%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL504+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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:38 AM UTC 2026
% Result : Theorem 11.48s 2.50s
% Output : Refutation 12.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 96
% Number of leaves : 18
% Syntax : Number of formulae : 206 ( 113 unt; 0 def)
% Number of atoms : 326 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 224 ( 104 ~; 99 |; 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 : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 380 ( 378 !; 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(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
fof(f18,axiom,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f44,negated_conjecture,
~ implies_2,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ implies_2,
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,implies(X0,X1)),implies(X0,X1)))
=> implies_2 ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f50,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f51,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f54,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f51]) ).
fof(f55,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f50]) ).
fof(f57,plain,
( implies_2
| ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),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,
( implies_2
| ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),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,
( implies_2
| ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),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,
~ implies_2,
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,implies(sK0,sK1)),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,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f91,f95]) ).
fof(f99,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f94,f91]) ).
fof(f101,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0))
| is_a_theorem(X1) ),
inference(superposition,[],[f94,f95]) ).
fof(f102,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(not(and(X1,X2)),not(and(X2,X0)))) ),
inference(resolution,[],[f89,f94]) ).
fof(f104,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X0),implies(implies(X0,X1),not(and(not(X1),X2))))),
inference(superposition,[],[f89,f87]) ).
fof(f105,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),implies(not(and(X2,X0)),implies(X0,X1)))),
inference(superposition,[],[f89,f87]) ).
fof(f107,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f105,f95]) ).
fof(f109,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f102,f95]) ).
fof(f110,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f107,f95]) ).
fof(f113,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,not(X0)),or(X0,X1)))),
inference(superposition,[],[f110,f95]) ).
fof(f114,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f113,f97]) ).
fof(f117,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f114,f94]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f117,f94]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(and(X0,X1)))
| is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f101,f109]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f161,f87]) ).
fof(f167,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(X1,X1),X0))
| is_a_theorem(not(and(not(X0),X1))) ),
inference(resolution,[],[f166,f91]) ).
fof(f184,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f167,f90]) ).
fof(f189,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(and(X0,X1))) ),
inference(resolution,[],[f184,f161]) ).
fof(f191,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[],[f184,f87]) ).
fof(f192,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f191,f95]) ).
fof(f194,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f192,f137]) ).
fof(f198,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(superposition,[],[f189,f95]) ).
fof(f199,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f198,f87]) ).
fof(f200,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,X1),and(X2,X0)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f199,f109]) ).
fof(f201,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f199,f192]) ).
fof(f206,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f201,f94]) ).
fof(f213,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X2)) ),
inference(resolution,[],[f200,f94]) ).
fof(f217,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f213,f99]) ).
fof(f231,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(not(X0)) ),
inference(resolution,[],[f194,f101]) ).
fof(f232,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(not(X0),X2))
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[],[f194,f137]) ).
fof(f235,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X2,X1)) ),
inference(forward_demodulation,[],[f232,f95]) ).
fof(f242,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(and(not(X0),not(X0)),X1)) ),
inference(resolution,[],[f98,f235]) ).
fof(f249,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f242,f97]) ).
fof(f250,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f249,f95]) ).
fof(f253,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(resolution,[],[f250,f94]) ).
fof(f285,plain,
! [X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f231,f90]) ).
fof(f294,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f285,f87]) ).
fof(f300,plain,
! [X0,X1] :
( is_a_theorem(not(and(X1,X0)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f294,f189]) ).
fof(f312,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f300,f87]) ).
fof(f313,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f312,f206]) ).
fof(f317,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f313,f217]) ).
fof(f330,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[],[f317,f86]) ).
fof(f331,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f330,f91]) ).
fof(f332,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f330,f201]) ).
fof(f348,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(forward_demodulation,[],[f332,f95]) ).
fof(f349,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f331,f90]) ).
fof(f351,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f348,f192]) ).
fof(f352,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f349,f93]) ).
fof(f356,plain,
! [X0] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[],[f87,f352]) ).
fof(f363,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(superposition,[],[f90,f352]) ).
fof(f385,plain,
! [X0] : or(X0,X0) = not(not(X0)),
inference(forward_demodulation,[],[f356,f95]) ).
fof(f418,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f351,f93]) ).
