%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL553+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 11:52:55 AM UTC 2026
% Result : Theorem 10.62s 2.30s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 28
% Syntax : Number of formulae : 188 ( 94 unt; 2 def)
% Number of atoms : 319 ( 56 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 237 ( 106 ~; 97 |; 4 &)
% ( 11 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 294 ( 0 sgn 292 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
fof(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',adjunction) ).
fof(f35,axiom,
( substitution_strict_equiv
<=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_m1) ).
fof(f46,axiom,
( axiom_m2
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m2) ).
fof(f47,axiom,
( axiom_m3
<=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m3) ).
fof(f48,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_m5) ).
fof(f57,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',op_strict_equiv) ).
fof(f62,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f64,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f65,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f66,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f67,axiom,
adjunction,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f68,axiom,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f69,axiom,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(f70,axiom,
axiom_m3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m3) ).
fof(f71,axiom,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f72,axiom,
axiom_m5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m5) ).
fof(f73,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f74,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f77,conjecture,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f78,negated_conjecture,
~ implies_2,
inference(negated_conjecture,[status(cth)],[f77]) ).
fof(f79,plain,
~ implies_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(f82,plain,
( axiom_m3
=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) ),
inference(unused_predicate_definition_removal,[],[f47]) ).
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(implies(X0,implies(X0,X1)),implies(X0,X1)))
=> implies_2 ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f95,plain,
( implies_2
| ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(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(f106,plain,
( ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))
| ~ axiom_m3 ),
inference(ennf_transformation,[],[f82]) ).
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,
( 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)],[f95]) ).
fof(f114,plain,
( implies_2
| ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(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(f123,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))
| ~ axiom_m3 ),
inference(cnf_transformation,[],[f106]) ).
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(f139,plain,
axiom_m3,
inference(cnf_transformation,[],[f70]) ).
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,
~ implies_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(f152,plain,
! [X2,X0,X1] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))),
inference(forward_subsumption_resolution,[],[f123,f139]) ).
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(implies(sK0,implies(sK0,sK1)),implies(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(f166,plain,
! [X0,X1] : strict_implies(not(X0),X1) = necessarily(or(X0,X1)),
inference(superposition,[],[f148,f163]) ).
fof(f168,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(f181,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,[],[f168,f156]) ).
fof(f182,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,and(X1,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f181,f151]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X1,X2)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f181,f153]) ).
fof(f186,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(resolution,[],[f184,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(f224,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,[],[f224,f154]) ).
fof(f240,plain,
! [X0] : is_a_theorem(strict_equiv(X0,and(X0,X0))),
inference(resolution,[],[f222,f151]) ).
fof(f257,plain,
! [X0,X1] : and(X0,X1) = and(X1,X0),
inference(resolution,[],[f155,f227]) ).
fof(f258,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f155,f240]) ).
fof(f278,plain,
! [X0] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[],[f159,f258]) ).
fof(f286,plain,
! [X0] : or(X0,X0) = not(not(X0)),
inference(forward_demodulation,[],[f278,f163]) ).
fof(f326,plain,
! [X0,X1] : implies(X1,X0) = not(and(not(X0),X1)),
inference(superposition,[],[f159,f257]) ).
fof(f329,plain,
! [X2,X0,X1] : is_a_theorem(strict_implies(and(X0,and(X1,X2)),and(X1,and(X2,X0)))),
inference(superposition,[],[f152,f257]) ).
fof(f342,plain,
! [X0] : strict_implies(not(X0),X0) = necessarily(not(not(X0))),
inference(superposition,[],[f166,f286]) ).
fof(f352,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(superposition,[],[f159,f326]) ).
fof(f357,plain,
! [X0,X1] : implies(not(X0),X1) = or(X1,X0),
inference(forward_demodulation,[],[f352,f163]) ).
fof(f361,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(forward_demodulation,[],[f357,f163]) ).
fof(f367,plain,
! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X1),X0),
inference(superposition,[],[f166,f361]) ).
