%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL505+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 : n016.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 3.98s 1.60s
% Output : Refutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 18
% Syntax : Number of formulae : 136 ( 68 unt; 0 def)
% Number of atoms : 228 ( 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 : 7 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 224 ( 221 !; 3 ?)
% 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(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_3) ).
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,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f44,negated_conjecture,
~ implies_3,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ implies_3,
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,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> implies_3 ),
inference(unused_predicate_definition_removal,[],[f6]) ).
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_3
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
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_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[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_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
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_3,
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(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))),
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(f104,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X0),implies(implies(X0,X1),not(and(not(X1),X2))))),
inference(superposition,[],[f89,f87]) ).
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(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(f152,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(f161,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(f166,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,[],[f161,f87]) ).
fof(f167,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(X1,X1),X0))
| is_a_theorem(not(and(not(X0),X1))) ),
inference(resolution,[],[f166,f91]) ).
fof(f184,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f167,f90]) ).
fof(f189,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(and(X0,X1))) ),
inference(resolution,[],[f184,f161]) ).
fof(f191,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[],[f184,f87]) ).
fof(f192,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f191,f95]) ).
fof(f194,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f192,f152]) ).
fof(f198,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(superposition,[],[f189,f95]) ).
fof(f199,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f198,f87]) ).
fof(f200,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,X1),and(X2,X0)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f199,f109]) ).
fof(f201,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f199,f192]) ).
fof(f206,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f201,f94]) ).
fof(f213,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X2)) ),
inference(resolution,[],[f200,f94]) ).
fof(f217,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f213,f99]) ).
fof(f231,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(not(X0)) ),
inference(resolution,[],[f194,f101]) ).
fof(f310,plain,
! [X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f231,f90]) ).
fof(f319,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f310,f87]) ).
fof(f325,plain,
! [X0,X1] :
( is_a_theorem(not(and(X1,X0)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f319,f189]) ).
fof(f338,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f325,f87]) ).
fof(f339,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f338,f206]) ).
fof(f343,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f339,f217]) ).
fof(f359,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[],[f343,f86]) ).
fof(f360,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f359,f91]) ).
fof(f361,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f359,f201]) ).
fof(f379,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(forward_demodulation,[],[f361,f95]) ).
fof(f380,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f360,f90]) ).
fof(f382,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f379,f192]) ).
fof(f383,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f380,f93]) ).
fof(f395,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(superposition,[],[f90,f383]) ).
fof(f465,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f382,f93]) ).
fof(f473,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X1,X0)),
inference(superposition,[],[f87,f465]) ).
fof(f474,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(superposition,[],[f95,f465]) ).
fof(f497,plain,
! [X0] : not(X0) = implies(X0,not(X0)),
inference(superposition,[],[f473,f383]) ).
fof(f508,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X0),implies(not(X0),not(X1))))),
inference(superposition,[],[f104,f473]) ).
fof(f539,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X0),or(X0,not(X1))))),
inference(forward_demodulation,[],[f508,f95]) ).
fof(f557,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),implies(not(X0),not(and(not(not(X0)),X1))))),
inference(superposition,[],[f104,f497]) ).
fof(f583,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,not(and(not(not(X0)),X1))))),
inference(forward_demodulation,[],[f557,f95]) ).
fof(f597,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,implies(not(not(X0)),not(X1))))),
inference(forward_demodulation,[],[f583,f473]) ).
fof(f607,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,or(not(X0),not(X1))))),
inference(forward_demodulation,[],[f597,f95]) ).
fof(f615,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,implies(X0,not(X1))))),
inference(forward_demodulation,[],[f607,f474]) ).
fof(f839,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),or(X0,not(X0)))),
inference(superposition,[],[f615,f497]) ).
fof(f1069,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),or(not(X0),not(not(X0))))),
inference(superposition,[],[f839,f95]) ).
fof(f1079,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,not(not(X0))))),
inference(forward_demodulation,[],[f1069,f474]) ).
fof(f1086,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,X0))),
inference(forward_demodulation,[],[f1079,f465]) ).
fof(f1091,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,[],[f1086,f359]) ).
fof(f1109,plain,
! [X0] : is_a_theorem(equiv(implies(X0,X0),or(X0,not(X0)))),
inference(forward_subsumption_resolution,[],[f1091,f839]) ).
fof(f1121,plain,
! [X0] : implies(X0,X0) = or(X0,not(X0)),
inference(resolution,[],[f1109,f93]) ).
fof(f1165,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(implies(not(X0),X1),or(X1,X0)))),
inference(superposition,[],[f114,f1121]) ).
fof(f1183,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(or(X0,X1),or(X1,X0)))),
inference(forward_demodulation,[],[f1165,f95]) ).
fof(f1275,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[],[f1183,f94]) ).
fof(f1293,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1275,f395]) ).
fof(f1305,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,[],[f1293,f359]) ).
fof(f1325,plain,
! [X0,X1] : is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1305,f1293]) ).
fof(f1327,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(resolution,[],[f1325,f93]) ).
fof(f1395,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X2,X1),or(not(X0),X1)))),
inference(superposition,[],[f539,f1327]) ).
fof(f1412,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X2,X1),implies(X0,X1)))),
inference(forward_demodulation,[],[f1395,f474]) ).
fof(f1425,plain,
$false,
inference(resolution,[],[f1412,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL505+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:59:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.98/1.60 % (2810492)Detected formulas, will run a generic FOF schedule.
