%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL476+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 : n012.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 11:52:33 AM UTC 2026
% Result : Theorem 4.96s 1.50s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 20
% Syntax : Number of formulae : 136 ( 58 unt; 0 def)
% Number of atoms : 243 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 196 ( 89 ~; 85 |; 2 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 11 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/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(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(f20,axiom,
( cn2
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
fof(f21,axiom,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
fof(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
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(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
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(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_or) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_modus_ponens) ).
fof(f36,axiom,
cn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn1) ).
fof(f37,axiom,
cn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn2) ).
fof(f38,axiom,
cn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn3) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(f40,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f41,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_equiv) ).
fof(f43,conjecture,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
fof(f44,negated_conjecture,
~ r2,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ r2,
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
=> r2 ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f47,plain,
( cn3
=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f48,plain,
( cn2
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f49,plain,
( cn1
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
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,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(ennf_transformation,[],[f49]) ).
fof(f58,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(ennf_transformation,[],[f48]) ).
fof(f59,plain,
( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(ennf_transformation,[],[f47]) ).
fof(f60,plain,
( r2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) ),
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] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f63,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f64,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f65,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f60]) ).
fof(f66,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f55]) ).
fof(f67,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f56]) ).
fof(f68,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(cnf_transformation,[],[f57]) ).
fof(f69,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(cnf_transformation,[],[f58]) ).
fof(f70,plain,
! [X0] :
( is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(cnf_transformation,[],[f59]) ).
fof(f71,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f72,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f61]) ).
fof(f73,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f62]) ).
fof(f74,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f63]) ).
fof(f75,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f64]) ).
fof(f76,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f78,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f79,plain,
cn1,
inference(cnf_transformation,[],[f36]) ).
fof(f80,plain,
cn2,
inference(cnf_transformation,[],[f37]) ).
fof(f81,plain,
cn3,
inference(cnf_transformation,[],[f38]) ).
fof(f82,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f83,plain,
op_implies_or,
inference(cnf_transformation,[],[f40]) ).
fof(f84,plain,
op_and,
inference(cnf_transformation,[],[f41]) ).
fof(f85,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f86,plain,
~ r2,
inference(cnf_transformation,[],[f45]) ).
fof(f87,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f75,f85]) ).
fof(f88,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[],[f74,f83]) ).
fof(f89,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f73,f84]) ).
fof(f90,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f72,f76]) ).
fof(f91,plain,
~ is_a_theorem(implies(sK1,or(sK0,sK1))),
inference(forward_subsumption_resolution,[],[f71,f86]) ).
fof(f92,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(forward_subsumption_resolution,[],[f70,f81]) ).
fof(f93,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(forward_subsumption_resolution,[],[f69,f80]) ).
fof(f94,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(forward_subsumption_resolution,[],[f68,f79]) ).
fof(f95,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f67,f82]) ).
fof(f96,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f66,f78]) ).
fof(f97,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[],[f89,f88]) ).
fof(f101,plain,
! [X2,X0,X1] : implies(and(not(X0),not(X1)),X2) = or(or(X0,X1),X2),
inference(superposition,[],[f88,f90]) ).
fof(f104,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f96,f93]) ).
fof(f105,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f96,f94]) ).
fof(f106,plain,
! [X0] :
( ~ is_a_theorem(implies(not(X0),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f96,f92]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f105,f96]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X2,X3),implies(X1,X3))))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f107,f94]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| is_a_theorem(implies(X0,implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(resolution,[],[f107,f105]) ).
fof(f111,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(not(X1),X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f107,f92]) ).
fof(f113,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f111,f93]) ).
fof(f114,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(not(X1),X0)) ),
inference(resolution,[],[f111,f105]) ).
fof(f120,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X1,not(X0))) ),
inference(resolution,[],[f110,f93]) ).
fof(f125,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f120,f111]) ).
fof(f130,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f114,f96]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(X2,X3),implies(X1,X3))) ),
inference(resolution,[],[f109,f96]) ).
fof(f278,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f125,f104]) ).
fof(f292,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f278,f125]) ).
fof(f329,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(X0,X1),implies(X0,not(X1))))
| is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[],[f106,f97]) ).
fof(f1056,plain,
! [X0,X1] :
( ~ is_a_theorem(not(and(X0,X1)))
| is_a_theorem(implies(X0,not(X1))) ),
inference(resolution,[],[f329,f292]) ).
fof(f1073,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),not(not(X1))))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f1056,f90]) ).
fof(f1076,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X1),X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1073,f125]) ).
fof(f1115,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(resolution,[],[f1076,f130]) ).
fof(f1320,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(superposition,[],[f1115,f88]) ).
fof(f1322,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X0))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1320,f1076]) ).
