%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL495+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:36 AM UTC 2026
% Result : Theorem 11.96s 2.39s
% Output : Refutation 12.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 26
% Syntax : Number of formulae : 193 ( 97 unt; 0 def)
% Number of atoms : 313 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 217 ( 97 ~; 93 |; 2 &)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 365 ( 363 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_3) ).
fof(f22,axiom,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
fof(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
fof(f24,axiom,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
fof(f25,axiom,
( r4
<=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
fof(f26,axiom,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
fof(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(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r4) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r5) ).
fof(f41,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f44,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f45,conjecture,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f46,negated_conjecture,
~ equivalence_3,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ equivalence_3,
inference(flattening,[],[f46]) ).
fof(f48,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
fof(f49,plain,
( r4
=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f25]) ).
fof(f50,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f51,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f52,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f53,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
=> equivalence_3 ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f54,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f55,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f56,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f55]) ).
fof(f57,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f54]) ).
fof(f59,plain,
( equivalence_3
| ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(ennf_transformation,[],[f53]) ).
fof(f60,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(ennf_transformation,[],[f52]) ).
fof(f61,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f51]) ).
fof(f62,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f50]) ).
fof(f63,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(ennf_transformation,[],[f49]) ).
fof(f64,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f48]) ).
fof(f65,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f66,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f67,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f69,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f70,plain,
( equivalence_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK0),equiv(sK0,sK1)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f59]) ).
fof(f71,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f57]) ).
fof(f72,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f58]) ).
fof(f73,plain,
( equivalence_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK0),equiv(sK0,sK1)))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f74,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f60]) ).
fof(f75,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f62]) ).
fof(f77,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f63]) ).
fof(f78,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f64]) ).
fof(f79,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f65]) ).
fof(f80,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f66]) ).
fof(f81,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f67]) ).
fof(f82,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f68]) ).
fof(f83,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f69]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f85,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
fof(f87,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f88,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f89,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f90,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f91,plain,
r4,
inference(cnf_transformation,[],[f39]) ).
fof(f92,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f93,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f41]) ).
fof(f94,plain,
op_or,
inference(cnf_transformation,[],[f42]) ).
fof(f95,plain,
op_implies_and,
inference(cnf_transformation,[],[f43]) ).
fof(f96,plain,
op_equiv,
inference(cnf_transformation,[],[f44]) ).
fof(f97,plain,
~ equivalence_3,
inference(cnf_transformation,[],[f47]) ).
fof(f98,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f83,f96]) ).
fof(f99,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[],[f82,f84]) ).
fof(f100,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f81,f95]) ).
fof(f101,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f80,f85]) ).
fof(f102,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f79,f94]) ).
fof(f103,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))),
inference(forward_subsumption_resolution,[],[f78,f92]) ).
fof(f104,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(forward_subsumption_resolution,[],[f77,f91]) ).
fof(f105,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f76,f90]) ).
fof(f106,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(forward_subsumption_resolution,[],[f75,f89]) ).
fof(f107,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f74,f88]) ).
fof(f108,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK0),equiv(sK0,sK1)))),
inference(forward_subsumption_resolution,[],[f73,f97]) ).
fof(f109,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f72,f93]) ).
fof(f110,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f71,f87]) ).
fof(f111,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[],[f101,f99]) ).
fof(f112,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f102,f100]) ).
fof(f120,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X1))),
inference(superposition,[],[f106,f99]) ).
fof(f132,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[],[f105,f99]) ).
fof(f133,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(superposition,[],[f105,f99]) ).
fof(f134,plain,
! [X2,X0,X1] : implies(X2,and(X0,not(X1))) = not(and(X2,implies(X0,X1))),
inference(superposition,[],[f100,f100]) ).
fof(f137,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X2,X0),or(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f110,f103]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,or(X1,X2)))
| is_a_theorem(or(X1,or(X0,X2))) ),
inference(resolution,[],[f110,f104]) ).
