%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL561+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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:53:03 AM UTC 2026
% Result : Theorem 9.86s 2.62s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 28
% Syntax : Number of formulae : 178 ( 86 unt; 2 def)
% Number of atoms : 306 ( 48 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 231 ( 103 ~; 95 |; 4 &)
% ( 10 <=>; 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 : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 264 ( 0 sgn 262 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
( equivalence_1
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_1) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(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(f75,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f77,conjecture,
equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f78,negated_conjecture,
~ equivalence_1,
inference(negated_conjecture,[status(cth)],[f77]) ).
fof(f79,plain,
~ equivalence_1,
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(equiv(X0,X1),implies(X0,X1)))
=> equivalence_1 ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f95,plain,
( equivalence_1
| ? [X0,X1] : ~ is_a_theorem(implies(equiv(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(f98,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
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,
( equivalence_1
| ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f95]) ).
fof(f114,plain,
( equivalence_1
| ~ is_a_theorem(implies(equiv(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(f117,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f98]) ).
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(f144,plain,
op_equiv,
inference(cnf_transformation,[],[f75]) ).
fof(f146,plain,
~ equivalence_1,
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(f158,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f117,f144]) ).
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(equiv(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(f168,plain,
! [X0,X1] : strict_implies(not(X0),X1) = necessarily(or(X0,X1)),
inference(superposition,[],[f148,f163]) ).
fof(f169,plain,
! [X0] : is_a_theorem(strict_implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[],[f151,f158]) ).
fof(f172,plain,
! [X0,X1] : is_a_theorem(strict_implies(equiv(X0,X1),implies(X0,X1))),
inference(superposition,[],[f153,f158]) ).
fof(f180,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(f189,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,[],[f180,f156]) ).
fof(f190,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,and(X1,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f189,f151]) ).
fof(f191,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X1,X1)))
| is_a_theorem(strict_implies(X0,equiv(X1,X1))) ),
inference(resolution,[],[f189,f169]) ).
fof(f194,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X1,X2)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f189,f153]) ).
fof(f207,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(resolution,[],[f194,f151]) ).
fof(f244,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(f251,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(and(X0,X0),X0))
| is_a_theorem(strict_equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f244,f151]) ).
fof(f253,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(equiv(X0,X0),implies(X0,X0)))
| is_a_theorem(strict_equiv(equiv(X0,X0),implies(X0,X0))) ),
inference(resolution,[],[f244,f169]) ).
fof(f258,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X0,X1)))
| is_a_theorem(strict_equiv(X0,and(X0,X1))) ),
inference(resolution,[],[f244,f153]) ).
fof(f261,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,[],[f244,f154]) ).
fof(f263,plain,
! [X0,X1] : is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))),
inference(forward_subsumption_resolution,[],[f261,f154]) ).
fof(f266,plain,
! [X0] : is_a_theorem(strict_equiv(equiv(X0,X0),implies(X0,X0))),
inference(forward_subsumption_resolution,[],[f253,f172]) ).
fof(f268,plain,
! [X0] : is_a_theorem(strict_equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f251,f153]) ).
fof(f310,plain,
! [X0] : equiv(X0,X0) = implies(X0,X0),
inference(resolution,[],[f155,f266]) ).
fof(f311,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f155,f268]) ).
fof(f312,plain,
! [X0,X1] : and(X0,X1) = and(X1,X0),
inference(resolution,[],[f155,f263]) ).
fof(f412,plain,
! [X0,X1] : implies(X1,X0) = not(and(not(X0),X1)),
inference(superposition,[],[f159,f312]) ).
fof(f458,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(superposition,[],[f159,f412]) ).
fof(f463,plain,
! [X0,X1] : implies(not(X0),X1) = or(X1,X0),
inference(forward_demodulation,[],[f458,f163]) ).
fof(f468,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(forward_demodulation,[],[f463,f163]) ).
fof(f474,plain,
! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X1),X0),
inference(superposition,[],[f168,f468]) ).