fof(f1347,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1322,f88]) ).
fof(f1356,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,not(X1)))
| is_a_theorem(not(X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1347,f104]) ).
fof(f1580,plain,
! [X0,X1] :
( is_a_theorem(not(implies(X0,not(X1))))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(not(not(X1)),X0)) ),
inference(resolution,[],[f1356,f114]) ).
fof(f1596,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(not(X1)),X0))
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ),
inference(forward_demodulation,[],[f1580,f97]) ).
fof(f1872,plain,
! [X0,X1] :
( is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1596,f278]) ).
fof(f1888,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1872,f87]) ).
fof(f1890,plain,
! [X0] :
( is_a_theorem(equiv(X0,implies(not(X0),X0)))
| ~ is_a_theorem(implies(X0,implies(not(X0),X0))) ),
inference(resolution,[],[f1888,f92]) ).
fof(f1891,plain,
! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[],[f1888,f113]) ).
fof(f1919,plain,
! [X0] : is_a_theorem(equiv(X0,X0)),
inference(forward_subsumption_resolution,[],[f1891,f113]) ).
fof(f1920,plain,
! [X0] : is_a_theorem(equiv(X0,implies(not(X0),X0))),
inference(forward_subsumption_resolution,[],[f1890,f93]) ).
fof(f1922,plain,
! [X0] : implies(not(X0),X0) = X0,
inference(resolution,[],[f1920,f95]) ).
fof(f1981,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(superposition,[],[f94,f1922]) ).
fof(f2071,plain,
! [X0] : is_a_theorem(implies(X0,implies(implies(X0,X0),X0))),
inference(superposition,[],[f1981,f1922]) ).
fof(f2081,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,X0)))
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(resolution,[],[f2071,f110]) ).
fof(f2160,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[],[f2081,f278]) ).
fof(f2173,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f2160,f113]) ).
fof(f2185,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f2173,f143]) ).
fof(f2415,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),X0))
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f2185,f1922]) ).
fof(f2432,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(equiv(X1,implies(X0,X1)))
| ~ is_a_theorem(implies(X1,implies(X0,X1))) ),
inference(resolution,[],[f2415,f1888]) ).
fof(f2463,plain,
! [X0,X1] :
( is_a_theorem(equiv(X1,implies(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f2432,f2173]) ).
fof(f2466,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| implies(X0,X1) = X1 ),
inference(resolution,[],[f2463,f95]) ).
fof(f2471,plain,
! [X0,X1] : implies(implies(X0,X0),X1) = X1,
inference(resolution,[],[f2466,f113]) ).
fof(f2489,plain,
! [X2,X0,X1] : implies(implies(X0,implies(X1,X0)),X2) = X2,
inference(resolution,[],[f2466,f2173]) ).
fof(f2506,plain,
! [X0,X1] : implies(equiv(X0,X0),X1) = X1,
inference(resolution,[],[f2466,f1919]) ).
fof(f2567,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,implies(X2,X2)),implies(X0,implies(X1,X0)))),
inference(superposition,[],[f94,f2471]) ).
fof(f2619,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(superposition,[],[f2173,f2471]) ).
fof(f2634,plain,
! [X0,X1] : not(not(X0)) = and(implies(X1,X1),X0),
inference(superposition,[],[f97,f2471]) ).
fof(f2945,plain,
! [X2,X0,X1] :
( is_a_theorem(equiv(implies(X0,implies(X1,X0)),implies(X1,implies(X2,X2))))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),implies(X1,implies(X2,X2)))) ),
inference(resolution,[],[f2567,f1888]) ).
fof(f2975,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X2,X2)))
| is_a_theorem(equiv(implies(X0,implies(X1,X0)),implies(X1,implies(X2,X2)))) ),
inference(forward_demodulation,[],[f2945,f2489]) ).
fof(f2985,plain,
! [X2,X0,X1] : is_a_theorem(equiv(implies(X0,implies(X1,X0)),implies(X1,implies(X2,X2)))),
inference(forward_subsumption_resolution,[],[f2975,f2619]) ).
fof(f3383,plain,
! [X2,X0,X1] : implies(X0,implies(X1,X0)) = implies(X1,implies(X2,X2)),
inference(resolution,[],[f2985,f95]) ).
fof(f3709,plain,
! [X2,X0,X1] : implies(X2,X2) = implies(X0,implies(equiv(X1,X1),X0)),
inference(superposition,[],[f2506,f3383]) ).
fof(f3784,plain,
! [X2,X0] : implies(X0,X0) = implies(X2,X2),
inference(forward_demodulation,[],[f3709,f2506]) ).
fof(f4150,plain,
! [X0,X1] : not(implies(X0,X0)) = and(not(X1),X1),
inference(superposition,[],[f97,f3784]) ).