fof(f369,plain,
! [X0,X1] : strict_implies(not(X0),X1) = strict_implies(not(X1),X0),
inference(forward_demodulation,[],[f367,f166]) ).
fof(f374,plain,
! [X2,X0,X1] : strict_implies(implies(X0,X1),X2) = strict_implies(not(X2),and(not(X1),X0)),
inference(superposition,[],[f369,f326]) ).
fof(f395,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,[],[f181,f369]) ).
fof(f396,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,f369]) ).
fof(f398,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(and(X0,X0)),X1))
| ~ is_a_theorem(strict_implies(not(X1),X0)) ),
inference(superposition,[],[f182,f369]) ).
fof(f399,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),X0))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f398,f258]) ).
fof(f403,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,not(not(X1))))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f395,f186]) ).
fof(f414,plain,
! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0)),
inference(resolution,[],[f399,f186]) ).
fof(f440,plain,
! [X0] : is_a_theorem(strict_implies(not(not(not(not(X0)))),X0)),
inference(resolution,[],[f403,f414]) ).
fof(f493,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,X1),X2))
| is_a_theorem(strict_implies(not(X2),not(X1))) ),
inference(superposition,[],[f184,f374]) ).
fof(f519,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(implies(X0,X1)),not(X1))),
inference(resolution,[],[f493,f186]) ).
fof(f535,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(not(X0)),implies(X1,X0))),
inference(superposition,[],[f519,f369]) ).
fof(f788,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,[],[f440,f396]) ).
fof(f806,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(not(X0))),not(X0))),
inference(forward_subsumption_resolution,[],[f788,f414]) ).
fof(f807,plain,
! [X0] : not(X0) = not(not(not(X0))),
inference(resolution,[],[f806,f155]) ).
fof(f827,plain,
! [X0,X1] : not(and(not(X0),X1)) = implies(X1,not(not(X0))),
inference(superposition,[],[f326,f807]) ).
fof(f855,plain,
! [X0,X1] : implies(X1,X0) = implies(X1,not(not(X0))),
inference(forward_demodulation,[],[f827,f326]) ).
fof(f902,plain,
! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,not(not(X1))),
inference(superposition,[],[f148,f855]) ).
fof(f922,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(X0,not(not(X1))),
inference(forward_demodulation,[],[f902,f148]) ).
fof(f937,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(not(not(X1))) ),
inference(superposition,[],[f157,f922]) ).
fof(f941,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,f922]) ).
fof(f1001,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(strict_equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f941,f414]) ).
fof(f1025,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f1001,f186]) ).
fof(f1030,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f1025,f155]) ).
fof(f1038,plain,
! [X0,X1] : not(implies(X0,X1)) = and(not(X1),X0),
inference(superposition,[],[f1030,f326]) ).
fof(f1039,plain,
! [X0] : necessarily(X0) = strict_implies(not(X0),X0),
inference(superposition,[],[f342,f1030]) ).
fof(f1044,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X0))),
inference(superposition,[],[f535,f1030]) ).
fof(f1052,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X1,X0)),
inference(superposition,[],[f159,f1030]) ).
fof(f1056,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X0,X1)),
inference(superposition,[],[f326,f1030]) ).
fof(f1083,plain,
! [X0,X1] : implies(X1,not(X0)) = implies(X0,not(X1)),
inference(forward_demodulation,[],[f1052,f1056]) ).
fof(f1093,plain,
! [X2,X0,X1] : implies(X2,implies(X0,X1)) = implies(and(not(X1),X0),not(X2)),
inference(superposition,[],[f1083,f326]) ).
fof(f1115,plain,
! [X0,X1] : strict_implies(X1,not(X0)) = necessarily(implies(X0,not(X1))),
inference(superposition,[],[f148,f1083]) ).
fof(f1136,plain,
! [X0,X1] : strict_implies(X0,not(X1)) = strict_implies(X1,not(X0)),
inference(forward_demodulation,[],[f1115,f148]) ).
fof(f1396,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(X0,implies(X2,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1044,f181]) ).