fof(f420,plain,
! [X0,X1] : and(X0,not(X1)) = not(implies(X0,X1)),
inference(superposition,[],[f418,f87]) ).
fof(f425,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X1,X0)),
inference(superposition,[],[f87,f418]) ).
fof(f426,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(superposition,[],[f95,f418]) ).
fof(f427,plain,
! [X2,X0,X1] : implies(implies(X1,not(X0)),X2) = or(and(X1,X0),X2),
inference(superposition,[],[f97,f418]) ).
fof(f446,plain,
! [X0] : not(X0) = implies(X0,not(X0)),
inference(superposition,[],[f425,f352]) ).
fof(f456,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X0),implies(not(X0),not(X1))))),
inference(superposition,[],[f104,f425]) ).
fof(f482,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X0),or(X0,not(X1))))),
inference(forward_demodulation,[],[f456,f95]) ).
fof(f498,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),implies(not(X0),not(and(not(not(X0)),X1))))),
inference(superposition,[],[f104,f446]) ).
fof(f522,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,not(and(not(not(X0)),X1))))),
inference(forward_demodulation,[],[f498,f95]) ).
fof(f535,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,implies(not(not(X0)),not(X1))))),
inference(forward_demodulation,[],[f522,f425]) ).
fof(f544,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,or(not(X0),not(X1))))),
inference(forward_demodulation,[],[f535,f95]) ).
fof(f551,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,implies(X0,not(X1))))),
inference(forward_demodulation,[],[f544,f426]) ).
fof(f599,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X1)),X0)),
inference(superposition,[],[f90,f420]) ).
fof(f632,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0)),
inference(forward_demodulation,[],[f599,f95]) ).
fof(f665,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(resolution,[],[f632,f199]) ).
fof(f668,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(forward_demodulation,[],[f665,f95]) ).
fof(f769,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),or(X0,not(X0)))),
inference(superposition,[],[f551,f446]) ).
fof(f824,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),or(not(X0),not(not(X0))))),
inference(superposition,[],[f769,f95]) ).
fof(f834,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,not(not(X0))))),
inference(forward_demodulation,[],[f824,f426]) ).
fof(f841,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,X0))),
inference(forward_demodulation,[],[f834,f418]) ).
fof(f846,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,[],[f841,f330]) ).
fof(f864,plain,
! [X0] : is_a_theorem(equiv(implies(X0,X0),or(X0,not(X0)))),
inference(forward_subsumption_resolution,[],[f846,f769]) ).
fof(f876,plain,
! [X0] : implies(X0,X0) = or(X0,not(X0)),
inference(resolution,[],[f864,f93]) ).
fof(f920,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(implies(not(X0),X1),or(X1,X0)))),
inference(superposition,[],[f114,f876]) ).
fof(f921,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),implies(X0,X0)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(superposition,[],[f117,f876]) ).
fof(f935,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),implies(X0,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f921,f426]) ).
fof(f936,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(or(X0,X1),or(X1,X0)))),
inference(forward_demodulation,[],[f920,f95]) ).
fof(f1049,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[],[f936,f94]) ).
fof(f1067,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1049,f363]) ).
fof(f1079,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,[],[f1067,f330]) ).
fof(f1097,plain,
! [X0,X1] : is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f1079,f1067]) ).
fof(f1099,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(resolution,[],[f1097,f93]) ).
fof(f1164,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X2,X1),or(not(X0),X1)))),
inference(superposition,[],[f482,f1099]) ).
fof(f1169,plain,
! [X0,X1] : implies(X1,X0) = or(X0,not(X1)),
inference(superposition,[],[f426,f1099]) ).
fof(f1179,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X2,X1),implies(X0,X1)))),
inference(forward_demodulation,[],[f1164,f426]) ).
fof(f1218,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X1))),
inference(superposition,[],[f668,f1169]) ).
fof(f1264,plain,
! [X2,X0,X1] :
( is_a_theorem(not(and(not(X0),X1)))
| ~ is_a_theorem(implies(implies(X2,X1),X0)) ),
inference(resolution,[],[f1218,f166]) ).
fof(f1272,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(not(X0),not(X1)))
| ~ is_a_theorem(implies(implies(X2,X1),X0)) ),
inference(forward_demodulation,[],[f1264,f425]) ).
