%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL515+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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:49 AM UTC 2026
% Result : Theorem 7.58s 2.04s
% Output : Refutation 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 18
% Syntax : Number of formulae : 137 ( 70 unt; 0 def)
% Number of atoms : 226 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 161 ( 72 ~; 68 |; 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 : 229 ( 226 !; 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(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(f19,axiom,
( cn1
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn1) ).
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(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_implies_and) ).
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',luka_op_or) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_equiv) ).
fof(f43,conjecture,
cn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn1) ).
fof(f44,negated_conjecture,
~ cn1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ cn1,
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> cn1 ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f47,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(f48,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f49,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
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(f55,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f51]) ).
fof(f56,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f50]) ).
fof(f58,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(ennf_transformation,[],[f49]) ).
fof(f59,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f48]) ).
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,[],[f47]) ).
fof(f61,plain,
( cn1
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f46]) ).
fof(f62,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f63,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f64,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f65,plain,
( cn1
| ~ 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)],[f61]) ).
fof(f66,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f56]) ).
fof(f67,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f57]) ).
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,
( cn1
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f72,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f63]) ).
fof(f74,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f64]) ).
fof(f76,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f78,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f79,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f80,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f81,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f82,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f83,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f84,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
~ cn1,
inference(cnf_transformation,[],[f45]) ).
fof(f86,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f74,f84]) ).
fof(f87,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f73,f76]) ).
fof(f88,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f72,f83]) ).
fof(f89,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))),
inference(forward_subsumption_resolution,[],[f71,f85]) ).
fof(f90,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,f81]) ).
fof(f91,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f69,f80]) ).
fof(f92,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[],[f68,f79]) ).
fof(f93,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f67,f82]) ).
fof(f94,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f66,f78]) ).
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,f92]) ).
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,[],[f90,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,[],[f90,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,[],[f90,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(f130,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),not(and(not(X2),X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f104,f94]) ).
fof(f160,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,[],[f130,f94]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(not(and(not(X1),X0))) ),
inference(resolution,[],[f160,f91]) ).
fof(f177,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(f198,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f172,f92]) ).
fof(f201,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(not(and(not(X1),not(X0)))) ),
inference(superposition,[],[f172,f95]) ).
fof(f202,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(not(X1),X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(forward_demodulation,[],[f201,f87]) ).
fof(f203,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(forward_demodulation,[],[f202,f95]) ).
fof(f204,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(and(X0,X1))) ),
inference(resolution,[],[f198,f177]) ).
fof(f206,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[],[f198,f87]) ).
fof(f207,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f206,f95]) ).
fof(f211,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(superposition,[],[f204,f95]) ).
fof(f212,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f211,f87]) ).
fof(f217,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,X1),and(X2,X0)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f212,f109]) ).
fof(f218,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f212,f207]) ).
fof(f223,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f218,f94]) ).
fof(f228,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X2)) ),
inference(resolution,[],[f217,f94]) ).
fof(f232,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f228,f99]) ).
fof(f273,plain,
! [X0,X1] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(resolution,[],[f203,f207]) ).
fof(f281,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[],[f273,f87]) ).
fof(f285,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f281,f101]) ).
fof(f294,plain,
! [X0,X1] :
( is_a_theorem(not(and(X1,X0)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f285,f204]) ).
fof(f305,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f294,f87]) ).
fof(f306,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f305,f223]) ).
fof(f309,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f306,f232]) ).
fof(f323,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(f324,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f323,f92]) ).
fof(f325,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f323,f218]) ).
fof(f341,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(forward_demodulation,[],[f325,f95]) ).
fof(f342,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f324,f91]) ).
fof(f344,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f341,f207]) ).
fof(f345,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f342,f93]) ).
fof(f355,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(superposition,[],[f91,f345]) ).
fof(f421,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f344,f93]) ).
fof(f428,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X1,X0)),
inference(superposition,[],[f87,f421]) ).
fof(f429,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(superposition,[],[f95,f421]) ).
fof(f451,plain,
! [X0] : not(X0) = implies(X0,not(X0)),
inference(superposition,[],[f428,f345]) ).
fof(f462,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X0),implies(not(X0),not(X1))))),
inference(superposition,[],[f104,f428]) ).
fof(f491,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X0),or(X0,not(X1))))),
inference(forward_demodulation,[],[f462,f95]) ).
fof(f509,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),implies(not(X0),not(and(not(not(X0)),X1))))),
inference(superposition,[],[f104,f451]) ).
fof(f534,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,not(and(not(not(X0)),X1))))),
inference(forward_demodulation,[],[f509,f95]) ).
fof(f548,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,implies(not(not(X0)),not(X1))))),
inference(forward_demodulation,[],[f534,f428]) ).
fof(f558,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,or(not(X0),not(X1))))),
inference(forward_demodulation,[],[f548,f95]) ).
fof(f566,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,implies(X0,not(X1))))),
inference(forward_demodulation,[],[f558,f429]) ).
fof(f766,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),or(X0,not(X0)))),
inference(superposition,[],[f566,f451]) ).
fof(f871,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),or(not(X0),not(not(X0))))),
inference(superposition,[],[f766,f95]) ).