fof(f1807,plain,
! [X0,X1] :
( is_a_theorem(necessarily(implies(X0,X1)))
| ~ is_a_theorem(strict_implies(not(implies(X0,X1)),X1)) ),
inference(superposition,[],[f1396,f1039]) ).
fof(f1814,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(not(implies(X0,X1)),X1)) ),
inference(forward_demodulation,[],[f1807,f148]) ).
fof(f1826,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(and(not(X1),X0),X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1814,f1038]) ).
fof(f2276,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,not(and(not(not(X0)),X1))))
| is_a_theorem(strict_implies(X1,not(X0))) ),
inference(superposition,[],[f1826,f1136]) ).
fof(f2277,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X1,not(not(not(X0))))))
| is_a_theorem(strict_implies(X1,not(X0))) ),
inference(forward_demodulation,[],[f2276,f1056]) ).
fof(f2283,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X1,not(X0))))
| is_a_theorem(strict_implies(X1,not(X0))) ),
inference(forward_demodulation,[],[f2277,f855]) ).
fof(f2410,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),implies(X1,X0)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(superposition,[],[f2283,f1030]) ).
fof(f2423,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(not(X1),X1)) ),
inference(resolution,[],[f2410,f1396]) ).
fof(f2442,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f2423,f1039]) ).
fof(f2773,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1)
| is_a_theorem(not(not(X0))) ),
inference(resolution,[],[f2442,f937]) ).
fof(f2836,definition,
( spl2_5
<=> ! [X1] : ~ is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f2837,plain,
( ! [X1] : ~ is_a_theorem(X1)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f2836]) ).
fof(f2839,definition,
( spl2_6
<=> ! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f2840,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f2839]) ).
fof(f2850,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1) ),
inference(forward_demodulation,[],[f2773,f1030]) ).
fof(f2851,plain,
( spl2_5
| spl2_6 ),
inference(avatar_split_clause,[],[f2850,f2839,f2836]) ).
fof(f2907,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_6 ),
inference(superposition,[],[f2840,f148]) ).
fof(f2912,plain,
( ! [X0] : is_a_theorem(implies(X0,X0))
| ~ spl2_6 ),
inference(resolution,[],[f2907,f186]) ).
fof(f4648,plain,
! [X2,X0,X1] : is_a_theorem(strict_implies(and(X0,and(X2,X1)),and(X2,and(X0,X1)))),
inference(superposition,[],[f329,f257]) ).
fof(f5048,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(and(X0,and(X1,X2)),and(X1,and(X0,X2))))
| is_a_theorem(strict_equiv(and(X0,and(X1,X2)),and(X1,and(X0,X2)))) ),
inference(resolution,[],[f4648,f213]) ).
fof(f5071,plain,
! [X2,X0,X1] : is_a_theorem(strict_equiv(and(X0,and(X1,X2)),and(X1,and(X0,X2)))),
inference(forward_subsumption_resolution,[],[f5048,f4648]) ).
fof(f5072,plain,
! [X2,X0,X1] : and(X0,and(X1,X2)) = and(X1,and(X0,X2)),
inference(resolution,[],[f5071,f155]) ).
fof(f5202,plain,
! [X2,X0,X1] : implies(and(X0,X2),X1) = not(and(X0,and(not(X1),X2))),
inference(superposition,[],[f326,f5072]) ).
fof(f5213,plain,
! [X2,X0,X1] : implies(and(X0,X2),X1) = implies(and(not(X1),X2),not(X0)),
inference(forward_demodulation,[],[f5202,f1056]) ).
fof(f5239,plain,
! [X2,X0,X1] : implies(X0,implies(X2,X1)) = implies(and(X0,X2),X1),
inference(forward_demodulation,[],[f5213,f1093]) ).
fof(f5258,plain,
! [X0,X1] : implies(X0,X1) = implies(X0,implies(X0,X1)),
inference(superposition,[],[f5239,f258]) ).
fof(f5390,plain,
! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,implies(X0,X1)),
inference(superposition,[],[f148,f5258]) ).