fof(f476,plain,
! [X0,X1] : strict_implies(not(X0),X1) = strict_implies(not(X1),X0),
inference(forward_demodulation,[],[f474,f168]) ).
fof(f481,plain,
! [X2,X0,X1] : strict_implies(implies(X0,X1),X2) = strict_implies(not(X2),and(not(X1),X0)),
inference(superposition,[],[f476,f412]) ).
fof(f505,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,[],[f189,f476]) ).
fof(f506,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,[],[f244,f476]) ).
fof(f511,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(and(X0,X0)),X1))
| ~ is_a_theorem(strict_implies(not(X1),X0)) ),
inference(superposition,[],[f190,f476]) ).
fof(f512,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),X0))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f511,f311]) ).
fof(f518,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,not(not(X1))))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f505,f207]) ).
fof(f529,plain,
! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0)),
inference(resolution,[],[f512,f207]) ).
fof(f557,plain,
! [X0] : is_a_theorem(strict_implies(not(not(not(not(X0)))),X0)),
inference(resolution,[],[f518,f529]) ).
fof(f558,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),X0)),
inference(resolution,[],[f518,f153]) ).
fof(f612,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,X1),X2))
| is_a_theorem(strict_implies(not(X2),not(X1))) ),
inference(superposition,[],[f194,f481]) ).
fof(f724,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(implies(X0,X1)),not(X1))),
inference(resolution,[],[f612,f207]) ).
fof(f740,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(not(X0)),implies(X1,X0))),
inference(superposition,[],[f724,f476]) ).
fof(f797,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,[],[f557,f506]) ).
fof(f819,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(not(X0))),not(X0))),
inference(forward_subsumption_resolution,[],[f797,f529]) ).
fof(f820,plain,
! [X0] : not(X0) = not(not(not(X0))),
inference(resolution,[],[f819,f155]) ).
fof(f839,plain,
! [X0,X1] : not(and(not(X0),X1)) = implies(X1,not(not(X0))),
inference(superposition,[],[f412,f820]) ).
fof(f861,plain,
! [X0,X1] : implies(X1,X0) = implies(X1,not(not(X0))),
inference(forward_demodulation,[],[f839,f412]) ).
fof(f900,plain,
! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,not(not(X1))),
inference(superposition,[],[f148,f861]) ).
fof(f930,plain,
! [X0,X1] : strict_implies(X0,X1) = strict_implies(X0,not(not(X1))),
inference(forward_demodulation,[],[f900,f148]) ).
fof(f966,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,[],[f244,f930]) ).
fof(f1017,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(strict_equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f966,f529]) ).
fof(f1036,plain,
! [X0] : is_a_theorem(strict_equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f1017,f207]) ).
fof(f1040,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f1036,f155]) ).
fof(f1048,plain,
! [X0,X1] : not(implies(X0,X1)) = and(not(X1),X0),
inference(superposition,[],[f1040,f412]) ).
fof(f1053,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X0))),
inference(superposition,[],[f740,f1040]) ).
fof(f1064,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X0,X1)),
inference(superposition,[],[f412,f1040]) ).
fof(f1147,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(X0,implies(X2,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1053,f189]) ).
fof(f1189,plain,
! [X0,X1] : strict_implies(X1,not(X0)) = necessarily(not(and(X0,X1))),
inference(superposition,[],[f148,f1064]) ).
fof(f1596,plain,
! [X0] : necessarily(not(X0)) = strict_implies(X0,not(X0)),
inference(superposition,[],[f1189,f311]) ).
fof(f1615,plain,
! [X0] : necessarily(X0) = strict_implies(not(X0),X0),
inference(superposition,[],[f1596,f1040]) ).
fof(f1632,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,[],[f189,f1596]) ).
fof(f1953,plain,
! [X0,X1] :
( is_a_theorem(necessarily(implies(X0,X1)))
| ~ is_a_theorem(strict_implies(not(implies(X0,X1)),X1)) ),
inference(superposition,[],[f1147,f1615]) ).