fof(f141,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f110,f105]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,implies(X0,X1)))
| is_a_theorem(or(not(X0),or(X2,X1))) ),
inference(superposition,[],[f140,f99]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| is_a_theorem(or(X1,or(not(X0),X2))) ),
inference(superposition,[],[f140,f99]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| is_a_theorem(or(X1,implies(X0,X2))) ),
inference(forward_demodulation,[],[f144,f99]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,implies(X0,X1)))
| is_a_theorem(implies(X0,or(X2,X1))) ),
inference(forward_demodulation,[],[f143,f99]) ).
fof(f149,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(or(X1,X0),X1))),
inference(resolution,[],[f145,f105]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,implies(X0,X1)))
| is_a_theorem(or(not(X0),implies(X2,X1))) ),
inference(superposition,[],[f145,f99]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,implies(X0,X1)))
| is_a_theorem(implies(X0,implies(X2,X1))) ),
inference(forward_demodulation,[],[f150,f99]) ).
fof(f154,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X0,X2)))),
inference(resolution,[],[f153,f103]) ).
fof(f155,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[],[f153,f120]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[],[f137,f110]) ).
fof(f176,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(not(X0),X2),implies(X0,X1)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(superposition,[],[f137,f99]) ).
fof(f178,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),or(X0,X2)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f154,f110]) ).
fof(f190,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X2),implies(X0,X1)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(forward_demodulation,[],[f176,f99]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X2,X1)) ),
inference(resolution,[],[f190,f110]) ).
fof(f201,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| is_a_theorem(implies(implies(X0,X3),X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(resolution,[],[f195,f190]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X0,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f195,f106]) ).
fof(f204,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X0),X1))
| is_a_theorem(implies(X2,X1)) ),
inference(resolution,[],[f195,f155]) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X0,X1),X2))
| is_a_theorem(implies(or(X1,X0),X2)) ),
inference(resolution,[],[f195,f105]) ).
fof(f207,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(or(X0,X1),X2))
| is_a_theorem(implies(or(X0,X3),X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(resolution,[],[f195,f137]) ).
fof(f217,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),implies(X0,X1)))
| ~ is_a_theorem(or(not(X0),X2)) ),
inference(superposition,[],[f178,f99]) ).
fof(f218,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),implies(X0,X1)))
| ~ is_a_theorem(implies(X0,X2)) ),
inference(forward_demodulation,[],[f217,f99]) ).
fof(f234,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(superposition,[],[f133,f99]) ).
fof(f239,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f132,f110]) ).
fof(f250,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(not(X0),X2))
| is_a_theorem(or(X1,X2)) ),
inference(resolution,[],[f239,f174]) ).
fof(f252,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[],[f239,f99]) ).
fof(f254,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X1,X2)) ),
inference(forward_demodulation,[],[f250,f112]) ).
fof(f351,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[],[f202,f133]) ).
fof(f359,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(forward_demodulation,[],[f351,f112]) ).
fof(f361,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0)),
inference(resolution,[],[f359,f141]) ).
fof(f544,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),X0))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f207,f107]) ).
fof(f558,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f544,f206]) ).
fof(f572,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(resolution,[],[f558,f110]) ).
fof(f747,plain,
! [X0] : is_a_theorem(implies(X0,not(or(not(X0),not(X0))))),
inference(resolution,[],[f252,f107]) ).
fof(f755,plain,
! [X0] : is_a_theorem(implies(X0,not(implies(X0,not(X0))))),
inference(forward_demodulation,[],[f747,f99]) ).
fof(f758,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(forward_demodulation,[],[f755,f111]) ).
fof(f759,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(implies(X1,X1),implies(X1,X1)))),
inference(resolution,[],[f758,f204]) ).
fof(f775,plain,
! [X0,X1] : is_a_theorem(implies(X0,equiv(X1,X1))),
inference(forward_demodulation,[],[f759,f98]) ).
fof(f781,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(equiv(X0,X0),X1))
| is_a_theorem(implies(X2,X1)) ),
inference(resolution,[],[f775,f195]) ).