fof(f5428,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(sK0,sK1))),
inference(superposition,[],[f161,f5258]) ).
fof(f5429,plain,
( $false
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f5428,f2912]) ).
fof(f5430,plain,
~ spl2_6,
inference(avatar_contradiction_clause,[],[f5429]) ).
fof(f5441,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(X0,implies(X0,X1)),
inference(forward_demodulation,[],[f5390,f148]) ).
fof(f5480,plain,
! [X2,X0,X1] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(implies(X0,X1),X2)),strict_implies(X0,X2))),
inference(superposition,[],[f150,f5441]) ).
fof(f5517,plain,
( $false
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f5480,f2837]) ).
fof(f5518,plain,
~ spl2_5,
inference(avatar_contradiction_clause,[],[f5517]) ).
cnf(s6,plain,
( spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f2851]) ).
cnf(s15,plain,
~ spl2_6,
inference(sat_conversion,[],[f5430]) ).
cnf(s18,plain,
~ spl2_5,
inference(sat_conversion,[],[f5518]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s6,s15,s18]) ).
fof(f5527,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL553+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 16:06:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.56/2.26 % (3752597)Detected formulas, will run a generic FOF schedule.
% 9.56/2.26 % (3752606)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=494015813:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.56/2.26 % (3752606)Refutation not found, incomplete strategy
% 9.56/2.26 % (3752606)------------------------------
% 9.56/2.26 % (3752606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.26 % (3752606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.26 % (3752606)CaDiCaL version: 2.1.3
% 9.56/2.26 % (3752606)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.26 % (3752606)Time elapsed: 0.0000 s
% 9.56/2.26 % (3752606)Peak memory usage: 87 MB
% 9.56/2.26 % (3752602)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=1173835531:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.56/2.26 % (3752603)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=2781176169:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.56/2.26 % (3752608)dis-21_1_sil=8000:lcm=predicate:random_seed=2007316202: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)
% 9.56/2.26 % (3752607)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2032996317:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.56/2.26 % (3752605)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3348671267:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.56/2.26 % (3752604)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=3181869131:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.56/2.26 % (3752605)Refutation not found, incomplete strategy
% 9.56/2.26 % (3752605)------------------------------
% 9.56/2.26 % (3752605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.26 % (3752605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.26 % (3752605)CaDiCaL version: 2.1.3
% 9.56/2.26 % (3752605)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.26 % (3752605)Time elapsed: 0.001 s
% 9.56/2.26 % (3752605)Peak memory usage: 86 MB
% 9.56/2.26 % (3752608)Refutation not found, incomplete strategy
% 9.56/2.26 % (3752608)------------------------------
% 9.56/2.26 % (3752608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.26 % (3752608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.26 % (3752608)CaDiCaL version: 2.1.3
% 9.56/2.26 % (3752608)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.26 % (3752608)Time elapsed: 0.001 s
% 9.56/2.26 % (3752608)Peak memory usage: 88 MB
% 9.56/2.26 % (3752608)Instructions burned: 1 (million)
% 9.56/2.26 % (3752607)Instruction limit reached!
