.39/2.09 % (3748438)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748438)------------------------------
% 8.39/2.09 % (3748438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748438)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748438)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748438)Time elapsed: 0.0000 s
% 8.39/2.09 % (3748438)Peak memory usage: 87 MB
% 8.39/2.09 % (3748437)lrs+10_1_sil=8000:sp=occurrence:random_seed=2994786365:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.39/2.09 % (3748437)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748437)------------------------------
% 8.39/2.09 % (3748437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748437)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748437)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748437)Time elapsed: 0.001 s
% 8.39/2.09 % (3748437)Peak memory usage: 87 MB
% 8.39/2.09 % (3748426)------------------------------
% 8.39/2.09 % (3748426)------------------------------
% 8.39/2.09 % (3748429)------------------------------
% 8.39/2.09 % (3748429)------------------------------
% 8.39/2.09 % (3748438)------------------------------
% 8.39/2.09 % (3748438)------------------------------
% 8.39/2.09 % (3748442)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=3843346193:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 8.39/2.09 % (3748441)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2196303332:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 8.39/2.09 % (3748441)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748441)------------------------------
% 8.39/2.09 % (3748441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748441)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748441)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748441)Time elapsed: 0.001 s
% 8.39/2.09 % (3748441)Peak memory usage: 87 MB
% 8.39/2.09 % (3748443)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=561558547:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.39/2.09 % (3748443)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748443)------------------------------
% 8.39/2.09 % (3748443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748443)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748443)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748443)Time elapsed: 0.0000 s
% 8.39/2.09 % (3748443)Peak memory usage: 87 MB
% 8.39/2.09 % (3748437)------------------------------
% 8.39/2.09 % (3748437)------------------------------
% 8.39/2.09 % (3748425)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748425)------------------------------
% 8.39/2.09 % (3748425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748425)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748425)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748425)Time elapsed: 0.558 s
% 8.39/2.09 % (3748425)Peak memory usage: 125 MB
% 8.39/2.09 % (3748425)Instructions burned: 825 (million)
% 8.39/2.09 % (3748442)Instruction limit reached!
% 8.39/2.09 % (3748442)------------------------------
% 8.39/2.09 % (3748442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748442)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748442)Termination reason: Instruction limit
% 8.39/2.09 % (3748442)Termination phase: Saturation
% 8.39/2.09 % (3748442)Time elapsed: 0.165 s
% 8.39/2.09 % (3748442)Peak memory usage: 93 MB
% 8.39/2.09 % (3748442)Instructions burned: 249 (million)
% 8.39/2.09 % (3748443)------------------------------
% 8.39/2.09 % (3748443)------------------------------
% 8.39/2.09 % (3748447)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=656471460:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 8.39/2.09 % (3748441)------------------------------
% 8.39/2.09 % (3748441)------------------------------
% 8.39/2.09 % (3748449)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2925717812:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 8.39/2.09 % (3748448)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3246106788:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 8.39/2.09 % (3748448)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748448)------------------------------
% 8.39/2.09 % (3748448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748448)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748448)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748448)Time elapsed: 0.001 s
% 8.39/2.09 % (3748448)Peak memory usage: 88 MB
% 8.39/2.09 % (3748449)Instruction limit reached!
% 8.39/2.09 % (3748449)------------------------------
% 8.39/2.09 % (3748449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748449)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748449)Termination reason: Instruction limit
% 8.39/2.09 % (3748449)Termination phase: Saturation
% 8.39/2.09 % (3748449)Time elapsed: 0.037 s
% 8.39/2.09 % (3748449)Peak memory usage: 89 MB
% 8.39/2.09 % (3748449)Instructions burned: 127 (million)
% 8.39/2.09 % (3748423)First to succeed.
% 8.39/2.09 % (3748423)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3748418"
% 8.39/2.09 % (3748451)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2891295350:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 8.39/2.09 % (3748451)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748451)------------------------------
% 8.39/2.09 % (3748451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748451)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748451)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748451)Time elapsed: 0.001 s
% 8.39/2.09 % (3748451)Peak memory usage: 87 MB
% 8.39/2.09 % (3748454)lrs+10_1_sil=8000:sp=occurrence:random_seed=1113107243:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 8.39/2.09 % (3748454)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748454)------------------------------
% 8.39/2.09 % (3748454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748454)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748454)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748454)Time elapsed: 0.0000 s
% 8.39/2.09 % (3748454)Peak memory usage: 87 MB
% 8.39/2.09 % (3748425)------------------------------
% 8.39/2.09 % (3748425)------------------------------
% 8.39/2.09 % (3748454)------------------------------
% 8.39/2.09 % (3748454)------------------------------
% 8.39/2.09 % (3748448)------------------------------
% 8.39/2.09 % (3748448)------------------------------
% 8.39/2.09 % (3748457)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2195705531:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 8.39/2.09 % (3748457)Refutation not found, incomplete strategy
% 8.39/2.09 % (3748457)------------------------------
% 8.39/2.09 % (3748457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.39/2.09 % (3748457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.39/2.09 % (3748457)CaDiCaL version: 2.1.3
% 8.39/2.09 % (3748457)Termination reason: Refutation not found, incomplete strategy
% 8.39/2.09 % (3748457)Time elapsed: 0.001 s
% 8.39/2.09 % (3748457)Peak memory usage: 88 MB
% 8.39/2.09 % (3748423)Refutation found. Thanks to Tanya!
% 8.39/2.09 % SZS status Theorem for theBenchmark
% 8.39/2.09 % SZS output start Proof for theBenchmark
% See solution above
% 8.90/2.18 % (3748423)------------------------------
% 8.90/2.18 % (3748423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.18 % (3748423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.18 % (3748423)CaDiCaL version: 2.1.3
% 8.90/2.18 % (3748423)Termination reason: Refutation
% 8.90/2.18 % (3748423)Time elapsed: 0.769 s
% 8.90/2.18 % (3748423)Peak memory usage: 129 MB
% 8.90/2.18 % (3748423)Instructions burned: 1129 (million)
% 8.90/2.18 % (3748423)------------------------------
% 8.90/2.18 % (3748423)------------------------------
% 8.90/2.18 % (3748418)Success in time 1.194 s
% 8.90/2.18 % Vampire exiting
%------------------------------------------------------------------------------