fof(f1275,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(implies(implies(X2,X1),X0)) ),
inference(forward_demodulation,[],[f1272,f95]) ).
fof(f1277,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X2,X1),X0))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f1275,f1169]) ).
fof(f1283,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),or(X1,not(X2))))),
inference(resolution,[],[f1277,f482]) ).
fof(f1306,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),implies(X2,X1)))),
inference(forward_demodulation,[],[f1283,f1169]) ).
fof(f1360,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(implies(X1,not(X0)),not(X0)))),
inference(superposition,[],[f1306,f446]) ).
fof(f1363,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(and(X1,X0),not(X0)))),
inference(forward_demodulation,[],[f1360,f427]) ).
fof(f1369,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(X0,and(X1,X0)))),
inference(forward_demodulation,[],[f1363,f1169]) ).
fof(f1409,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,and(X1,not(X0))))),
inference(superposition,[],[f1369,f95]) ).
fof(f1411,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,not(implies(X1,X0))))),
inference(forward_demodulation,[],[f1409,f420]) ).
fof(f1416,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(implies(X1,X0),X0))),
inference(forward_demodulation,[],[f1411,f1169]) ).
fof(f1428,plain,
! [X2,X0,X1] :
( is_a_theorem(not(and(not(X0),X1)))
| ~ is_a_theorem(implies(implies(implies(X1,X2),X2),X0)) ),
inference(resolution,[],[f1416,f166]) ).
fof(f1438,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(not(X0),not(X1)))
| ~ is_a_theorem(implies(implies(implies(X1,X2),X2),X0)) ),
inference(forward_demodulation,[],[f1428,f425]) ).
fof(f1441,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(implies(implies(implies(X1,X2),X2),X0)) ),
inference(forward_demodulation,[],[f1438,f95]) ).
fof(f1443,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(implies(X1,X2),X2),X0))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f1441,f1169]) ).
fof(f1445,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X1)))
| ~ is_a_theorem(implies(X1,implies(X0,X1))) ),
inference(resolution,[],[f1443,f935]) ).
fof(f1479,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(forward_subsumption_resolution,[],[f1445,f1218]) ).
fof(f1490,plain,
! [X2,X0,X1] :
( is_a_theorem(not(and(not(X0),X1)))
| ~ is_a_theorem(implies(implies(X2,X2),X0)) ),
inference(resolution,[],[f1479,f166]) ).
fof(f1494,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,X1))),
inference(superposition,[],[f1479,f95]) ).
fof(f1497,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(not(X0),not(X1)))
| ~ is_a_theorem(implies(implies(X2,X2),X0)) ),
inference(forward_demodulation,[],[f1490,f425]) ).
fof(f1507,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(implies(implies(X2,X2),X0)) ),
inference(forward_demodulation,[],[f1497,f95]) ).
fof(f1509,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X2,X2),X0))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f1507,f1169]) ).
fof(f1526,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,implies(X2,X2)))),
inference(resolution,[],[f1509,f1218]) ).
fof(f2343,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X0),X1))
| is_a_theorem(X1) ),
inference(resolution,[],[f1494,f253]) ).
fof(f2375,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X0),X1),X1)),
inference(resolution,[],[f2343,f1416]) ).
fof(f2413,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X1,X1),X0)))
| is_a_theorem(equiv(X0,implies(implies(X1,X1),X0))) ),
inference(resolution,[],[f2375,f330]) ).
fof(f2423,plain,
! [X0,X1] : is_a_theorem(equiv(X0,implies(implies(X1,X1),X0))),
inference(forward_subsumption_resolution,[],[f2413,f1218]) ).
fof(f2515,plain,
! [X0,X1] : implies(implies(X1,X1),X0) = X0,
inference(resolution,[],[f2423,f93]) ).
fof(f2614,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,implies(X2,X2)),implies(X0,implies(X1,X0)))),
inference(superposition,[],[f1179,f2515]) ).
fof(f2780,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),implies(X1,implies(X2,X2))))
| is_a_theorem(equiv(implies(X0,implies(X1,X0)),implies(X1,implies(X2,X2)))) ),
inference(resolution,[],[f2614,f330]) ).
fof(f2800,plain,
! [X2,X0,X1] : is_a_theorem(equiv(implies(X0,implies(X1,X0)),implies(X1,implies(X2,X2)))),
inference(forward_subsumption_resolution,[],[f2780,f1526]) ).
