%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL502+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 : n013.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 11:52:37 AM UTC 2026
% Result : Theorem 6.48s 1.93s
% Output : Refutation 7.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 18
% Syntax : Number of formulae : 131 ( 62 unt; 0 def)
% Number of atoms : 224 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 171 ( 78 ~; 72 |; 2 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 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 : 207 ( 205 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
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,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f44,negated_conjecture,
~ modus_tollens,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ modus_tollens,
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(implies(not(X1),not(X0)),implies(X0,X1)))
=> modus_tollens ),
inference(unused_predicate_definition_removal,[],[f3]) ).
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,
( modus_tollens
| ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f58,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(ennf_transformation,[],[f48]) ).
fof(f59,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f47]) ).
fof(f60,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(ennf_transformation,[],[f46]) ).
fof(f61,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f62,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f57]) ).
fof(f65,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f55]) ).
fof(f66,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f56]) ).
fof(f67,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f68,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f69,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f78,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f81,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f82,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
~ modus_tollens,
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(not(sK1),not(sK0)),implies(sK0,sK1))),
inference(forward_subsumption_resolution,[],[f67,f85]) ).
fof(f93,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f66,f81]) ).
fof(f94,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f65,f77]) ).
fof(f95,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f88,f87]) ).
fof(f97,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[],[f95,f87]) ).
fof(f98,plain,
~ is_a_theorem(implies(or(sK1,not(sK0)),implies(sK0,sK1))),
inference(superposition,[],[f92,f95]) ).
fof(f100,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f94,f91]) ).
fof(f102,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0))
| is_a_theorem(X1) ),
inference(superposition,[],[f94,f95]) ).
fof(f103,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(X2,X0),implies(implies(X0,X1),not(and(not(X1),X2))))),
inference(superposition,[],[f89,f87]) ).
fof(f106,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(X2,X0),or(and(X0,X1),not(and(X1,X2))))),
inference(superposition,[],[f89,f95]) ).
fof(f108,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f106,f95]) ).
fof(f110,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f103,f95]) ).
fof(f111,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f108,f95]) ).
fof(f114,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,not(X0)),or(X0,X1)))),
inference(superposition,[],[f111,f95]) ).
fof(f115,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f114,f97]) ).
fof(f116,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f115,f94]) ).
fof(f131,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),not(and(not(X2),X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f105,f94]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(not(and(not(X2),X0))) ),
inference(resolution,[],[f131,f94]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(not(and(not(X1),X0))) ),
inference(resolution,[],[f140,f90]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f116,f94]) ).
fof(f186,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f150,f91]) ).
fof(f193,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[],[f186,f87]) ).
fof(f194,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f193,f95]) ).
fof(f195,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f194,f163]) ).
fof(f223,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,[],[f102,f110]) ).
fof(f226,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(not(X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f102,f195]) ).
fof(f231,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(and(X0,X1))) ),
inference(resolution,[],[f223,f186]) ).
fof(f238,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(superposition,[],[f231,f95]) ).
fof(f239,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f238,f87]) ).
fof(f241,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,X1),and(X2,X0)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f239,f110]) ).
fof(f242,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f239,f194]) ).
fof(f248,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f242,f94]) ).
fof(f253,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X2)) ),
inference(resolution,[],[f241,f94]) ).
fof(f256,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f253,f100]) ).
fof(f281,plain,
! [X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f226,f90]) ).
fof(f290,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f281,f87]) ).
fof(f297,plain,
! [X0,X1] :
( is_a_theorem(not(and(X1,X0)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f290,f231]) ).
fof(f310,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f297,f87]) ).
fof(f311,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f310,f248]) ).
fof(f314,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f311,f256]) ).
fof(f329,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[],[f314,f86]) ).
fof(f330,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f329,f91]) ).
fof(f331,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f329,f242]) ).
fof(f347,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(forward_demodulation,[],[f331,f95]) ).
fof(f348,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f330,f90]) ).
fof(f350,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f347,f194]) ).
fof(f351,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f348,f93]) ).
fof(f361,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(superposition,[],[f90,f351]) ).
fof(f362,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,not(and(X0,X1))))),
inference(superposition,[],[f107,f351]) ).
fof(f426,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f350,f93]) ).
fof(f435,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(superposition,[],[f95,f426]) ).
fof(f747,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),or(X0,not(X0)))),
inference(superposition,[],[f362,f351]) ).
fof(f1014,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),or(not(X0),not(not(X0))))),
inference(superposition,[],[f747,f95]) ).
fof(f1026,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,not(not(X0))))),
inference(forward_demodulation,[],[f1014,f435]) ).
fof(f1035,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,X0))),
inference(forward_demodulation,[],[f1026,f426]) ).
fof(f1039,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,[],[f1035,f329]) ).
fof(f1060,plain,
! [X0] : is_a_theorem(equiv(implies(X0,X0),or(X0,not(X0)))),
inference(forward_subsumption_resolution,[],[f1039,f747]) ).