% 9.56/2.26 % (3752607)------------------------------
% 9.56/2.26 % (3752607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.26 % (3752607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.26 % (3752607)CaDiCaL version: 2.1.3
% 9.56/2.26 % (3752607)Termination reason: Instruction limit
% 9.56/2.26 % (3752607)Termination phase: Saturation
% 9.56/2.26 % (3752607)Time elapsed: 0.092 s
% 9.56/2.26 % (3752607)Peak memory usage: 90 MB
% 9.56/2.26 % (3752607)Instructions burned: 140 (million)
% 9.56/2.26 % (3752606)------------------------------
% 9.56/2.26 % (3752606)------------------------------
% 9.56/2.26 % (3752617)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2701938459:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.56/2.26 % (3752617)Refutation not found, incomplete strategy
% 9.56/2.26 % (3752617)------------------------------
% 9.56/2.26 % (3752617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.26 % (3752617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.26 % (3752617)CaDiCaL version: 2.1.3
% 9.56/2.26 % (3752617)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.26 % (3752617)Time elapsed: 0.001 s
% 9.56/2.26 % (3752617)Peak memory usage: 87 MB
% 9.56/2.26 % (3752608)------------------------------
% 9.56/2.26 % (3752608)------------------------------
% 9.56/2.30 % (3752605)------------------------------
% 9.56/2.30 % (3752605)------------------------------
% 9.56/2.30 % (3752616)lrs+10_1_sil=8000:sp=occurrence:random_seed=3195673473:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.56/2.30 % (3752616)Refutation not found, incomplete strategy
% 9.56/2.30 % (3752616)------------------------------
% 9.56/2.30 % (3752616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752616)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752616)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.30 % (3752616)Time elapsed: 0.001 s
% 9.56/2.30 % (3752616)Peak memory usage: 87 MB
% 9.56/2.30 % (3752617)------------------------------
% 9.56/2.30 % (3752617)------------------------------
% 9.56/2.30 % (3752621)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=3859120015:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 9.56/2.30 % (3752620)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2012558116:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 9.56/2.30 % (3752620)Refutation not found, incomplete strategy
% 9.56/2.30 % (3752620)------------------------------
% 9.56/2.30 % (3752620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752620)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752620)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.30 % (3752620)Time elapsed: 0.001 s
% 9.56/2.30 % (3752620)Peak memory usage: 87 MB
% 9.56/2.30 % (3752622)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2873350701:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 9.56/2.30 % (3752622)Refutation not found, incomplete strategy
% 9.56/2.30 % (3752622)------------------------------
% 9.56/2.30 % (3752622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752622)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752622)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.30 % (3752622)Time elapsed: 0.0000 s
% 9.56/2.30 % (3752622)Peak memory usage: 87 MB
% 9.56/2.30 % (3752616)------------------------------
% 9.56/2.30 % (3752616)------------------------------
% 9.56/2.30 % (3752621)Instruction limit reached!
% 9.56/2.30 % (3752621)------------------------------
% 9.56/2.30 % (3752621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752621)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752621)Termination reason: Instruction limit
% 9.56/2.30 % (3752621)Termination phase: Saturation
% 9.56/2.30 % (3752621)Time elapsed: 0.147 s
% 9.56/2.30 % (3752621)Peak memory usage: 92 MB
% 9.56/2.30 % (3752621)Instructions burned: 249 (million)
% 9.56/2.30 % (3752604)Refutation not found, incomplete strategy
% 9.56/2.30 % (3752604)------------------------------
% 9.56/2.30 % (3752604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752604)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752604)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.30 % (3752604)Time elapsed: 0.565 s
% 9.56/2.30 % (3752604)Peak memory usage: 125 MB
% 9.56/2.30 % (3752604)Instructions burned: 829 (million)
% 9.56/2.30 % (3752622)------------------------------
% 9.56/2.30 % (3752622)------------------------------
% 9.56/2.30 % (3752620)------------------------------
% 9.56/2.30 % (3752620)------------------------------
% 9.56/2.30 % (3752626)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4276916229:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 9.56/2.30 % (3752627)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3321237079:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 9.56/2.30 % (3752627)Refutation not found, incomplete strategy
% 9.56/2.30 % (3752627)------------------------------
% 9.56/2.30 % (3752627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752627)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752627)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.30 % (3752627)Time elapsed: 0.001 s
% 9.56/2.30 % (3752627)Peak memory usage: 88 MB
% 9.56/2.30 % (3752628)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=928370551:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 9.56/2.30 % (3752628)Instruction limit reached!