fof(f3375,plain,
! [X2,X0,X1] : implies(X0,implies(X1,X0)) = implies(X1,implies(X2,X2)),
inference(resolution,[],[f2800,f93]) ).
fof(f3395,plain,
! [X0,X1] : implies(not(X0),not(X0)) = implies(X0,implies(X1,X1)),
inference(superposition,[],[f3375,f446]) ).
fof(f3743,plain,
! [X0,X1] : or(X0,not(X0)) = implies(X0,implies(X1,X1)),
inference(forward_demodulation,[],[f3395,f95]) ).
fof(f3755,plain,
! [X0,X1] : implies(X0,X0) = implies(X0,implies(X1,X1)),
inference(forward_demodulation,[],[f3743,f876]) ).
fof(f4355,plain,
! [X0,X1] : implies(X0,X0) = implies(X1,implies(X0,X1)),
inference(superposition,[],[f3375,f3755]) ).
fof(f5238,plain,
! [X0,X1] : or(X1,not(X1)) = implies(X0,implies(not(X1),X0)),
inference(superposition,[],[f95,f4355]) ).
fof(f5397,plain,
! [X0,X1] : or(X1,not(X1)) = implies(X0,or(X1,X0)),
inference(forward_demodulation,[],[f5238,f95]) ).
fof(f5433,plain,
! [X0,X1] : implies(X1,X1) = implies(X0,or(X1,X0)),
inference(forward_demodulation,[],[f5397,f876]) ).
fof(f5736,plain,
! [X0,X1] : implies(X0,X0) = or(X1,or(X0,not(X1))),
inference(superposition,[],[f95,f5433]) ).
fof(f5749,plain,
! [X0,X1] : implies(X0,X0) = or(X1,implies(X1,X0)),
inference(forward_demodulation,[],[f5736,f1169]) ).
fof(f6246,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X0),implies(implies(implies(X1,X0),X2),or(X2,X1)))),
inference(superposition,[],[f114,f5749]) ).
fof(f6267,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X1,X0),X2),or(X2,X1))),
inference(forward_demodulation,[],[f6246,f2515]) ).
fof(f8652,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),not(not(X0)))),
inference(superposition,[],[f6267,f385]) ).
fof(f8664,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),X0),X0)),
inference(forward_demodulation,[],[f8652,f418]) ).
fof(f8708,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(implies(X0,X1),X0)))
| is_a_theorem(equiv(X0,implies(implies(X0,X1),X0))) ),
inference(resolution,[],[f8664,f330]) ).
fof(f8754,plain,
! [X0,X1] : is_a_theorem(equiv(X0,implies(implies(X0,X1),X0))),
inference(forward_subsumption_resolution,[],[f8708,f1218]) ).
fof(f8958,plain,
! [X0,X1] : implies(implies(X0,X1),X0) = X0,
inference(resolution,[],[f8754,f93]) ).
fof(f9034,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,implies(X0,X1)),
inference(superposition,[],[f8958,f8958]) ).
fof(f9403,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(sK0,sK1))),
inference(superposition,[],[f92,f9034]) ).
fof(f9404,plain,
$false,
inference(forward_subsumption_resolution,[],[f9403,f363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL504+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n009.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 15:53:49 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 10.31/2.30 % (2209406)Detected formulas, will run a generic FOF schedule.