fof(f922,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f572,f359]) ).
fof(f989,plain,
! [X2,X0,X1] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[],[f99,f111]) ).
fof(f991,plain,
! [X2,X0,X1] : or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(superposition,[],[f112,f111]) ).
fof(f1007,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(implies(X0,X1),implies(X0,X2))) ),
inference(resolution,[],[f201,f190]) ).
fof(f1106,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),or(not(X1),not(X0)))),
inference(superposition,[],[f132,f989]) ).
fof(f1212,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))),
inference(forward_demodulation,[],[f1106,f99]) ).
fof(f1432,plain,
! [X0,X1] : is_a_theorem(or(implies(or(X0,X1),X0),X1)),
inference(resolution,[],[f149,f141]) ).
fof(f1505,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(or(X0,X1),X0),X2))
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[],[f1432,f254]) ).
fof(f1688,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(superposition,[],[f361,f991]) ).
fof(f1827,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(superposition,[],[f1688,f98]) ).
fof(f2023,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,not(X1)),and(X1,X0))),
inference(resolution,[],[f1212,f141]) ).
fof(f2039,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),and(X1,X0))),
inference(forward_demodulation,[],[f2023,f991]) ).
fof(f2048,plain,
! [X0,X1] : is_a_theorem(implies(and(implies(X1,X0),implies(X0,X1)),equiv(X0,X1))),
inference(superposition,[],[f2039,f98]) ).
fof(f2049,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X1,X0),equiv(X0,X1))),
inference(forward_demodulation,[],[f2048,f98]) ).
fof(f2058,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(equiv(X0,X1),X2))
| is_a_theorem(implies(equiv(X1,X0),X2)) ),
inference(resolution,[],[f2049,f195]) ).
fof(f2062,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(resolution,[],[f2058,f1827]) ).
fof(f2087,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(equiv(X1,X0),X1))),
inference(resolution,[],[f2062,f153]) ).
fof(f2099,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(equiv(X0,X1),X0),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f2087,f195]) ).
fof(f2268,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,or(X1,implies(equiv(X2,X0),X2)))),
inference(resolution,[],[f2099,f106]) ).
fof(f2680,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X1)))
| is_a_theorem(implies(implies(X2,X0),implies(X2,X1))) ),
inference(resolution,[],[f1007,f107]) ).
fof(f2817,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| is_a_theorem(or(implies(X0,X1),X2)) ),
inference(resolution,[],[f1505,f218]) ).
fof(f2826,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,not(or(not(X0),X1))),X1)),
inference(resolution,[],[f1505,f234]) ).
fof(f2860,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,or(not(X0),X1)),X1)),
inference(forward_demodulation,[],[f2826,f991]) ).
fof(f2862,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,implies(X0,X1)),X1)),
inference(forward_demodulation,[],[f2860,f99]) ).
fof(f2867,plain,
! [X2,X0,X1] : is_a_theorem(or(implies(X0,X1),implies(equiv(X2,X0),X2))),
inference(resolution,[],[f2817,f2268]) ).
fof(f2892,plain,
! [X0,X1] : is_a_theorem(or(implies(or(X0,X1),X1),X0)),
inference(resolution,[],[f2817,f105]) ).
fof(f2978,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(or(X0,X1),X1),X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f2892,f254]) ).
fof(f2998,plain,
! [X0,X1] : is_a_theorem(implies(X0,not(and(X1,implies(X1,not(X0)))))),
inference(resolution,[],[f2862,f252]) ).
fof(f3006,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X1,not(not(X0)))))),
inference(forward_demodulation,[],[f2998,f134]) ).
fof(f3074,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X0,X1),or(implies(X1,X2),X0))),
inference(resolution,[],[f2867,f146]) ).
fof(f3084,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,or(implies(X1,X2),X1))),
inference(resolution,[],[f3074,f781]) ).