% 3.98/1.60 % (2810497)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=1840360084:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.98/1.60 % (2810500)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2451291709:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.98/1.60 % (2810498)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=3732666253:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.98/1.60 % (2810499)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=1272013159:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.98/1.60 % (2810501)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4121023809:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.98/1.60 % (2810501)Refutation not found, incomplete strategy
% 3.98/1.60 % (2810501)------------------------------
% 3.98/1.60 % (2810501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.60 % (2810501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.60 % (2810500)Refutation not found, incomplete strategy
% 3.98/1.60 % (2810500)------------------------------
% 3.98/1.60 % (2810500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.60 % (2810501)CaDiCaL version: 2.1.3
% 3.98/1.60 % (2810501)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.60 % (2810501)Time elapsed: 0.001 s
% 3.98/1.60 % (2810500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.60 % (2810501)Peak memory usage: 86 MB
% 3.98/1.60 % (2810500)CaDiCaL version: 2.1.3
% 3.98/1.60 % (2810500)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.60 % (2810500)Time elapsed: 0.001 s
% 3.98/1.60 % (2810500)Peak memory usage: 87 MB
% 3.98/1.60 % (2810502)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2762045899:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.98/1.60 % (2810503)dis-21_1_sil=8000:lcm=predicate:random_seed=349963664: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)
% 3.98/1.60 % (2810503)Refutation not found, incomplete strategy
% 3.98/1.60 % (2810503)------------------------------
% 3.98/1.60 % (2810503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.60 % (2810503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.60 % (2810503)CaDiCaL version: 2.1.3
% 3.98/1.60 % (2810503)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.60 % (2810503)Time elapsed: 0.002 s
% 3.98/1.60 % (2810503)Peak memory usage: 88 MB
% 3.98/1.60 % (2810503)Instructions burned: 1 (million)
% 3.98/1.60 % (2810502)Instruction limit reached!
% 3.98/1.60 % (2810502)------------------------------
% 3.98/1.60 % (2810502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.60 % (2810502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.60 % (2810502)CaDiCaL version: 2.1.3
% 3.98/1.60 % (2810502)Termination reason: Instruction limit
% 3.98/1.60 % (2810502)Termination phase: Saturation
% 3.98/1.60 % (2810502)Time elapsed: 0.093 s
% 3.98/1.60 % (2810502)Peak memory usage: 90 MB
% 3.98/1.60 % (2810502)Instructions burned: 140 (million)
% 3.98/1.60 % (2810501)------------------------------
% 3.98/1.60 % (2810501)------------------------------
% 3.98/1.60 % (2810500)------------------------------
% 3.98/1.60 % (2810500)------------------------------
% 3.98/1.60 % (2810503)------------------------------
% 3.98/1.60 % (2810503)------------------------------
% 3.98/1.60 % (2810511)lrs+10_1_sil=8000:sp=occurrence:random_seed=831171244:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.98/1.60 % (2810511)Refutation not found, incomplete strategy
% 3.98/1.60 % (2810511)------------------------------
% 3.98/1.60 % (2810511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.60 % (2810511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.60 % (2810511)CaDiCaL version: 2.1.3
% 3.98/1.60 % (2810511)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.60 % (2810511)Time elapsed: 0.001 s
% 3.98/1.60 % (2810511)Peak memory usage: 87 MB
% 3.98/1.60 % (2810497)First to succeed.
% 3.98/1.60 % (2810497)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2810492"
% 3.98/1.60 % (2810515)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=4050714809:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.98/1.60 % (2810513)lrs+1011_1_sil=32000:sp=occurrence:random_seed=111424862:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 3.98/1.60 % (2810512)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3790871898:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 3.98/1.60 % (2810513)Refutation not found, incomplete strategy
% 3.98/1.60 % (2810513)------------------------------
% 3.98/1.60 % (2810513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.60 % (2810513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.60 % (2810512)Refutation not found, incomplete strategy
% 3.98/1.60 % (2810512)------------------------------
% 3.98/1.60 % (2810512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.60 % (2810513)CaDiCaL version: 2.1.3
% 3.98/1.60 % (2810512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.60 % (2810513)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.60 % (2810513)Time elapsed: 0.001 s
% 3.98/1.60 % (2810513)Peak memory usage: 87 MB
% 3.98/1.60 % (2810512)CaDiCaL version: 2.1.3
% 3.98/1.60 % (2810512)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.60 % (2810512)Time elapsed: 0.001 s
% 3.98/1.60 % (2810512)Peak memory usage: 87 MB
% 3.98/1.60 % (2810511)------------------------------
% 3.98/1.60 % (2810511)------------------------------
% 3.98/1.60 % (2810499)Refutation not found, incomplete strategy
% 3.98/1.60 % (2810499)------------------------------
% 3.98/1.60 % (2810499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.60 % (2810499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.60 % (2810499)CaDiCaL version: 2.1.3
% 3.98/1.60 % (2810499)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.60 % (2810499)Time elapsed: 0.563 s
% 3.98/1.60 % (2810499)Peak memory usage: 126 MB
% 3.98/1.60 % (2810499)Instructions burned: 828 (million)
% 3.98/1.60 % (2810497)Refutation found. Thanks to Tanya!
% 3.98/1.60 % SZS status Theorem for theBenchmark
% 3.98/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 5.80/1.79 % (2810497)------------------------------
% 5.80/1.79 % (2810497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.80/1.79 % (2810497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.79 % (2810497)CaDiCaL version: 2.1.3
% 5.80/1.79 % (2810497)Termination reason: Refutation
% 5.80/1.79 % (2810497)Time elapsed: 0.428 s
% 5.80/1.79 % (2810497)Peak memory usage: 130 MB
% 5.80/1.79 % (2810497)Instructions burned: 1137 (million)
% 5.80/1.79 % (2810497)------------------------------
% 5.80/1.79 % (2810497)------------------------------
% 5.80/1.79 % (2810492)Success in time 0.747 s
% 5.80/1.79 % Vampire exiting
%------------------------------------------------------------------------------