%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL559+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:57 AM UTC 2026
% Result : Theorem 7.34s 13.69s
% Output : Refutation 9.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 26
% Syntax : Number of formulae : 166 ( 78 unt; 2 def)
% Number of atoms : 293 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 231 ( 104 ~; 95 |; 4 &)
% ( 10 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 242 ( 0 sgn 240 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
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(f33,axiom,
( modus_ponens_strict_implies
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
fof(f34,axiom,
( adjunction
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adjunction) ).
fof(f35,axiom,
( substitution_strict_equiv
<=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_strict_equiv) ).
fof(f45,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m1) ).
fof(f46,axiom,
( axiom_m2
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m2) ).
fof(f48,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m4) ).
fof(f49,axiom,
( axiom_m5
<=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m5) ).
fof(f57,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f58,axiom,
( op_strict_equiv
=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_equiv) ).
fof(f62,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f64,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f65,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f66,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f67,axiom,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f68,axiom,
axiom_m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f69,axiom,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(f71,axiom,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f72,axiom,
axiom_m5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m5) ).
fof(f73,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f74,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f77,conjecture,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f78,negated_conjecture,
~ or_2,
inference(negated_conjecture,[status(cth)],[f77]) ).
fof(f79,plain,
~ or_2,
inference(flattening,[],[f78]) ).
fof(f80,plain,
( axiom_m5
=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
inference(unused_predicate_definition_removal,[],[f49]) ).
fof(f81,plain,
( axiom_m4
=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f48]) ).
fof(f83,plain,
( axiom_m2
=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f84,plain,
( axiom_m1
=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f45]) ).
fof(f85,plain,
( substitution_strict_equiv
=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f86,plain,
( adjunction
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) ) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f87,plain,
( modus_ponens_strict_implies
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f88,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
=> or_2 ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f95,plain,
( or_2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f88]) ).
fof(f96,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f97,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f99,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(strict_implies(X0,X1)) )
| ~ modus_ponens_strict_implies ),
inference(ennf_transformation,[],[f87]) ).
fof(f100,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(strict_implies(X0,X1)) )
| ~ modus_ponens_strict_implies ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ adjunction ),
inference(ennf_transformation,[],[f86]) ).
fof(f102,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ adjunction ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) )
| ~ substitution_strict_equiv ),
inference(ennf_transformation,[],[f85]) ).
fof(f104,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(ennf_transformation,[],[f84]) ).
fof(f105,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(ennf_transformation,[],[f83]) ).
fof(f107,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(ennf_transformation,[],[f81]) ).
fof(f108,plain,
( ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ axiom_m5 ),
inference(ennf_transformation,[],[f80]) ).
fof(f110,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f57]) ).
fof(f111,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f58]) ).
fof(f112,plain,
( or_2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f95]) ).
fof(f114,plain,
( or_2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f112]) ).
fof(f115,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f96]) ).
fof(f116,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f97]) ).
fof(f118,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f100]) ).
fof(f119,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ adjunction ),
inference(cnf_transformation,[],[f102]) ).
fof(f120,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1))
| ~ substitution_strict_equiv ),
inference(cnf_transformation,[],[f103]) ).
fof(f121,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(cnf_transformation,[],[f104]) ).
fof(f122,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[],[f105]) ).
fof(f124,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(cnf_transformation,[],[f107]) ).
fof(f125,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ axiom_m5 ),
inference(cnf_transformation,[],[f108]) ).
fof(f127,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f110]) ).
fof(f128,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f111]) ).
fof(f131,plain,
op_strict_implies,
inference(cnf_transformation,[],[f62]) ).
fof(f133,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f64]) ).
fof(f134,plain,
modus_ponens_strict_implies,
inference(cnf_transformation,[],[f65]) ).
fof(f135,plain,
substitution_strict_equiv,
inference(cnf_transformation,[],[f66]) ).
fof(f136,plain,
adjunction,
inference(cnf_transformation,[],[f67]) ).
fof(f137,plain,
axiom_m1,
inference(cnf_transformation,[],[f68]) ).
fof(f138,plain,
axiom_m2,
inference(cnf_transformation,[],[f69]) ).
fof(f140,plain,
axiom_m4,
inference(cnf_transformation,[],[f71]) ).
fof(f141,plain,
axiom_m5,
inference(cnf_transformation,[],[f72]) ).