fof(f1073,plain,
! [X0] : implies(X0,X0) = or(X0,not(X0)),
inference(resolution,[],[f1060,f93]) ).
fof(f1122,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(implies(not(X0),X1),or(X1,X0)))),
inference(superposition,[],[f115,f1073]) ).
fof(f1139,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(or(X0,X1),or(X1,X0)))),
inference(forward_demodulation,[],[f1122,f95]) ).
fof(f1219,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[],[f1139,f94]) ).
fof(f1238,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1219,f361]) ).
fof(f1249,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,[],[f1238,f329]) ).
fof(f1267,plain,
! [X0,X1] : is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1249,f1238]) ).
fof(f1269,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(resolution,[],[f1267,f93]) ).
fof(f1343,plain,
! [X0,X1] : implies(X1,X0) = or(X0,not(X1)),
inference(superposition,[],[f435,f1269]) ).
fof(f1413,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(sK0,sK1))),
inference(superposition,[],[f98,f1343]) ).
fof(f1414,plain,
$false,
inference(forward_subsumption_resolution,[],[f1413,f361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL502+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 % Computer : n013.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Sun Sep 27 15:53:23 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.12/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.48/1.93 % (375718)Detected formulas, will run a generic FOF schedule.
% 6.48/1.93 % (375727)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2515709201:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.48/1.93 % (375727)Refutation not found, incomplete strategy
% 6.48/1.93 % (375727)------------------------------
% 6.48/1.93 % (375727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375727)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375727)Termination reason: Refutation not found, incomplete strategy
% 6.48/1.93 % (375727)Time elapsed: 0.0000 s
% 6.48/1.93 % (375727)Peak memory usage: 86 MB
% 6.48/1.93 % (375723)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=2173895895:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.48/1.93 % (375729)dis-21_1_sil=8000:lcm=predicate:random_seed=2743095404:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.48/1.93 % (375729)Refutation not found, incomplete strategy
% 6.48/1.93 % (375729)------------------------------
% 6.48/1.93 % (375729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375729)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375729)Termination reason: Refutation not found, incomplete strategy
% 6.48/1.93 % (375729)Time elapsed: 0.002 s
% 6.48/1.93 % (375729)Peak memory usage: 88 MB
% 6.48/1.93 % (375729)Instructions burned: 1 (million)
% 6.48/1.93 % (375725)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=3894800468:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.48/1.93 % (375728)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3761606836:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.48/1.93 % (375724)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=2369326273:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.48/1.93 % (375726)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3830413822:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.48/1.93 % (375726)Refutation not found, incomplete strategy
% 6.48/1.93 % (375726)------------------------------
% 6.48/1.93 % (375726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375726)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375726)Termination reason: Refutation not found, incomplete strategy
% 6.48/1.93 % (375726)Time elapsed: 0.001 s
% 6.48/1.93 % (375726)Peak memory usage: 86 MB
% 6.48/1.93 % (375728)Instruction limit reached!
% 6.48/1.93 % (375728)------------------------------
% 6.48/1.93 % (375728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375728)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375728)Termination reason: Instruction limit
% 6.48/1.93 % (375728)Termination phase: Saturation
% 6.48/1.93 % (375728)Time elapsed: 0.090 s
% 6.48/1.93 % (375728)Peak memory usage: 90 MB
% 6.48/1.93 % (375728)Instructions burned: 139 (million)
% 6.48/1.93 % (375727)------------------------------
% 6.48/1.93 % (375727)------------------------------
% 6.48/1.93 % (375738)lrs+10_1_sil=32000:urr=on:br=off:random_seed=730552626:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.48/1.93 % (375738)Refutation not found, incomplete strategy
% 6.48/1.93 % (375738)------------------------------
% 6.48/1.93 % (375738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375738)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375738)Termination reason: Refutation not found, incomplete strategy
% 6.48/1.93 % (375738)Time elapsed: 0.0000 s
% 6.48/1.93 % (375738)Peak memory usage: 87 MB
% 6.48/1.93 % (375737)lrs+10_1_sil=8000:sp=occurrence:random_seed=379356451:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.48/1.93 % (375729)------------------------------
% 6.48/1.93 % (375729)------------------------------
% 6.48/1.93 % (375726)------------------------------
% 6.48/1.93 % (375726)------------------------------
% 6.48/1.93 % (375741)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3358411151:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 6.48/1.93 % (375741)Refutation not found, incomplete strategy
% 6.48/1.93 % (375741)------------------------------
% 6.48/1.93 % (375741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375741)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375741)Termination reason: Refutation not found, incomplete strategy
% 6.48/1.93 % (375741)Time elapsed: 0.001 s
% 6.48/1.93 % (375741)Peak memory usage: 87 MB
% 6.48/1.93 % (375738)------------------------------
% 6.48/1.93 % (375738)------------------------------
% 6.48/1.93 % (375742)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=2564938376:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.48/1.93 % (375737)Instruction limit reached!