fof(f881,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,not(not(X0))))),
inference(forward_demodulation,[],[f871,f429]) ).
fof(f888,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,X0))),
inference(forward_demodulation,[],[f881,f421]) ).
fof(f892,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,[],[f888,f323]) ).
fof(f909,plain,
! [X0] : is_a_theorem(equiv(implies(X0,X0),or(X0,not(X0)))),
inference(forward_subsumption_resolution,[],[f892,f766]) ).
fof(f921,plain,
! [X0] : implies(X0,X0) = or(X0,not(X0)),
inference(resolution,[],[f909,f93]) ).
fof(f965,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(implies(not(X0),X1),or(X1,X0)))),
inference(superposition,[],[f114,f921]) ).
fof(f983,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(or(X0,X1),or(X1,X0)))),
inference(forward_demodulation,[],[f965,f95]) ).
fof(f1057,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[],[f983,f94]) ).
fof(f1075,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1057,f355]) ).
fof(f1086,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,[],[f1075,f323]) ).
fof(f1103,plain,
! [X0,X1] : is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1086,f1075]) ).
fof(f1105,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(resolution,[],[f1103,f93]) ).
fof(f1174,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X2,X1),or(not(X0),X1)))),
inference(superposition,[],[f491,f1105]) ).
fof(f1192,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X2,X1),implies(X0,X1)))),
inference(forward_demodulation,[],[f1174,f429]) ).
fof(f1205,plain,
$false,
inference(resolution,[],[f1192,f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL515+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 : n017.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:50:50 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
% 7.58/2.04 % (2761969)Detected formulas, will run a generic FOF schedule.
% 7.58/2.04 % (2761980)dis-21_1_sil=8000:lcm=predicate:random_seed=1537802285: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)
% 7.58/2.04 % (2761980)Refutation not found, incomplete strategy
% 7.58/2.04 % (2761980)------------------------------
% 7.58/2.04 % (2761980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761980)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761980)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2761980)Time elapsed: 0.001 s
% 7.58/2.04 % (2761980)Peak memory usage: 88 MB
% 7.58/2.04 % (2761980)Instructions burned: 1 (million)
% 7.58/2.04 % (2761976)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=1954073380:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.58/2.04 % (2761975)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=1086192669:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.58/2.04 % (2761978)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1715436279:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.58/2.04 % (2761974)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=4108807950:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.58/2.04 % (2761977)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2788342688:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.58/2.04 % (2761978)Refutation not found, incomplete strategy
% 7.58/2.04 % (2761978)------------------------------
% 7.58/2.04 % (2761978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761977)Refutation not found, incomplete strategy
% 7.58/2.04 % (2761977)------------------------------
% 7.58/2.04 % (2761977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761978)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761978)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2761978)Time elapsed: 0.001 s
% 7.58/2.04 % (2761977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761978)Peak memory usage: 86 MB
% 7.58/2.04 % (2761977)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761977)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2761977)Time elapsed: 0.001 s
% 7.58/2.04 % (2761977)Peak memory usage: 86 MB
% 7.58/2.04 % (2761979)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2710870741:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.58/2.04 % (2761979)Instruction limit reached!
% 7.58/2.04 % (2761979)------------------------------
% 7.58/2.04 % (2761979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761979)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761979)Termination reason: Instruction limit
% 7.58/2.04 % (2761979)Termination phase: Saturation
% 7.58/2.04 % (2761979)Time elapsed: 0.094 s
% 7.58/2.04 % (2761979)Peak memory usage: 90 MB
% 7.58/2.04 % (2761979)Instructions burned: 140 (million)
% 7.58/2.04 % (2761980)------------------------------
% 7.58/2.04 % (2761980)------------------------------
% 7.58/2.04 % (2761977)------------------------------
% 7.58/2.04 % (2761977)------------------------------
% 7.58/2.04 % (2761988)lrs+10_1_sil=8000:sp=occurrence:random_seed=3711575034:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.58/2.04 % (2761988)Refutation not found, incomplete strategy
% 7.58/2.04 % (2761988)------------------------------
% 7.58/2.04 % (2761988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761988)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761988)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2761988)Time elapsed: 0.0000 s
% 7.58/2.04 % (2761988)Peak memory usage: 86 MB
% 7.58/2.04 % (2761978)------------------------------
% 7.58/2.04 % (2761978)------------------------------
% 7.58/2.04 % (2761989)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2620364132:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.58/2.04 % (2761989)Refutation not found, incomplete strategy
% 7.58/2.04 % (2761989)------------------------------
% 7.58/2.04 % (2761989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761989)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761989)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2761989)Time elapsed: 0.001 s
% 7.58/2.04 % (2761989)Peak memory usage: 87 MB
% 7.58/2.04 % (2761988)------------------------------
% 7.58/2.04 % (2761988)------------------------------
% 7.58/2.04 % (2761992)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=3021245470:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 7.58/2.04 % (2761991)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3906740292:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 7.58/2.04 % (2761991)Refutation not found, incomplete strategy
% 7.58/2.04 % (2761991)------------------------------
% 7.58/2.04 % (2761991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761991)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761991)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2761991)Time elapsed: 0.001 s
% 7.58/2.04 % (2761991)Peak memory usage: 86 MB
% 7.58/2.04 % (2761989)------------------------------
% 7.58/2.04 % (2761989)------------------------------
% 7.58/2.04 % (2761994)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3164686082:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 7.58/2.04 % (2761994)Refutation not found, incomplete strategy
% 7.58/2.04 % (2761994)------------------------------
% 7.58/2.04 % (2761994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761994)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761994)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2761994)Time elapsed: 0.0000 s
% 7.58/2.04 % (2761994)Peak memory usage: 86 MB
% 7.58/2.04 % (2761976)Refutation not found, incomplete strategy
% 7.58/2.04 % (2761976)------------------------------
% 7.58/2.04 % (2761976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761976)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761976)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2761976)Time elapsed: 0.564 s
% 7.58/2.04 % (2761976)Peak memory usage: 125 MB
% 7.58/2.04 % (2761976)Instructions burned: 828 (million)
% 7.58/2.04 % (2761992)Instruction limit reached!