% 10.31/2.30 % (2209415)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=38847406:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.31/2.30 % (2209415)Refutation not found, incomplete strategy
% 10.31/2.30 % (2209415)------------------------------
% 10.31/2.30 % (2209415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.31/2.30 % (2209415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.31/2.30 % (2209415)CaDiCaL version: 2.1.3
% 10.31/2.30 % (2209415)Termination reason: Refutation not found, incomplete strategy
% 10.31/2.30 % (2209415)Time elapsed: 0.0000 s
% 10.31/2.30 % (2209415)Peak memory usage: 87 MB
% 10.31/2.30 % (2209411)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=2110852535:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.31/2.30 % (2209413)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=3911875085:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.31/2.30 % (2209412)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=3938458304:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.31/2.30 % (2209417)dis-21_1_sil=8000:lcm=predicate:random_seed=3553727802: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)
% 10.31/2.30 % (2209414)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2670313640:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.31/2.30 % (2209416)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3446926658:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.31/2.30 % (2209414)Refutation not found, incomplete strategy
% 10.31/2.30 % (2209414)------------------------------
% 10.31/2.30 % (2209414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.31/2.30 % (2209414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.31/2.30 % (2209414)CaDiCaL version: 2.1.3
% 10.31/2.30 % (2209414)Termination reason: Refutation not found, incomplete strategy
% 10.31/2.30 % (2209414)Time elapsed: 0.001 s
% 10.31/2.30 % (2209414)Peak memory usage: 87 MB
% 10.31/2.30 % (2209417)Refutation not found, incomplete strategy
% 10.31/2.30 % (2209417)------------------------------
% 10.31/2.30 % (2209417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.31/2.30 % (2209417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.31/2.30 % (2209417)CaDiCaL version: 2.1.3
% 10.31/2.30 % (2209417)Termination reason: Refutation not found, incomplete strategy
% 10.31/2.30 % (2209417)Time elapsed: 0.002 s
% 10.31/2.30 % (2209417)Peak memory usage: 88 MB
% 10.31/2.30 % (2209417)Instructions burned: 1 (million)
% 10.31/2.30 % (2209416)Instruction limit reached!
% 10.31/2.30 % (2209416)------------------------------
% 10.31/2.30 % (2209416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.31/2.30 % (2209416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.31/2.30 % (2209416)CaDiCaL version: 2.1.3
% 10.31/2.30 % (2209416)Termination reason: Instruction limit
% 10.31/2.30 % (2209416)Termination phase: Saturation
% 10.31/2.30 % (2209416)Time elapsed: 0.093 s
% 10.31/2.30 % (2209416)Peak memory usage: 90 MB
% 10.31/2.30 % (2209416)Instructions burned: 140 (million)
% 10.31/2.30 % (2209415)------------------------------
% 10.31/2.30 % (2209415)------------------------------
% 10.31/2.30 % (2209426)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3555937710:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.31/2.30 % (2209426)Refutation not found, incomplete strategy
% 10.31/2.30 % (2209426)------------------------------
% 10.31/2.30 % (2209426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.31/2.30 % (2209426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.31/2.30 % (2209426)CaDiCaL version: 2.1.3
% 10.31/2.30 % (2209426)Termination reason: Refutation not found, incomplete strategy
% 10.31/2.30 % (2209426)Time elapsed: 0.0000 s
% 10.31/2.30 % (2209426)Peak memory usage: 87 MB
% 10.31/2.30 % (2209425)lrs+10_1_sil=8000:sp=occurrence:random_seed=3432154827:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.74/2.42 % (2209425)Refutation not found, incomplete strategy
% 10.74/2.42 % (2209425)------------------------------
% 10.74/2.42 % (2209425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.74/2.42 % (2209425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.74/2.42 % (2209425)CaDiCaL version: 2.1.3
% 10.74/2.42 % (2209425)Termination reason: Refutation not found, incomplete strategy
% 10.74/2.42 % (2209425)Time elapsed: 0.001 s
% 10.74/2.42 % (2209425)Peak memory usage: 87 MB
% 10.74/2.42 % (2209417)------------------------------
% 10.74/2.42 % (2209417)------------------------------
% 10.74/2.42 % (2209414)------------------------------
% 10.74/2.42 % (2209414)------------------------------