fof(f4433,plain,
! [X0,X1] : or(not(X1),X1) = not(not(implies(X0,X0))),
inference(superposition,[],[f90,f4150]) ).
fof(f4443,plain,
! [X0,X1] : implies(X1,X1) = not(not(implies(X0,X0))),
inference(forward_demodulation,[],[f4433,f88]) ).
fof(f4742,plain,
! [X2,X3,X0,X1] : or(or(not(implies(X1,X1)),X2),X3) = implies(and(implies(X0,X0),not(X2)),X3),
inference(superposition,[],[f101,f4443]) ).
fof(f4864,plain,
! [X2,X3,X1] : or(or(not(implies(X1,X1)),X2),X3) = implies(not(not(not(X2))),X3),
inference(forward_demodulation,[],[f4742,f2634]) ).
fof(f4911,plain,
! [X2,X3,X1] : implies(not(not(not(X2))),X3) = or(implies(implies(X1,X1),X2),X3),
inference(forward_demodulation,[],[f4864,f88]) ).
fof(f4924,plain,
! [X2,X3] : or(X2,X3) = implies(not(not(not(X2))),X3),
inference(forward_demodulation,[],[f4911,f2471]) ).
fof(f5207,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(superposition,[],[f2173,f4924]) ).
fof(f5442,plain,
$false,
inference(resolution,[],[f5207,f91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL476+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 15:48:49 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 4.96/1.50 % (2541500)Detected formulas, will run a generic FOF schedule.
% 4.96/1.50 % (2541509)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1425475957:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.96/1.50 % (2541511)dis-21_1_sil=8000:lcm=predicate:random_seed=2740025219: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)
% 4.96/1.50 % (2541506)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=3390302269:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.96/1.50 % (2541508)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2987575370:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.96/1.50 % (2541510)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3383878334:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.96/1.50 % (2541507)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=2761088058:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.96/1.50 % (2541505)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=4056475674:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.96/1.50 % (2541509)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541509)------------------------------
% 4.96/1.50 % (2541509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541508)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541508)------------------------------
% 4.96/1.50 % (2541508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541509)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541509)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541509)Time elapsed: 0.0000 s
% 4.96/1.50 % (2541508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541509)Peak memory usage: 86 MB
% 4.96/1.50 % (2541508)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541508)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541508)Time elapsed: 0.0000 s
% 4.96/1.50 % (2541508)Peak memory usage: 86 MB
% 4.96/1.50 % (2541511)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541511)------------------------------
% 4.96/1.50 % (2541511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541511)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541511)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541511)Time elapsed: 0.001 s
% 4.96/1.50 % (2541511)Peak memory usage: 88 MB
% 4.96/1.50 % (2541511)Instructions burned: 1 (million)
% 4.96/1.50 % (2541510)Instruction limit reached!
% 4.96/1.50 % (2541510)------------------------------
% 4.96/1.50 % (2541510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541510)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541510)Termination reason: Instruction limit
% 4.96/1.50 % (2541510)Termination phase: Saturation
% 4.96/1.50 % (2541510)Time elapsed: 0.049 s
% 4.96/1.50 % (2541510)Peak memory usage: 90 MB
% 4.96/1.50 % (2541510)Instructions burned: 139 (million)
% 4.96/1.50 % (2541509)------------------------------
% 4.96/1.50 % (2541509)------------------------------
% 4.96/1.50 % (2541508)------------------------------
% 4.96/1.50 % (2541508)------------------------------
% 4.96/1.50 % (2541511)------------------------------
% 4.96/1.50 % (2541511)------------------------------
% 4.96/1.50 % (2541519)lrs+10_1_sil=8000:sp=occurrence:random_seed=2466528217:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.96/1.50 % (2541519)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541519)------------------------------
% 4.96/1.50 % (2541519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541519)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541519)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541519)Time elapsed: 0.0000 s
% 4.96/1.50 % (2541519)Peak memory usage: 87 MB
% 4.96/1.50 % (2541522)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=267080138:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.96/1.50 % (2541521)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3726263812:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.96/1.50 % (2541520)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2053667939:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.96/1.50 % (2541520)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541520)------------------------------
% 4.96/1.50 % (2541520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541521)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541521)------------------------------
% 4.96/1.50 % (2541521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541520)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541521)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541520)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541520)Time elapsed: 0.0000 s
% 4.96/1.50 % (2541521)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541521)Time elapsed: 0.0000 s
% 4.96/1.50 % (2541520)Peak memory usage: 86 MB
% 4.96/1.50 % (2541521)Peak memory usage: 86 MB
% 4.96/1.50 % (2541507)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541507)------------------------------
% 4.96/1.50 % (2541507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541507)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541507)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541507)Time elapsed: 0.321 s
% 4.96/1.50 % (2541507)Peak memory usage: 124 MB
% 4.96/1.50 % (2541507)Instructions burned: 829 (million)
% 4.96/1.50 % (2541519)------------------------------
% 4.96/1.50 % (2541519)------------------------------
% 4.96/1.50 % (2541522)Instruction limit reached!