fof(f1963,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(not(implies(X0,X1)),X1)) ),
inference(forward_demodulation,[],[f1953,f148]) ).
fof(f1976,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(and(not(X1),X0),X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1963,f1048]) ).
fof(f2329,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,[],[f1976,f1632]) ).
fof(f2351,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,not(X1)))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(forward_subsumption_resolution,[],[f2329,f558]) ).
fof(f2414,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(X2,implies(X0,X1)))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f2351,f412]) ).
fof(f2426,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(X2,implies(X0,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f2414,f148]) ).
fof(f2439,definition,
( spl2_1
<=> ! [X1] : ~ is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f2440,plain,
( ! [X1] : ~ is_a_theorem(X1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f2439]) ).
fof(f2492,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(strict_implies(X1,equiv(X0,X0))) ),
inference(resolution,[],[f2426,f191]) ).
fof(f2496,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X2)
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f2426,f157]) ).
fof(f2534,definition,
( spl2_6
<=> ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f2535,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f2534]) ).
fof(f2536,plain,
( spl2_1
| spl2_6 ),
inference(avatar_split_clause,[],[f2496,f2534,f2439]) ).
fof(f2541,plain,
! [X0,X1] : is_a_theorem(strict_implies(X1,equiv(X0,X0))),
inference(forward_subsumption_resolution,[],[f2492,f207]) ).
fof(f2548,plain,
! [X0,X1] : is_a_theorem(strict_implies(X1,implies(X0,X0))),
inference(forward_demodulation,[],[f2541,f310]) ).
fof(f2574,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(implies(X0,X0)),X1)),
inference(superposition,[],[f2548,f476]) ).
fof(f2575,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(not(X0),X0),X1)),
inference(forward_demodulation,[],[f2574,f1048]) ).
fof(f2619,plain,
! [X0,X1] : is_a_theorem(strict_equiv(and(not(X0),X0),and(and(not(X0),X0),X1))),
inference(resolution,[],[f2575,f258]) ).
fof(f2666,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f2619,f2440]) ).
fof(f2667,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f2666]) ).
fof(f2732,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ spl2_6 ),
inference(resolution,[],[f2535,f172]) ).
fof(f3030,plain,
( $false
| ~ spl2_6 ),
inference(resolution,[],[f2732,f161]) ).
fof(f3042,plain,
~ spl2_6,
inference(avatar_contradiction_clause,[],[f3030]) ).
cnf(s5,plain,
( spl2_1
| spl2_6 ),
inference(sat_conversion,[],[f2536]) ).
cnf(s26,plain,
~ spl2_1,
inference(sat_conversion,[],[f2667]) ).
cnf(s32,plain,
~ spl2_6,
inference(sat_conversion,[],[f3042]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s5,s32,s26]) ).
fof(f3045,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL561+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.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 16:02:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.86/2.62 % (1417902)Detected formulas, will run a generic FOF schedule.
% 9.86/2.62 % (1417992)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3438078447:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.86/2.62 % (1417992)Refutation not found, incomplete strategy
% 9.86/2.62 % (1417992)------------------------------
% 9.86/2.62 % (1417992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1417992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1417992)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1417992)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1417992)Time elapsed: 0.0000 s
% 9.86/2.62 % (1417992)Peak memory usage: 87 MB
% 9.86/2.62 % (1417988)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=2034369329:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.86/2.62 % (1417987)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=1785513096:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.86/2.62 % (1417995)dis-21_1_sil=8000:lcm=predicate:random_seed=2268664067: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)
% 9.86/2.62 % (1417994)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3370897967:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.86/2.62 % (1417995)Refutation not found, incomplete strategy
% 9.86/2.62 % (1417995)------------------------------
% 9.86/2.62 % (1417995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1417995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1417995)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1417995)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1417995)Time elapsed: 0.002 s
% 9.86/2.62 % (1417995)Peak memory usage: 88 MB
% 9.86/2.62 % (1417991)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=3690828552:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.86/2.62 % (1417993)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2593035020:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.86/2.62 % (1417993)Refutation not found, incomplete strategy
% 9.86/2.62 % (1417993)------------------------------
% 9.86/2.62 % (1417993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1417993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1417993)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1417993)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1417993)Time elapsed: 0.001 s
% 9.86/2.62 % (1417993)Peak memory usage: 86 MB
% 9.86/2.62 % (1417994)Instruction limit reached!