% 10.74/2.42 % (2209426)------------------------------
% 10.74/2.42 % (2209426)------------------------------
% 10.74/2.42 % (2209429)lrs+1011_1_sil=32000:sp=occurrence:random_seed=483882874:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 10.74/2.42 % (2209429)Refutation not found, incomplete strategy
% 10.74/2.42 % (2209429)------------------------------
% 10.74/2.42 % (2209429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.74/2.42 % (2209429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.74/2.42 % (2209429)CaDiCaL version: 2.1.3
% 10.74/2.42 % (2209429)Termination reason: Refutation not found, incomplete strategy
% 10.74/2.42 % (2209429)Time elapsed: 0.001 s
% 10.74/2.42 % (2209429)Peak memory usage: 87 MB
% 10.74/2.42 % (2209430)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=2150496427:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 10.74/2.42 % (2209425)------------------------------
% 10.74/2.42 % (2209425)------------------------------
% 10.74/2.42 % (2209431)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4024846737:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 10.74/2.42 % (2209431)Refutation not found, incomplete strategy
% 10.74/2.42 % (2209431)------------------------------
% 10.74/2.42 % (2209431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.74/2.42 % (2209431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.74/2.42 % (2209431)CaDiCaL version: 2.1.3
% 10.74/2.42 % (2209431)Termination reason: Refutation not found, incomplete strategy
% 10.74/2.42 % (2209431)Time elapsed: 0.0000 s
% 10.74/2.42 % (2209431)Peak memory usage: 87 MB
% 10.74/2.42 % (2209413)Refutation not found, incomplete strategy
% 10.74/2.42 % (2209413)------------------------------
% 10.74/2.42 % (2209413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.74/2.42 % (2209413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.74/2.42 % (2209413)CaDiCaL version: 2.1.3
% 10.74/2.42 % (2209413)Termination reason: Refutation not found, incomplete strategy
% 10.74/2.42 % (2209413)Time elapsed: 0.562 s
% 10.74/2.42 % (2209413)Peak memory usage: 125 MB
% 10.74/2.42 % (2209413)Instructions burned: 829 (million)
% 10.74/2.42 % (2209430)Instruction limit reached!
% 10.74/2.42 % (2209430)------------------------------
% 10.74/2.42 % (2209430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.74/2.42 % (2209430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.74/2.42 % (2209430)CaDiCaL version: 2.1.3
% 10.74/2.42 % (2209430)Termination reason: Instruction limit
% 10.74/2.42 % (2209430)Termination phase: Saturation
% 10.74/2.42 % (2209430)Time elapsed: 0.166 s
% 10.74/2.42 % (2209430)Peak memory usage: 92 MB
% 10.74/2.42 % (2209430)Instructions burned: 248 (million)
% 10.74/2.42 % (2209429)------------------------------
% 10.74/2.42 % (2209429)------------------------------
% 10.74/2.42 % (2209431)------------------------------
% 10.74/2.42 % (2209431)------------------------------
% 10.74/2.42 % (2209434)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1812865312:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 10.74/2.42 % (2209436)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=469482594:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 10.74/2.42 % (2209436)Refutation not found, incomplete strategy
% 10.74/2.42 % (2209436)------------------------------
% 10.74/2.42 % (2209436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.74/2.42 % (2209436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.50 % (2209436)CaDiCaL version: 2.1.3
% 11.48/2.50 % (2209436)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.50 % (2209436)Time elapsed: 0.001 s
% 11.48/2.50 % (2209436)Peak memory usage: 88 MB
% 11.48/2.50 % (2209439)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1249243159:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 11.48/2.50 % (2209439)Refutation not found, incomplete strategy
% 11.48/2.50 % (2209439)------------------------------
% 11.48/2.50 % (2209439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.50 % (2209439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.50 % (2209439)CaDiCaL version: 2.1.3
% 11.48/2.50 % (2209439)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.50 % (2209439)Time elapsed: 0.001 s
% 11.48/2.50 % (2209439)Peak memory usage: 87 MB
% 11.48/2.50 % (2209413)------------------------------
% 11.48/2.50 % (2209413)------------------------------
% 11.48/2.50 % (2209437)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3925689460:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 11.48/2.50 % (2209437)Instruction limit reached!