% 4.96/1.50 % (2541522)------------------------------
% 4.96/1.50 % (2541522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541522)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541522)Termination reason: Instruction limit
% 4.96/1.50 % (2541522)Termination phase: Saturation
% 4.96/1.50 % (2541522)Time elapsed: 0.086 s
% 4.96/1.50 % (2541522)Peak memory usage: 92 MB
% 4.96/1.50 % (2541522)Instructions burned: 248 (million)
% 4.96/1.50 % (2541521)------------------------------
% 4.96/1.50 % (2541521)------------------------------
% 4.96/1.50 % (2541520)------------------------------
% 4.96/1.50 % (2541520)------------------------------
% 4.96/1.50 % (2541507)------------------------------
% 4.96/1.50 % (2541507)------------------------------
% 4.96/1.50 % (2541527)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=263671415:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.96/1.50 % (2541527)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541527)------------------------------
% 4.96/1.50 % (2541527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541527)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541527)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541527)Time elapsed: 0.0000 s
% 4.96/1.50 % (2541527)Peak memory usage: 86 MB
% 4.96/1.50 % (2541528)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1967716788:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.96/1.50 % (2541530)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2670382984:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 4.96/1.50 % (2541529)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1537976420:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.96/1.50 % (2541529)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541529)------------------------------
% 4.96/1.50 % (2541529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541529)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541529)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541529)Time elapsed: 0.001 s
% 4.96/1.50 % (2541529)Peak memory usage: 88 MB
% 4.96/1.50 % (2541532)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=283295235:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 4.96/1.50 % (2541532)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541532)------------------------------
% 4.96/1.50 % (2541532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541532)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541532)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541532)Time elapsed: 0.0000 s
% 4.96/1.50 % (2541532)Peak memory usage: 87 MB
% 4.96/1.50 % (2541530)Instruction limit reached!
% 4.96/1.50 % (2541530)------------------------------
% 4.96/1.50 % (2541530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541530)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541530)Termination reason: Instruction limit
% 4.96/1.50 % (2541530)Termination phase: Saturation
% 4.96/1.50 % (2541530)Time elapsed: 0.040 s
% 4.96/1.50 % (2541530)Peak memory usage: 88 MB
% 4.96/1.50 % (2541530)Instructions burned: 129 (million)
% 4.96/1.50 % (2541527)------------------------------
% 4.96/1.50 % (2541527)------------------------------
% 4.96/1.50 % (2541505)First to succeed.
% 4.96/1.50 % (2541505)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2541500"
% 4.96/1.50 % (2541529)------------------------------
% 4.96/1.50 % (2541529)------------------------------
% 4.96/1.50 % (2541537)lrs+10_1_sil=8000:sp=occurrence:random_seed=320528248:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 4.96/1.50 % (2541532)------------------------------
% 4.96/1.50 % (2541532)------------------------------
% 4.96/1.50 % (2541538)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=959115952:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 4.96/1.50 % (2541538)Refutation not found, incomplete strategy
% 4.96/1.50 % (2541538)------------------------------
% 4.96/1.50 % (2541538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.50 % (2541538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.50 % (2541538)CaDiCaL version: 2.1.3
% 4.96/1.50 % (2541538)Termination reason: Refutation not found, incomplete strategy
% 4.96/1.50 % (2541538)Time elapsed: 0.001 s
% 4.96/1.50 % (2541538)Peak memory usage: 88 MB
% 4.96/1.50 % (2541505)Refutation found. Thanks to Tanya!
% 4.96/1.50 % SZS status Theorem for theBenchmark
% 4.96/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/1.60 % (2541505)------------------------------
% 0.08/1.60 % (2541505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.60 % (2541505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.60 % (2541505)CaDiCaL version: 2.1.3
% 0.08/1.60 % (2541505)Termination reason: Refutation
% 0.08/1.60 % (2541505)Time elapsed: 0.653 s
% 0.08/1.60 % (2541505)Peak memory usage: 134 MB
% 0.08/1.60 % (2541505)Instructions burned: 1747 (million)
% 0.08/1.60 % (2541505)------------------------------
% 0.08/1.60 % (2541505)------------------------------
% 0.08/1.60 % (2541500)Success in time 0.961 s
% 0.08/1.60 % Vampire exiting
%------------------------------------------------------------------------------