% 7.58/2.04 % (2761992)------------------------------
% 7.58/2.04 % (2761992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761992)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761992)Termination reason: Instruction limit
% 7.58/2.04 % (2761992)Termination phase: Saturation
% 7.58/2.04 % (2761992)Time elapsed: 0.166 s
% 7.58/2.04 % (2761992)Peak memory usage: 92 MB
% 7.58/2.04 % (2761992)Instructions burned: 248 (million)
% 7.58/2.04 % (2761991)------------------------------
% 7.58/2.04 % (2761991)------------------------------
% 7.58/2.04 % (2761998)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3519715100:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 7.58/2.04 % (2761994)------------------------------
% 7.58/2.04 % (2761994)------------------------------
% 7.58/2.04 % (2761999)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1180588821:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 7.58/2.04 % (2761999)Refutation not found, incomplete strategy
% 7.58/2.04 % (2761999)------------------------------
% 7.58/2.04 % (2761999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2761999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2761999)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2761999)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2761999)Time elapsed: 0.001 s
% 7.58/2.04 % (2761999)Peak memory usage: 88 MB
% 7.58/2.04 % (2761974)First to succeed.
% 7.58/2.04 % (2761974)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2761969"
% 7.58/2.04 % (2761976)------------------------------
% 7.58/2.04 % (2761976)------------------------------
% 7.58/2.04 % (2762000)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2756733246:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 7.58/2.04 % (2762002)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=587378713:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 7.58/2.04 % (2762002)Refutation not found, incomplete strategy
% 7.58/2.04 % (2762002)------------------------------
% 7.58/2.04 % (2762002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2762002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2762002)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2762002)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2762002)Time elapsed: 0.0000 s
% 7.58/2.04 % (2762002)Peak memory usage: 87 MB
% 7.58/2.04 % (2762000)Instruction limit reached!
% 7.58/2.04 % (2762000)------------------------------
% 7.58/2.04 % (2762000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2762000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2762000)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2762000)Termination reason: Instruction limit
% 7.58/2.04 % (2762000)Termination phase: Saturation
% 7.58/2.04 % (2762000)Time elapsed: 0.068 s
% 7.58/2.04 % (2762000)Peak memory usage: 88 MB
% 7.58/2.04 % (2762000)Instructions burned: 128 (million)
% 7.58/2.04 % (2762002)------------------------------
% 7.58/2.04 % (2762002)------------------------------
% 7.58/2.04 % (2761999)------------------------------
% 7.58/2.04 % (2761999)------------------------------
% 7.58/2.04 % (2762006)lrs+10_1_sil=8000:sp=occurrence:random_seed=3041098985:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 7.58/2.04 % (2762006)Refutation not found, incomplete strategy
% 7.58/2.04 % (2762006)------------------------------
% 7.58/2.04 % (2762006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (2762006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (2762006)CaDiCaL version: 2.1.3
% 7.58/2.04 % (2762006)Termination reason: Refutation not found, incomplete strategy
% 7.58/2.04 % (2762006)Time elapsed: 0.001 s
% 7.58/2.04 % (2762006)Peak memory usage: 87 MB
% 7.58/2.04 % (2761974)Refutation found. Thanks to Tanya!
% 7.58/2.04 % SZS status Theorem for theBenchmark
% 7.58/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 9.04/2.23 % (2761974)------------------------------
% 9.04/2.23 % (2761974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.04/2.23 % (2761974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.04/2.23 % (2761974)CaDiCaL version: 2.1.3
% 9.04/2.23 % (2761974)Termination reason: Refutation
% 9.04/2.23 % (2761974)Time elapsed: 0.754 s
% 9.04/2.23 % (2761974)Peak memory usage: 128 MB
% 9.04/2.23 % (2761974)Instructions burned: 1102 (million)
% 9.04/2.23 % (2761974)------------------------------
% 9.04/2.23 % (2761974)------------------------------
% 9.04/2.23 % (2761969)Success in time 1.195 s
% 9.04/2.23 % Vampire exiting
%------------------------------------------------------------------------------