fof(f142,plain,
op_or,
inference(cnf_transformation,[],[f73]) ).
fof(f143,plain,
op_implies_and,
inference(cnf_transformation,[],[f74]) ).
fof(f146,plain,
~ or_2,
inference(cnf_transformation,[],[f79]) ).
fof(f147,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f128,f133]) ).
fof(f148,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f127,f131]) ).
fof(f150,plain,
! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))),
inference(forward_subsumption_resolution,[],[f125,f141]) ).
fof(f151,plain,
! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[],[f124,f140]) ).
fof(f153,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f122,f138]) ).
fof(f154,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
inference(forward_subsumption_resolution,[],[f121,f137]) ).
fof(f155,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f120,f135]) ).
fof(f156,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f119,f136]) ).
fof(f157,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f118,f134]) ).
fof(f159,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f116,f143]) ).
fof(f160,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f115,f142]) ).
fof(f161,plain,
~ is_a_theorem(implies(sK1,or(sK0,sK1))),
inference(forward_subsumption_resolution,[],[f114,f146]) ).
fof(f163,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f160,f159]) ).
fof(f164,plain,
! [X0,X1] : strict_implies(not(X0),X1) = necessarily(or(X0,X1)),
inference(superposition,[],[f148,f163]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(strict_implies(X0,X1),strict_implies(X1,X2)))
| is_a_theorem(strict_implies(X0,X2)) ),
inference(resolution,[],[f150,f157]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X0,X2))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f169,f156]) ).
fof(f180,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,and(X1,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f179,f151]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X1,X2)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f179,f153]) ).
fof(f190,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(resolution,[],[f181,f151]) ).
fof(f213,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_equiv(X0,X1)) ),
inference(superposition,[],[f156,f147]) ).
fof(f222,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X0,X1)))
| is_a_theorem(strict_equiv(X0,and(X0,X1))) ),
inference(resolution,[],[f213,f153]) ).
fof(f225,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))) ),
inference(resolution,[],[f213,f154]) ).
fof(f227,plain,
! [X0,X1] : is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))),
inference(forward_subsumption_resolution,[],[f225,f154]) ).
fof(f240,plain,
! [X0] : is_a_theorem(strict_equiv(X0,and(X0,X0))),
inference(resolution,[],[f222,f151]) ).
fof(f254,plain,
! [X0,X1] : and(X0,X1) = and(X1,X0),
inference(resolution,[],[f155,f227]) ).
fof(f255,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f155,f240]) ).
fof(f319,plain,
! [X0,X1] : implies(X1,X0) = not(and(not(X0),X1)),
inference(superposition,[],[f159,f254]) ).
fof(f340,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(superposition,[],[f159,f319]) ).
fof(f343,plain,
! [X0,X1] : implies(not(X0),X1) = or(X1,X0),
inference(forward_demodulation,[],[f340,f163]) ).
fof(f348,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(forward_demodulation,[],[f343,f163]) ).
fof(f352,plain,
~ is_a_theorem(implies(sK1,or(sK1,sK0))),
inference(superposition,[],[f161,f348]) ).
fof(f353,plain,
! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X1),X0),
inference(superposition,[],[f164,f348]) ).
fof(f354,plain,
! [X0,X1] : strict_implies(not(X0),X1) = strict_implies(not(X1),X0),
inference(forward_demodulation,[],[f353,f164]) ).
fof(f380,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(strict_implies(X2,not(X1)))
| is_a_theorem(strict_implies(X2,X0)) ),
inference(superposition,[],[f179,f354]) ).
fof(f381,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(strict_implies(X0,not(X1)))
| is_a_theorem(strict_equiv(X0,not(X1))) ),
inference(superposition,[],[f213,f354]) ).
fof(f382,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(and(X0,X1)),X2))
| is_a_theorem(strict_implies(not(X2),X0)) ),
inference(superposition,[],[f181,f354]) ).
fof(f383,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(and(X0,X0)),X1))
| ~ is_a_theorem(strict_implies(not(X1),X0)) ),
inference(superposition,[],[f180,f354]) ).
fof(f384,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),X0))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f383,f255]) ).
fof(f388,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,not(not(X1))))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f380,f190]) ).
fof(f399,plain,
! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0)),
inference(resolution,[],[f384,f190]) ).
fof(f423,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),X0)),
inference(resolution,[],[f388,f153]) ).