fof(f3120,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X2,X1)))
| is_a_theorem(or(implies(X0,X1),X2)) ),
inference(resolution,[],[f2978,f218]) ).
fof(f3211,plain,
! [X2,X0,X1] : is_a_theorem(or(implies(X0,X1),implies(X1,X2))),
inference(resolution,[],[f3084,f3120]) ).
fof(f3304,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,or(implies(X1,X0),X2))),
inference(resolution,[],[f3211,f146]) ).
fof(f3325,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X2,X1)))),
inference(resolution,[],[f3304,f2680]) ).
fof(f3380,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),implies(X2,X1)))),
inference(resolution,[],[f3325,f153]) ).
fof(f3720,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f3380,f110]) ).
fof(f3775,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f3720,f922]) ).
fof(f3812,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,not(implies(X0,not(X1))))) ),
inference(resolution,[],[f3775,f252]) ).
fof(f3822,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(forward_demodulation,[],[f3812,f111]) ).
fof(f3855,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f3822,f98]) ).
fof(f3880,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f3855,f110]) ).
fof(f3917,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(resolution,[],[f3880,f758]) ).
fof(f4010,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f3917,f1688]) ).
fof(f4020,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f4010,f109]) ).
fof(f4041,plain,
! [X0] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[],[f100,f4020]) ).
fof(f4045,plain,
! [X0] : or(X0,X0) = not(not(X0)),
inference(forward_demodulation,[],[f4041,f112]) ).
fof(f4169,plain,
! [X0] : implies(X0,not(X0)) = not(not(not(X0))),
inference(superposition,[],[f99,f4045]) ).
fof(f4927,plain,
! [X0,X1] : is_a_theorem(implies(not(not(X0)),implies(X1,and(X1,not(implies(X0,not(X0))))))),
inference(superposition,[],[f3006,f4169]) ).
fof(f4930,plain,
! [X0,X1] : is_a_theorem(or(not(X0),implies(X1,and(X1,not(implies(X0,not(X0))))))),
inference(forward_demodulation,[],[f4927,f112]) ).
fof(f5027,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X1,not(implies(X0,not(X0))))))),
inference(forward_demodulation,[],[f4930,f99]) ).
fof(f5099,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X1,and(X0,X0))))),
inference(forward_demodulation,[],[f5027,f111]) ).
fof(f5138,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X1,X0)))),
inference(forward_demodulation,[],[f5099,f4020]) ).
fof(f6373,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),implies(implies(X0,X1),equiv(X0,X1)))),
inference(superposition,[],[f5138,f98]) ).
fof(f6403,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(resolution,[],[f6373,f153]) ).
fof(f6451,plain,
$false,
inference(resolution,[],[f6403,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL495+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 15:51:30 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.16/2.11 % (2208518)Detected formulas, will run a generic FOF schedule.
% 10.16/2.11 % (2208528)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=303024418:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.16/2.11 % (2208527)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3548309904:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.16/2.11 % (2208529)dis-21_1_sil=8000:lcm=predicate:random_seed=1276677177:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 10.16/2.11 % (2208526)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=461528094:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.16/2.11 % (2208523)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=910454029:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.16/2.11 % (2208524)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=379877780:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.16/2.11 % (2208525)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=2017592585:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.16/2.11 % (2208527)Refutation not found, incomplete strategy
% 10.16/2.11 % (2208527)------------------------------
% 10.16/2.11 % (2208527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.16/2.11 % (2208527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/2.11 % (2208527)CaDiCaL version: 2.1.3
% 10.16/2.11 % (2208527)Termination reason: Refutation not found, incomplete strategy
% 10.16/2.11 % (2208527)Time elapsed: 0.0000 s
% 10.16/2.11 % (2208527)Peak memory usage: 87 MB
% 10.16/2.11 % (2208526)Refutation not found, incomplete strategy
% 10.16/2.11 % (2208526)------------------------------
% 10.16/2.11 % (2208526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.16/2.11 % (2208526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/2.11 % (2208526)CaDiCaL version: 2.1.3
% 10.16/2.11 % (2208526)Termination reason: Refutation not found, incomplete strategy
% 10.16/2.11 % (2208526)Time elapsed: 0.001 s
% 10.16/2.11 % (2208526)Peak memory usage: 87 MB
% 10.16/2.11 % (2208529)Refutation not found, incomplete strategy
% 10.16/2.11 % (2208529)------------------------------
% 10.16/2.11 % (2208529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.16/2.11 % (2208529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/2.11 % (2208529)CaDiCaL version: 2.1.3
% 10.16/2.11 % (2208529)Termination reason: Refutation not found, incomplete strategy
% 10.16/2.11 % (2208529)Time elapsed: 0.001 s
% 10.16/2.11 % (2208529)Peak memory usage: 88 MB
% 10.16/2.11 % (2208529)Instructions burned: 1 (million)
% 10.16/2.11 % (2208528)Instruction limit reached!