% 6.48/1.93 % (375737)------------------------------
% 6.48/1.93 % (375737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375737)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375737)Termination reason: Instruction limit
% 6.48/1.93 % (375737)Termination phase: Saturation
% 6.48/1.93 % (375737)Time elapsed: 0.165 s
% 6.48/1.93 % (375737)Peak memory usage: 92 MB
% 6.48/1.93 % (375737)Instructions burned: 285 (million)
% 6.48/1.93 % (375744)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3716537689:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 6.48/1.93 % (375744)Refutation not found, incomplete strategy
% 6.48/1.93 % (375744)------------------------------
% 6.48/1.93 % (375744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375744)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375744)Termination reason: Refutation not found, incomplete strategy
% 6.48/1.93 % (375744)Time elapsed: 0.0000 s
% 6.48/1.93 % (375744)Peak memory usage: 86 MB
% 6.48/1.93 % (375746)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3044033523:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.48/1.93 % (375742)Instruction limit reached!
% 6.48/1.93 % (375742)------------------------------
% 6.48/1.93 % (375742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375742)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375742)Termination reason: Instruction limit
% 6.48/1.93 % (375742)Termination phase: Saturation
% 6.48/1.93 % (375742)Time elapsed: 0.158 s
% 6.48/1.93 % (375742)Peak memory usage: 92 MB
% 6.48/1.93 % (375742)Instructions burned: 248 (million)
% 6.48/1.93 % (375725)Refutation not found, incomplete strategy
% 6.48/1.93 % (375725)------------------------------
% 6.48/1.93 % (375725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375725)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375725)Termination reason: Refutation not found, incomplete strategy
% 6.48/1.93 % (375725)Time elapsed: 0.561 s
% 6.48/1.93 % (375725)Peak memory usage: 126 MB
% 6.48/1.93 % (375725)Instructions burned: 825 (million)
% 6.48/1.93 % (375741)------------------------------
% 6.48/1.93 % (375741)------------------------------
% 6.48/1.93 % (375744)------------------------------
% 6.48/1.93 % (375744)------------------------------
% 6.48/1.93 % (375749)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1020453722:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 6.48/1.93 % (375749)Refutation not found, incomplete strategy
% 6.48/1.93 % (375749)------------------------------
% 6.48/1.93 % (375749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375749)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375749)Termination reason: Refutation not found, incomplete strategy
% 6.48/1.93 % (375749)Time elapsed: 0.001 s
% 6.48/1.93 % (375749)Peak memory usage: 88 MB
% 6.48/1.93 % (375723)First to succeed.
% 6.48/1.93 % (375723)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-375718"
% 6.48/1.93 % (375751)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4122115121:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.48/1.93 % (375750)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1120027596:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.48/1.93 % (375751)Refutation not found, incomplete strategy
% 6.48/1.93 % (375751)------------------------------
% 6.48/1.93 % (375751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375751)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375751)Termination reason: Refutation not found, incomplete strategy
% 6.48/1.93 % (375751)Time elapsed: 0.001 s
% 6.48/1.93 % (375751)Peak memory usage: 87 MB
% 6.48/1.93 % (375725)------------------------------
% 6.48/1.93 % (375725)------------------------------
% 6.48/1.93 % (375750)Instruction limit reached!
% 6.48/1.93 % (375750)------------------------------
% 6.48/1.93 % (375750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.48/1.93 % (375750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.48/1.93 % (375750)CaDiCaL version: 2.1.3
% 6.48/1.93 % (375750)Termination reason: Instruction limit
% 6.48/1.93 % (375750)Termination phase: Saturation
% 6.48/1.93 % (375750)Time elapsed: 0.067 s
% 6.48/1.93 % (375750)Peak memory usage: 88 MB
% 6.48/1.93 % (375750)Instructions burned: 128 (million)
% 6.48/1.93 % (375723)Refutation found. Thanks to Tanya!
% 6.48/1.93 % SZS status Theorem for theBenchmark
% 6.48/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 7.88/2.12 % (375723)------------------------------
% 7.88/2.12 % (375723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.88/2.12 % (375723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.88/2.12 % (375723)CaDiCaL version: 2.1.3
% 7.88/2.12 % (375723)Termination reason: Refutation
% 7.88/2.12 % (375723)Time elapsed: 0.725 s
% 7.88/2.12 % (375723)Peak memory usage: 129 MB
% 7.88/2.12 % (375723)Instructions burned: 1124 (million)
% 7.88/2.12 % (375723)------------------------------
% 7.88/2.12 % (375723)------------------------------
% 7.88/2.12 % (375718)Success in time 1.038 s
% 7.88/2.12 % Vampire exiting
%------------------------------------------------------------------------------