fof(f425,plain,
! [X0] : is_a_theorem(strict_implies(not(not(not(not(X0)))),X0)),
inference(resolution,[],[f388,f399]) ).
fof(f468,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,X1),X2))
| is_a_theorem(strict_implies(not(X2),X0)) ),
inference(superposition,[],[f382,f159]) ).
fof(f478,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(implies(X0,X1)),X0)),
inference(resolution,[],[f468,f190]) ).
fof(f492,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(X0),implies(X0,X1))),
inference(superposition,[],[f478,f354]) ).
fof(f529,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(not(not(not(X0))),not(X0)))
| is_a_theorem(strict_equiv(not(not(not(X0))),not(X0))) ),
inference(resolution,[],[f425,f381]) ).
fof(f544,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(not(X0))),not(X0))),
inference(forward_subsumption_resolution,[],[f529,f399]) ).
fof(f545,plain,
! [X0] : not(X0) = not(not(not(X0))),
inference(resolution,[],[f544,f155]) ).
fof(f562,plain,
! [X0,X1] : not(and(not(X0),X1)) = implies(X1,not(not(X0))),
inference(superposition,[],[f319,f545]) ).
fof(f577,plain,
! [X0,X1] : implies(X1,X0) = implies(X1,not(not(X0))),
inference(forward_demodulation,[],[f562,f319]) ).
fof(f608,plain,
! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,not(not(X1))),
inference(superposition,[],[f148,f577]) ).
fof(f622,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(X0,not(not(X1))),
inference(forward_demodulation,[],[f608,f148]) ).
fof(f640,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(not(not(X1))) ),
inference(superposition,[],[f157,f622]) ).
fof(f644,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(not(X1)),X0))
| ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_equiv(not(not(X1)),X0)) ),
inference(superposition,[],[f213,f622]) ).
fof(f718,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(strict_equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f644,f399]) ).
fof(f737,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f718,f190]) ).
fof(f742,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f737,f155]) ).
fof(f750,plain,
! [X0,X1] : and(not(X1),X0) = not(implies(X0,X1)),
inference(superposition,[],[f742,f319]) ).
fof(f764,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X0,X1)),
inference(superposition,[],[f319,f742]) ).
fof(f774,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,implies(not(X0),X1))),
inference(superposition,[],[f492,f742]) ).
fof(f781,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,or(X0,X1))),
inference(forward_demodulation,[],[f774,f163]) ).
fof(f895,plain,
! [X0,X1] : strict_implies(X1,not(X0)) = necessarily(not(and(X0,X1))),
inference(superposition,[],[f148,f764]) ).
fof(f904,plain,
! [X0,X1] : not(and(X0,not(X1))) = or(X1,not(X0)),
inference(superposition,[],[f163,f764]) ).
fof(f905,plain,
! [X0,X1] : implies(X0,X1) = or(X1,not(X0)),
inference(forward_demodulation,[],[f904,f159]) ).
fof(f922,plain,
! [X0,X1] : is_a_theorem(strict_implies(X1,implies(X0,X1))),
inference(superposition,[],[f781,f905]) ).
fof(f941,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(X0,implies(X2,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f922,f179]) ).
fof(f1542,plain,
! [X0] : necessarily(not(X0)) = strict_implies(X0,not(X0)),
inference(superposition,[],[f895,f255]) ).
fof(f1562,plain,
! [X0] : necessarily(X0) = strict_implies(not(X0),X0),
inference(superposition,[],[f1542,f742]) ).
fof(f1577,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,not(X0)))
| ~ is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f179,f1542]) ).
fof(f2091,plain,
! [X0,X1] :
( is_a_theorem(necessarily(implies(X0,X1)))
| ~ is_a_theorem(strict_implies(not(implies(X0,X1)),X1)) ),
inference(superposition,[],[f941,f1562]) ).
fof(f2114,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(not(implies(X0,X1)),X1)) ),
inference(forward_demodulation,[],[f2091,f148]) ).
fof(f2130,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(and(not(X1),X0),X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f2114,f750]) ).
fof(f2147,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,not(X1)))
| ~ is_a_theorem(strict_implies(and(not(not(X1)),X0),X1))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(resolution,[],[f2130,f1577]) ).
fof(f2169,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,not(X1)))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(forward_subsumption_resolution,[],[f2147,f423]) ).
fof(f2231,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(superposition,[],[f2169,f742]) ).