% 9.56/2.30 % (3752628)------------------------------
% 9.56/2.30 % (3752628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752628)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752628)Termination reason: Instruction limit
% 9.56/2.30 % (3752628)Termination phase: Saturation
% 9.56/2.30 % (3752628)Time elapsed: 0.036 s
% 9.56/2.30 % (3752628)Peak memory usage: 88 MB
% 9.56/2.30 % (3752628)Instructions burned: 128 (million)
% 9.56/2.30 % (3752604)------------------------------
% 9.56/2.30 % (3752604)------------------------------
% 9.56/2.30 % (3752630)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1396643345:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 9.56/2.30 % (3752630)Refutation not found, incomplete strategy
% 9.56/2.30 % (3752630)------------------------------
% 9.56/2.30 % (3752630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752630)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752630)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.30 % (3752630)Time elapsed: 0.001 s
% 9.56/2.30 % (3752630)Peak memory usage: 87 MB
% 9.56/2.30 % (3752633)lrs+10_1_sil=8000:sp=occurrence:random_seed=613389753:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 9.56/2.30 % (3752633)Refutation not found, incomplete strategy
% 9.56/2.30 % (3752633)------------------------------
% 9.56/2.30 % (3752633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752633)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752633)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.30 % (3752633)Time elapsed: 0.0000 s
% 9.56/2.30 % (3752633)Peak memory usage: 87 MB
% 9.56/2.30 % (3752627)------------------------------
% 9.56/2.30 % (3752627)------------------------------
% 9.56/2.30 % (3752635)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3705221596:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 9.56/2.30 % (3752602)First to succeed.
% 9.56/2.30 % (3752635)Refutation not found, incomplete strategy
% 9.56/2.30 % (3752635)------------------------------
% 9.56/2.30 % (3752635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752635)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752635)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.30 % (3752635)Time elapsed: 0.001 s
% 9.56/2.30 % (3752635)Peak memory usage: 88 MB
% 9.56/2.30 % (3752602)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3752597"
% 9.56/2.30 % (3752630)------------------------------
% 9.56/2.30 % (3752630)------------------------------
% 9.56/2.30 % (3752633)------------------------------
% 9.56/2.30 % (3752633)------------------------------
% 9.56/2.30 % (3752637)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1883067707:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 9.56/2.30 % (3752640)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2004315382:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 9.56/2.30 % (3752640)Refutation not found, incomplete strategy
% 9.56/2.30 % (3752640)------------------------------
% 9.56/2.30 % (3752640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.56/2.30 % (3752640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.56/2.30 % (3752640)CaDiCaL version: 2.1.3
% 9.56/2.30 % (3752640)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.30 % (3752640)Time elapsed: 0.0000 s
% 9.56/2.30 % (3752640)Peak memory usage: 87 MB
% 9.56/2.30 % (3752635)------------------------------
% 9.56/2.30 % (3752635)------------------------------
% 10.62/2.30 % (3752639)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1700071454:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 10.62/2.30 % (3752639)Refutation not found, incomplete strategy
% 10.62/2.30 % (3752639)------------------------------
% 10.62/2.30 % (3752639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.62/2.30 % (3752639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.62/2.30 % (3752639)CaDiCaL version: 2.1.3
% 10.62/2.30 % (3752639)Termination reason: Refutation not found, incomplete strategy
% 10.62/2.30 % (3752639)Time elapsed: 0.002 s
% 10.62/2.30 % (3752639)Peak memory usage: 89 MB
% 10.62/2.30 % (3752602)Refutation found. Thanks to Tanya!
% 10.62/2.30 % SZS status Theorem for theBenchmark
% 10.62/2.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/2.50 % (3752602)------------------------------
% 0.17/2.50 % (3752602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.50 % (3752602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.50 % (3752602)CaDiCaL version: 2.1.3
% 0.17/2.50 % (3752602)Termination reason: Refutation
% 0.17/2.50 % (3752602)Time elapsed: 0.991 s
% 0.17/2.50 % (3752602)Peak memory usage: 132 MB
% 0.17/2.50 % (3752602)Instructions burned: 1464 (million)
% 0.17/2.50 % (3752602)------------------------------
% 0.17/2.50 % (3752602)------------------------------
% 0.17/2.50 % (3752597)Success in time 1.438 s
% 0.17/2.50 % Vampire exiting
%------------------------------------------------------------------------------