% 9.86/2.62 % (1417994)------------------------------
% 9.86/2.62 % (1417994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1417994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1417994)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1417994)Termination reason: Instruction limit
% 9.86/2.62 % (1417994)Termination phase: Saturation
% 9.86/2.62 % (1417994)Time elapsed: 0.091 s
% 9.86/2.62 % (1417994)Peak memory usage: 90 MB
% 9.86/2.62 % (1417994)Instructions burned: 140 (million)
% 9.86/2.62 % (1417992)------------------------------
% 9.86/2.62 % (1417992)------------------------------
% 9.86/2.62 % (1418023)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2823359788:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.86/2.62 % (1418023)Refutation not found, incomplete strategy
% 9.86/2.62 % (1418023)------------------------------
% 9.86/2.62 % (1418023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1418023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1418023)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1418023)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1418023)Time elapsed: 0.001 s
% 9.86/2.62 % (1418023)Peak memory usage: 87 MB
% 9.86/2.62 % (1417995)------------------------------
% 9.86/2.62 % (1417995)------------------------------
% 9.86/2.62 % (1418022)lrs+10_1_sil=8000:sp=occurrence:random_seed=3690587716:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.86/2.62 % (1418022)Refutation not found, incomplete strategy
% 9.86/2.62 % (1418022)------------------------------
% 9.86/2.62 % (1418022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1418022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1418022)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1418022)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1418022)Time elapsed: 0.005 s
% 9.86/2.62 % (1418022)Peak memory usage: 88 MB
% 9.86/2.62 % (1417993)------------------------------
% 9.86/2.62 % (1417993)------------------------------
% 9.86/2.62 % (1418023)------------------------------
% 9.86/2.62 % (1418023)------------------------------
% 9.86/2.62 % (1418030)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2404371625:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 9.86/2.62 % (1418030)Refutation not found, incomplete strategy
% 9.86/2.62 % (1418030)------------------------------
% 9.86/2.62 % (1418030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1418030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1418030)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1418030)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1418030)Time elapsed: 0.001 s
% 9.86/2.62 % (1418030)Peak memory usage: 87 MB
% 9.86/2.62 % (1418047)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=3384496125:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 9.86/2.62 % (1418022)------------------------------
% 9.86/2.62 % (1418022)------------------------------
% 9.86/2.62 % (1418057)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1978879747:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 9.86/2.62 % (1418057)Refutation not found, incomplete strategy
% 9.86/2.62 % (1418057)------------------------------
% 9.86/2.62 % (1418057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1418057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1418057)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1418057)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1418057)Time elapsed: 0.001 s
% 9.86/2.62 % (1418057)Peak memory usage: 87 MB
% 9.86/2.62 % (1417991)Refutation not found, incomplete strategy
% 9.86/2.62 % (1417991)------------------------------
% 9.86/2.62 % (1417991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1417991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1417991)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1417991)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1417991)Time elapsed: 0.734 s
% 9.86/2.62 % (1417991)Peak memory usage: 127 MB
% 9.86/2.62 % (1417991)Instructions burned: 830 (million)
% 9.86/2.62 % (1418047)Instruction limit reached!
