%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL514+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 13.95s 3.16s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 18
% Syntax : Number of formulae : 142 ( 70 unt; 0 def)
% Number of atoms : 238 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 175 ( 79 ~; 75 |; 2 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 234 ( 232 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2) ).
fof(f18,axiom,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f44,negated_conjecture,
~ equivalence_3,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ equivalence_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] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
=> equivalence_3 ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f50,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f51,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f54,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f51]) ).
fof(f55,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f50]) ).
fof(f57,plain,
( equivalence_3
| ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(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,
( equivalence_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK0),equiv(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,
( equivalence_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK0),equiv(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,
~ equivalence_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,sK0),equiv(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(f99,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[],[f95,f87]) ).
fof(f105,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f94,f91]) ).
fof(f109,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0))
| is_a_theorem(X1) ),
inference(superposition,[],[f94,f95]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(not(and(X1,X2)),not(and(X2,X0)))) ),
inference(resolution,[],[f89,f94]) ).
fof(f115,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),implies(not(and(X2,X0)),implies(X0,X1)))),
inference(superposition,[],[f89,f87]) ).
fof(f116,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X0),or(and(X0,X1),not(and(X1,X2))))),
inference(superposition,[],[f89,f95]) ).
fof(f117,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f115,f95]) ).
fof(f121,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f110,f95]) ).
fof(f122,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f117,f95]) ).
fof(f126,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,not(X0)),or(X0,X1)))),
inference(superposition,[],[f122,f95]) ).
fof(f127,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f126,f99]) ).
fof(f128,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f127,f94]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f128,f94]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(and(X0,X1)))
| is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f109,f121]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f165,f87]) ).
fof(f171,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(X1,X1),X0))
| is_a_theorem(not(and(not(X0),X1))) ),
inference(resolution,[],[f170,f91]) ).
fof(f192,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f171,f90]) ).
fof(f197,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(and(X0,X1))) ),
inference(resolution,[],[f192,f165]) ).
fof(f199,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[],[f192,f87]) ).
fof(f200,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f199,f95]) ).
fof(f202,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f200,f141]) ).
fof(f206,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(superposition,[],[f197,f95]) ).
fof(f207,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f206,f87]) ).
fof(f208,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,X1),and(X2,X0)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f207,f121]) ).
fof(f209,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f207,f200]) ).
fof(f214,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f209,f94]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X2)) ),
inference(resolution,[],[f208,f94]) ).
fof(f224,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f221,f105]) ).
fof(f241,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(not(X0)) ),
inference(resolution,[],[f202,f109]) ).
fof(f295,plain,
! [X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f241,f90]) ).
fof(f304,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f295,f87]) ).
fof(f310,plain,
! [X0,X1] :
( is_a_theorem(not(and(X1,X0)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f304,f197]) ).
fof(f323,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f310,f87]) ).
fof(f324,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f323,f214]) ).
fof(f328,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f324,f224]) ).
fof(f344,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[],[f328,f86]) ).
fof(f345,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f344,f91]) ).
fof(f346,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f344,f209]) ).
fof(f363,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(forward_demodulation,[],[f346,f95]) ).
fof(f364,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f345,f90]) ).
fof(f366,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f363,f200]) ).
fof(f368,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f364,f93]) ).
fof(f376,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,not(and(X0,X1))))),
inference(superposition,[],[f116,f368]) ).
fof(f377,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X0),not(X0)))),
inference(superposition,[],[f116,f368]) ).
fof(f393,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(superposition,[],[f91,f368]) ).
fof(f464,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),or(X0,not(X0)))),
inference(superposition,[],[f376,f368]) ).
fof(f473,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f366,f93]) ).
fof(f476,plain,
! [X0,X1] : and(X0,not(X1)) = not(implies(X0,X1)),
inference(superposition,[],[f473,f87]) ).
fof(f481,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X1,X0)),
inference(superposition,[],[f87,f473]) ).
fof(f482,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(superposition,[],[f95,f473]) ).
fof(f738,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X1)),X0)),
inference(superposition,[],[f90,f476]) ).