fof(f2254,definition,
( spl2_1
<=> ! [X1] : ~ is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f2255,plain,
( ! [X1] : ~ is_a_theorem(X1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f2254]) ).
fof(f2274,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1)
| is_a_theorem(not(not(X0))) ),
inference(resolution,[],[f2231,f640]) ).
fof(f2310,definition,
( spl2_5
<=> ! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f2311,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f2310]) ).
fof(f2313,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1) ),
inference(forward_demodulation,[],[f2274,f742]) ).
fof(f2318,plain,
( spl2_1
| spl2_5 ),
inference(avatar_split_clause,[],[f2313,f2310,f2254]) ).
fof(f2324,plain,
( $false
| ~ spl2_1 ),
inference(resolution,[],[f2255,f190]) ).
fof(f2374,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f2324]) ).
fof(f2375,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_5 ),
inference(superposition,[],[f2311,f148]) ).
fof(f2387,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ spl2_5 ),
inference(resolution,[],[f2375,f781]) ).
fof(f2458,plain,
( $false
| ~ spl2_5 ),
inference(resolution,[],[f2387,f352]) ).
fof(f2467,plain,
~ spl2_5,
inference(avatar_contradiction_clause,[],[f2458]) ).
cnf(s7,plain,
( spl2_1
| spl2_5 ),
inference(sat_conversion,[],[f2318]) ).
cnf(s28,plain,
~ spl2_1,
inference(sat_conversion,[],[f2374]) ).
cnf(s29,plain,
~ spl2_5,
inference(sat_conversion,[],[f2467]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s7,s29,s28]) ).
fof(f2473,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL559+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/11.86 % Computer : n013.cluster.edu
% 0.17/11.86 % Model : x86_64 x86_64
% 0.17/11.86 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/11.86 % Memory : 8046.5625MB
% 0.17/11.86 % OS : Linux 6.8.0-71-generic
% 0.17/11.86 % CPULimit : 300
% 0.17/11.86 % WCLimit : 300
% 0.17/11.86 % DateTime : Sun Sep 27 16:01:19 UTC 2026
% 0.17/11.86 % CPUTime :
% 0.17/11.86 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/11.91 Running first-order theorem proving
% 0.22/11.91 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.34/13.68 % (379886)Detected formulas, will run a generic FOF schedule.
% 7.34/13.68 % (379891)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=1328028392:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.34/13.68 % (379893)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=2017117787:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.34/13.68 % (379895)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=874615064:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.34/13.68 % (379892)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=3883172272:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.34/13.68 % (379894)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1988309135:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.34/13.68 % (379897)dis-21_1_sil=8000:lcm=predicate:random_seed=3355961644:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 7.34/13.68 % (379895)Refutation not found, incomplete strategy
% 7.34/13.68 % (379895)------------------------------
% 7.34/13.68 % (379895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/13.68 % (379895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/13.68 % (379894)Refutation not found, incomplete strategy
% 7.34/13.68 % (379894)------------------------------
% 7.34/13.68 % (379894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/13.68 % (379894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/13.68 % (379895)CaDiCaL version: 2.1.3
% 7.34/13.68 % (379895)Termination reason: Refutation not found, incomplete strategy
% 7.34/13.68 % (379895)Time elapsed: 0.001 s
% 7.34/13.68 % (379894)CaDiCaL version: 2.1.3
% 7.34/13.68 % (379895)Peak memory usage: 86 MB
% 7.34/13.68 % (379894)Termination reason: Refutation not found, incomplete strategy
% 7.34/13.68 % (379894)Time elapsed: 0.001 s
% 7.34/13.68 % (379894)Peak memory usage: 87 MB
% 7.34/13.68 % (379897)Refutation not found, incomplete strategy
% 7.34/13.68 % (379897)------------------------------
% 7.34/13.68 % (379897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/13.68 % (379897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/13.68 % (379897)CaDiCaL version: 2.1.3
% 7.34/13.68 % (379897)Termination reason: Refutation not found, incomplete strategy
% 7.34/13.68 % (379897)Time elapsed: 0.002 s
% 7.34/13.68 % (379897)Peak memory usage: 88 MB
% 7.34/13.68 % (379896)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=820767248:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.34/13.68 % (379896)Instruction limit reached!