% 9.86/2.62 % (1418047)------------------------------
% 9.86/2.62 % (1418047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1418047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1418047)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1418047)Termination reason: Instruction limit
% 9.86/2.62 % (1418047)Termination phase: Saturation
% 9.86/2.62 % (1418047)Time elapsed: 0.232 s
% 9.86/2.62 % (1418047)Peak memory usage: 92 MB
% 9.86/2.62 % (1418047)Instructions burned: 249 (million)
% 9.86/2.62 % (1418067)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2056636693:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 9.86/2.62 % (1418057)------------------------------
% 9.86/2.62 % (1418057)------------------------------
% 9.86/2.62 % (1418030)------------------------------
% 9.86/2.62 % (1418030)------------------------------
% 9.86/2.62 % (1418072)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4273000514:cts=off:i=113:fsr=off:ss=included:sgt=4_2990 on theBenchmark for (2990ds/113Mi)
% 9.86/2.62 % (1418072)Refutation not found, incomplete strategy
% 9.86/2.62 % (1418072)------------------------------
% 9.86/2.62 % (1418072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1418072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1418072)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1418072)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1418072)Time elapsed: 0.002 s
% 9.86/2.62 % (1418072)Peak memory usage: 88 MB
% 9.86/2.62 % (1418074)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1896452458:i=127:av=off:fsr=off:sup=off_2989 on theBenchmark for (2989ds/127Mi)
% 9.86/2.62 % (1417991)------------------------------
% 9.86/2.62 % (1417991)------------------------------
% 9.86/2.62 % (1417987)First to succeed.
% 9.86/2.62 % (1417987)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1417902"
% 9.86/2.62 % (1418074)Instruction limit reached!
% 9.86/2.62 % (1418074)------------------------------
% 9.86/2.62 % (1418074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1418074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1418074)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1418074)Termination reason: Instruction limit
% 9.86/2.62 % (1418074)Termination phase: Saturation
% 9.86/2.62 % (1418074)Time elapsed: 0.064 s
% 9.86/2.62 % (1418074)Peak memory usage: 88 MB
% 9.86/2.62 % (1418074)Instructions burned: 127 (million)
% 9.86/2.62 % (1418075)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=663849866:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2988 on theBenchmark for (2988ds/114Mi)
% 9.86/2.62 % (1418075)Refutation not found, incomplete strategy
% 9.86/2.62 % (1418075)------------------------------
% 9.86/2.62 % (1418075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1418075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1418075)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1418075)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1418075)Time elapsed: 0.002 s
% 9.86/2.62 % (1418075)Peak memory usage: 87 MB
% 9.86/2.62 % (1418085)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1380985866:i=437:sd=1:aac=none:ss=included_2986 on theBenchmark for (2986ds/437Mi)
% 9.86/2.62 % (1418085)Refutation not found, incomplete strategy
% 9.86/2.62 % (1418085)------------------------------
% 9.86/2.62 % (1418085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.86/2.62 % (1418085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.86/2.62 % (1418085)CaDiCaL version: 2.1.3
% 9.86/2.62 % (1418085)Termination reason: Refutation not found, incomplete strategy
% 9.86/2.62 % (1418085)Time elapsed: 0.001 s
% 9.86/2.62 % (1418085)Peak memory usage: 88 MB
% 9.86/2.62 % (1418083)lrs+10_1_sil=8000:sp=occurrence:random_seed=980600056:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2987 on theBenchmark for (2987ds/907Mi)
% 9.86/2.62 % (1418072)------------------------------
% 9.86/2.62 % (1418072)------------------------------
% 9.86/2.62 % (1417987)Refutation found. Thanks to Tanya!
% 9.86/2.62 % SZS status Theorem for theBenchmark
% 9.86/2.62 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/2.90 % (1417987)------------------------------
% 0.16/2.90 % (1417987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.90 % (1417987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.90 % (1417987)CaDiCaL version: 2.1.3
% 0.16/2.90 % (1417987)Termination reason: Refutation
% 0.16/2.90 % (1417987)Time elapsed: 1.154 s
% 0.16/2.90 % (1417987)Peak memory usage: 132 MB
% 0.16/2.90 % (1417987)Instructions burned: 1258 (million)
% 0.16/2.90 % (1417987)------------------------------
% 0.16/2.90 % (1417987)------------------------------
% 0.16/2.90 % (1417902)Success in time 1.738 s
% 0.16/2.90 % Vampire exiting
%------------------------------------------------------------------------------