fof(f787,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0)),
inference(forward_demodulation,[],[f738,f95]) ).
fof(f824,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(resolution,[],[f787,f207]) ).
fof(f827,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(forward_demodulation,[],[f824,f95]) ).
fof(f1420,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),or(not(X0),not(not(X0))))),
inference(superposition,[],[f464,f95]) ).
fof(f1430,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,not(not(X0))))),
inference(forward_demodulation,[],[f1420,f482]) ).
fof(f1437,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,X0))),
inference(forward_demodulation,[],[f1430,f473]) ).
fof(f1442,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,[],[f1437,f344]) ).
fof(f1460,plain,
! [X0] : is_a_theorem(equiv(implies(X0,X0),or(X0,not(X0)))),
inference(forward_subsumption_resolution,[],[f1442,f464]) ).
fof(f1473,plain,
! [X0] : implies(X0,X0) = or(X0,not(X0)),
inference(resolution,[],[f1460,f93]) ).
fof(f1519,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(implies(not(X0),X1),or(X1,X0)))),
inference(superposition,[],[f127,f1473]) ).
fof(f1538,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(or(X0,X1),or(X1,X0)))),
inference(forward_demodulation,[],[f1519,f95]) ).
fof(f1637,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[],[f1538,f94]) ).
fof(f1655,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1637,f393]) ).
fof(f1667,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,[],[f1655,f344]) ).
fof(f1687,plain,
! [X0,X1] : is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1667,f1655]) ).
fof(f1690,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(resolution,[],[f1687,f93]) ).
fof(f1770,plain,
! [X0,X1] : implies(X1,X0) = or(X0,not(X1)),
inference(superposition,[],[f482,f1690]) ).
fof(f1866,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X1))),
inference(superposition,[],[f827,f1770]) ).
fof(f1926,plain,
! [X2,X0,X1] :
( is_a_theorem(not(and(not(X0),X1)))
| ~ is_a_theorem(implies(implies(X2,X1),X0)) ),
inference(resolution,[],[f1866,f170]) ).
fof(f1936,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(not(X0),not(X1)))
| ~ is_a_theorem(implies(implies(X2,X1),X0)) ),
inference(forward_demodulation,[],[f1926,f481]) ).
fof(f1941,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(implies(implies(X2,X1),X0)) ),
inference(forward_demodulation,[],[f1936,f95]) ).
fof(f1943,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X2,X1),X0))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f1941,f1770]) ).
fof(f1978,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(and(X0,X1),not(X1)))),
inference(resolution,[],[f1943,f377]) ).
fof(f1998,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(forward_demodulation,[],[f1978,f1770]) ).
fof(f2021,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(superposition,[],[f1998,f86]) ).
fof(f2249,plain,
$false,
inference(resolution,[],[f2021,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL514+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 % Computer : n008.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 27 15:55:24 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.95/3.16 % (1414797)Detected formulas, will run a generic FOF schedule.
% 13.95/3.16 % (1414803)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=3619583385:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 13.95/3.16 % (1414807)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=501168997:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 13.95/3.16 % (1414802)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=2004900781:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 13.95/3.16 % (1414805)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2244703883:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 13.95/3.16 % (1414805)Refutation not found, incomplete strategy
% 13.95/3.16 % (1414805)------------------------------
% 13.95/3.16 % (1414805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414805)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414805)Termination reason: Refutation not found, incomplete strategy
% 13.95/3.16 % (1414805)Time elapsed: 0.001 s
% 13.95/3.16 % (1414805)Peak memory usage: 86 MB
% 13.95/3.16 % (1414806)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1719458522:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 13.95/3.16 % (1414808)dis-21_1_sil=8000:lcm=predicate:random_seed=4131460025: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)
% 13.95/3.16 % (1414804)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=800556287:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 13.95/3.16 % (1414806)Refutation not found, incomplete strategy
% 13.95/3.16 % (1414806)------------------------------
% 13.95/3.16 % (1414806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414806)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414806)Termination reason: Refutation not found, incomplete strategy
% 13.95/3.16 % (1414806)Time elapsed: 0.001 s
% 13.95/3.16 % (1414806)Peak memory usage: 86 MB
% 13.95/3.16 % (1414808)Refutation not found, incomplete strategy
% 13.95/3.16 % (1414808)------------------------------
% 13.95/3.16 % (1414808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414808)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414808)Termination reason: Refutation not found, incomplete strategy
% 13.95/3.16 % (1414808)Time elapsed: 0.003 s
% 13.95/3.16 % (1414808)Peak memory usage: 88 MB
% 13.95/3.16 % (1414808)Instructions burned: 1 (million)
% 13.95/3.16 % (1414807)Instruction limit reached!