% 11.48/2.50 % (2209437)------------------------------
% 11.48/2.50 % (2209437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.50 % (2209437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.50 % (2209437)CaDiCaL version: 2.1.3
% 11.48/2.50 % (2209437)Termination reason: Instruction limit
% 11.48/2.50 % (2209437)Termination phase: Saturation
% 11.48/2.50 % (2209437)Time elapsed: 0.069 s
% 11.48/2.50 % (2209437)Peak memory usage: 89 MB
% 11.48/2.50 % (2209437)Instructions burned: 128 (million)
% 11.48/2.50 % (2209439)------------------------------
% 11.48/2.50 % (2209439)------------------------------
% 11.48/2.50 % (2209443)lrs+10_1_sil=8000:sp=occurrence:random_seed=922508989:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 11.48/2.50 % (2209443)Refutation not found, incomplete strategy
% 11.48/2.50 % (2209443)------------------------------
% 11.48/2.50 % (2209443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.50 % (2209443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.50 % (2209443)CaDiCaL version: 2.1.3
% 11.48/2.50 % (2209443)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.50 % (2209443)Time elapsed: 0.001 s
% 11.48/2.50 % (2209443)Peak memory usage: 87 MB
% 11.48/2.50 % (2209436)------------------------------
% 11.48/2.50 % (2209436)------------------------------
% 11.48/2.50 % (2209444)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3523581693:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 11.48/2.50 % (2209444)Refutation not found, incomplete strategy
% 11.48/2.50 % (2209444)------------------------------
% 11.48/2.50 % (2209444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.50 % (2209444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.50 % (2209444)CaDiCaL version: 2.1.3
% 11.48/2.50 % (2209444)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.50 % (2209444)Time elapsed: 0.001 s
% 11.48/2.50 % (2209444)Peak memory usage: 88 MB
% 11.48/2.50 % (2209445)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1152327818:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 11.48/2.50 % (2209447)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3583614604:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 11.48/2.50 % (2209447)Refutation not found, incomplete strategy
% 11.48/2.50 % (2209447)------------------------------
% 11.48/2.50 % (2209447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.50 % (2209447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.50 % (2209447)CaDiCaL version: 2.1.3
% 11.48/2.50 % (2209447)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.50 % (2209447)Time elapsed: 0.001 s
% 11.48/2.50 % (2209447)Peak memory usage: 89 MB
% 11.48/2.50 % (2209411)First to succeed.
% 11.48/2.50 % (2209411)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2209406"
% 11.48/2.50 % (2209443)------------------------------
% 11.48/2.50 % (2209443)------------------------------
% 11.48/2.50 [W927 15:53:51.990305968 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990331051 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990352650 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990364964 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990379453 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990384793 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990398338 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990403742 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990416491 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990433779 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990447251 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 [W927 15:53:51.990452521 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 11.48/2.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 11.48/2.50 % (2209444)------------------------------
% 11.48/2.50 % (2209444)------------------------------
% 11.48/2.50 % (2209451)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2682170185:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 11.48/2.50 % (2209445)Refutation not found, incomplete strategy
% 11.48/2.50 % (2209445)------------------------------
% 11.48/2.50 % (2209445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.50 % (2209445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.50 % (2209445)CaDiCaL version: 2.1.3
% 11.48/2.50 % (2209445)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.50 % (2209445)Time elapsed: 0.320 s
% 11.48/2.50 % (2209445)Peak memory usage: 125 MB
% 11.48/2.50 % (2209445)Instructions burned: 824 (million)
% 11.48/2.50 % (2209451)Refutation not found, incomplete strategy
% 11.48/2.50 % (2209451)------------------------------
% 11.48/2.50 % (2209451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.48/2.50 % (2209451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.48/2.50 % (2209451)CaDiCaL version: 2.1.3
% 11.48/2.50 % (2209451)Termination reason: Refutation not found, incomplete strategy
% 11.48/2.50 % (2209451)Time elapsed: 0.001 s
% 11.48/2.50 % (2209451)Peak memory usage: 87 MB
% 11.48/2.50 % (2209447)------------------------------
% 11.48/2.50 % (2209447)------------------------------
% 11.48/2.50 % (2209411)Refutation found. Thanks to Tanya!
% 11.48/2.50 % SZS status Theorem for theBenchmark
% 11.48/2.50 % SZS output start Proof for theBenchmark
% See solution above
% 12.09/2.69 % (2209411)------------------------------
% 12.09/2.69 % (2209411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.09/2.69 % (2209411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.09/2.69 % (2209411)CaDiCaL version: 2.1.3
% 12.09/2.69 % (2209411)Termination reason: Refutation
% 12.09/2.69 % (2209411)Time elapsed: 1.207 s
% 12.09/2.69 % (2209411)Peak memory usage: 135 MB
% 12.09/2.69 % (2209411)Instructions burned: 1815 (million)
% 12.09/2.69 % (2209411)------------------------------
% 12.09/2.69 % (2209411)------------------------------
% 12.09/2.69 % (2209406)Success in time 1.639 s
% 12.09/2.69 % Vampire exiting
%------------------------------------------------------------------------------