% 7.34/13.68 % (379896)------------------------------
% 7.34/13.68 % (379896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/13.68 % (379896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/13.68 % (379896)CaDiCaL version: 2.1.3
% 7.34/13.68 % (379896)Termination reason: Instruction limit
% 7.34/13.69 % (379896)Termination phase: Saturation
% 7.34/13.69 % (379896)Time elapsed: 0.156 s
% 7.34/13.69 % (379896)Peak memory usage: 90 MB
% 7.34/13.69 % (379896)Instructions burned: 139 (million)
% 7.34/13.69 % (379895)------------------------------
% 7.34/13.69 % (379895)------------------------------
% 7.34/13.69 % (379894)------------------------------
% 7.34/13.69 % (379894)------------------------------
% 7.34/13.69 % (379897)------------------------------
% 7.34/13.69 % (379897)------------------------------
% 7.34/13.69 % (379905)lrs+10_1_sil=8000:sp=occurrence:random_seed=2283308359:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 7.34/13.69 % (379905)Refutation not found, incomplete strategy
% 7.34/13.69 % (379905)------------------------------
% 7.34/13.69 % (379905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/13.69 % (379905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/13.69 % (379905)CaDiCaL version: 2.1.3
% 7.34/13.69 % (379905)Termination reason: Refutation not found, incomplete strategy
% 7.34/13.69 % (379905)Time elapsed: 0.001 s
% 7.34/13.69 % (379905)Peak memory usage: 87 MB
% 7.34/13.69 % (379891)First to succeed.
% 7.34/13.69 % (379891)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-379886"
% 7.34/13.69 % (379908)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=644009044:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 7.34/13.69 % (379906)lrs+10_1_sil=32000:urr=on:br=off:random_seed=411121462:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 7.34/13.69 % (379907)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1634562159:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 7.34/13.69 % (379907)Refutation not found, incomplete strategy
% 7.34/13.69 % (379907)------------------------------
% 7.34/13.69 % (379907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/13.69 % (379907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/13.69 % (379907)CaDiCaL version: 2.1.3
% 7.34/13.69 % (379907)Termination reason: Refutation not found, incomplete strategy
% 7.34/13.69 % (379907)Time elapsed: 0.001 s
% 7.34/13.69 % (379907)Peak memory usage: 87 MB
% 7.34/13.69 % (379906)Refutation not found, incomplete strategy
% 7.34/13.69 % (379906)------------------------------
% 7.34/13.69 % (379906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/13.69 % (379906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/13.69 % (379906)CaDiCaL version: 2.1.3
% 7.34/13.69 % (379906)Termination reason: Refutation not found, incomplete strategy
% 7.34/13.69 % (379906)Time elapsed: 0.002 s
% 7.34/13.69 % (379906)Peak memory usage: 87 MB
% 7.34/13.69 % (379905)------------------------------
% 7.34/13.69 % (379905)------------------------------
% 7.34/13.69 % (379893)Refutation not found, incomplete strategy
% 7.34/13.69 % (379893)------------------------------
% 7.34/13.69 % (379893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.34/13.69 % (379893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.34/13.69 % (379893)CaDiCaL version: 2.1.3
% 7.34/13.69 % (379893)Termination reason: Refutation not found, incomplete strategy
% 7.34/13.69 % (379893)Time elapsed: 0.895 s
% 7.34/13.69 % (379893)Peak memory usage: 126 MB
% 7.34/13.69 % (379893)Instructions burned: 829 (million)
% 7.34/13.69 % (379891)Refutation found. Thanks to Tanya!
% 7.34/13.69 % SZS status Theorem for theBenchmark
% 7.34/13.69 % SZS output start Proof for theBenchmark
% See solution above
% 9.27/13.88 % (379891)------------------------------
% 9.27/13.88 % (379891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/13.88 % (379891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/13.88 % (379891)CaDiCaL version: 2.1.3
% 9.27/13.88 % (379891)Termination reason: Refutation
% 9.27/13.88 % (379891)Time elapsed: 0.722 s
% 9.27/13.88 % (379891)Peak memory usage: 132 MB
% 9.27/13.88 % (379891)Instructions burned: 1201 (million)
% 9.27/13.88 % (379891)------------------------------
% 9.27/13.88 % (379891)------------------------------
% 9.27/13.88 % (379886)Success in time 1.207 s
% 9.27/13.88 % Vampire exiting
%------------------------------------------------------------------------------