% 13.95/3.16 % (1414807)------------------------------
% 13.95/3.16 % (1414807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414807)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414807)Termination reason: Instruction limit
% 13.95/3.16 % (1414807)Termination phase: Saturation
% 13.95/3.16 % (1414807)Time elapsed: 0.129 s
% 13.95/3.16 % (1414807)Peak memory usage: 90 MB
% 13.95/3.16 % (1414807)Instructions burned: 139 (million)
% 13.95/3.16 % (1414816)lrs+10_1_sil=8000:sp=occurrence:random_seed=2525617671:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 13.95/3.16 % (1414816)Refutation not found, incomplete strategy
% 13.95/3.16 % (1414816)------------------------------
% 13.95/3.16 % (1414816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414816)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414816)Termination reason: Refutation not found, incomplete strategy
% 13.95/3.16 % (1414816)Time elapsed: 0.002 s
% 13.95/3.16 % (1414816)Peak memory usage: 88 MB
% 13.95/3.16 % (1414805)------------------------------
% 13.95/3.16 % (1414805)------------------------------
% 13.95/3.16 % (1414806)------------------------------
% 13.95/3.16 % (1414806)------------------------------
% 13.95/3.16 % (1414808)------------------------------
% 13.95/3.16 % (1414808)------------------------------
% 13.95/3.16 % (1414818)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2900682683:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 13.95/3.16 % (1414818)Refutation not found, incomplete strategy
% 13.95/3.16 % (1414818)------------------------------
% 13.95/3.16 % (1414818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414818)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414818)Termination reason: Refutation not found, incomplete strategy
% 13.95/3.16 % (1414818)Time elapsed: 0.001 s
% 13.95/3.16 % (1414818)Peak memory usage: 87 MB
% 13.95/3.16 % (1414819)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4264690980:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 13.95/3.16 % (1414819)Refutation not found, incomplete strategy
% 13.95/3.16 % (1414819)------------------------------
% 13.95/3.16 % (1414819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414819)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414819)Termination reason: Refutation not found, incomplete strategy
% 13.95/3.16 % (1414819)Time elapsed: 0.001 s
% 13.95/3.16 % (1414819)Peak memory usage: 86 MB
% 13.95/3.16 % (1414820)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=4222815205:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 13.95/3.16 % (1414816)------------------------------
% 13.95/3.16 % (1414816)------------------------------
% 13.95/3.16 % (1414804)Refutation not found, incomplete strategy
% 13.95/3.16 % (1414804)------------------------------
% 13.95/3.16 % (1414804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414804)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414804)Termination reason: Refutation not found, incomplete strategy
% 13.95/3.16 % (1414804)Time elapsed: 0.904 s
% 13.95/3.16 % (1414804)Peak memory usage: 126 MB
% 13.95/3.16 % (1414804)Instructions burned: 829 (million)
% 13.95/3.16 % (1414820)Instruction limit reached!
% 13.95/3.16 % (1414820)------------------------------
% 13.95/3.16 % (1414820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414820)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414820)Termination reason: Instruction limit
% 13.95/3.16 % (1414820)Termination phase: Saturation
% 13.95/3.16 % (1414820)Time elapsed: 0.245 s
% 13.95/3.16 % (1414820)Peak memory usage: 92 MB
% 13.95/3.16 % (1414820)Instructions burned: 249 (million)
% 13.95/3.16 % (1414824)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=374686493:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2989 on theBenchmark for (2989ds/294Mi)
% 13.95/3.16 % (1414824)Refutation not found, incomplete strategy
% 13.95/3.16 % (1414824)------------------------------
% 13.95/3.16 % (1414824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414818)------------------------------
% 13.95/3.16 % (1414818)------------------------------
% 13.95/3.16 % (1414824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414824)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414824)Termination reason: Refutation not found, incomplete strategy
% 13.95/3.16 % (1414824)Time elapsed: 0.001 s
% 13.95/3.16 % (1414824)Peak memory usage: 86 MB
% 13.95/3.16 % (1414819)------------------------------
% 13.95/3.16 % (1414819)------------------------------
% 13.95/3.16 % (1414825)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3318925796:i=2350_2987 on theBenchmark for (2987ds/2350Mi)
% 13.95/3.16 % (1414802)First to succeed.
% 13.95/3.16 % (1414802)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1414797"
% 13.95/3.16 % (1414827)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2831489062:cts=off:i=113:fsr=off:ss=included:sgt=4_2987 on theBenchmark for (2987ds/113Mi)
% 13.95/3.16 % (1414827)Refutation not found, incomplete strategy
% 13.95/3.16 % (1414827)------------------------------
% 13.95/3.16 % (1414827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414827)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414827)Termination reason: Refutation not found, incomplete strategy
% 13.95/3.16 % (1414827)Time elapsed: 0.002 s
% 13.95/3.16 % (1414827)Peak memory usage: 88 MB
% 13.95/3.16 % (1414804)------------------------------
% 13.95/3.16 % (1414804)------------------------------
% 13.95/3.16 % (1414828)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2672886945:i=127:av=off:fsr=off:sup=off_2986 on theBenchmark for (2986ds/127Mi)
% 13.95/3.16 % (1414824)------------------------------
% 13.95/3.16 % (1414824)------------------------------
% 13.95/3.16 % (1414828)Instruction limit reached!
% 13.95/3.16 % (1414828)------------------------------
% 13.95/3.16 % (1414828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414828)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414828)Termination reason: Instruction limit
% 13.95/3.16 % (1414828)Termination phase: Saturation
% 13.95/3.16 % (1414828)Time elapsed: 0.114 s
% 13.95/3.16 % (1414828)Peak memory usage: 88 MB
% 13.95/3.16 % (1414828)Instructions burned: 127 (million)
% 13.95/3.16 % (1414831)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2045735635:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2984 on theBenchmark for (2984ds/114Mi)
% 13.95/3.16 % (1414831)Refutation not found, incomplete strategy
% 13.95/3.16 % (1414831)------------------------------
% 13.95/3.16 % (1414831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.95/3.16 % (1414831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.95/3.16 % (1414831)CaDiCaL version: 2.1.3
% 13.95/3.16 % (1414831)Termination reason: Refutation not found, incomplete strategy
% 13.95/3.16 % (1414831)Time elapsed: 0.002 s
% 13.95/3.16 % (1414831)Peak memory usage: 87 MB
% 13.95/3.16 % (1414833)lrs+10_1_sil=8000:sp=occurrence:random_seed=2774706651:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2983 on theBenchmark for (2983ds/907Mi)
% 13.95/3.16 % (1414802)Refutation found. Thanks to Tanya!
% 13.95/3.16 % SZS status Theorem for theBenchmark
% 13.95/3.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/3.41 % (1414802)------------------------------
% 0.25/3.41 % (1414802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.25/3.41 % (1414802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/3.41 % (1414802)CaDiCaL version: 2.1.3
% 0.25/3.41 % (1414802)Termination reason: Refutation
% 0.25/3.41 % (1414802)Time elapsed: 1.284 s
% 0.25/3.41 % (1414802)Peak memory usage: 130 MB
% 0.25/3.41 % (1414802)Instructions burned: 1232 (million)
% 0.25/3.41 % (1414802)------------------------------
% 0.25/3.41 % (1414802)------------------------------
% 0.25/3.41 % (1414797)Success in time 1.964 s
% 0.25/3.41 % Vampire exiting
%------------------------------------------------------------------------------