% 10.16/2.11 % (2208528)------------------------------
% 10.16/2.11 % (2208528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.16/2.11 % (2208528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/2.11 % (2208528)CaDiCaL version: 2.1.3
% 10.16/2.11 % (2208528)Termination reason: Instruction limit
% 10.16/2.11 % (2208528)Termination phase: Saturation
% 10.16/2.11 % (2208528)Time elapsed: 0.047 s
% 10.16/2.11 % (2208528)Peak memory usage: 90 MB
% 10.16/2.11 % (2208528)Instructions burned: 141 (million)
% 10.16/2.11 % (2208537)lrs+10_1_sil=8000:sp=occurrence:random_seed=1046149819:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.16/2.11 % (2208537)Refutation not found, incomplete strategy
% 10.16/2.11 % (2208537)------------------------------
% 10.16/2.11 % (2208537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.16/2.11 % (2208537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.16/2.11 % (2208537)CaDiCaL version: 2.1.3
% 10.16/2.11 % (2208537)Termination reason: Refutation not found, incomplete strategy
% 10.16/2.11 % (2208537)Time elapsed: 0.001 s
% 10.16/2.11 % (2208537)Peak memory usage: 88 MB
% 10.16/2.11 % (2208527)------------------------------
% 10.16/2.11 % (2208527)------------------------------
% 10.16/2.11 % (2208526)------------------------------
% 10.16/2.11 % (2208526)------------------------------
% 11.96/2.39 % (2208529)------------------------------
% 11.96/2.39 % (2208529)------------------------------
% 11.96/2.39 % (2208537)------------------------------
% 11.96/2.39 % (2208537)------------------------------
% 11.96/2.39 % (2208539)lrs+10_1_sil=32000:urr=on:br=off:random_seed=780759948:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 11.96/2.39 % (2208541)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=179118119:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 11.96/2.39 % (2208540)lrs+1011_1_sil=32000:sp=occurrence:random_seed=280744070:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 11.96/2.39 % (2208540)Refutation not found, incomplete strategy
% 11.96/2.39 % (2208540)------------------------------
% 11.96/2.39 % (2208540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208539)Refutation not found, incomplete strategy
% 11.96/2.39 % (2208539)------------------------------
% 11.96/2.39 % (2208539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208540)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208540)Termination reason: Refutation not found, incomplete strategy
% 11.96/2.39 % (2208540)Time elapsed: 0.001 s
% 11.96/2.39 % (2208540)Peak memory usage: 87 MB
% 11.96/2.39 % (2208539)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208539)Termination reason: Refutation not found, incomplete strategy
% 11.96/2.39 % (2208539)Time elapsed: 0.001 s
% 11.96/2.39 % (2208539)Peak memory usage: 87 MB
% 11.96/2.39 % (2208542)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1857516638:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 11.96/2.39 % (2208542)Refutation not found, incomplete strategy
% 11.96/2.39 % (2208542)------------------------------
% 11.96/2.39 % (2208542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208542)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208542)Termination reason: Refutation not found, incomplete strategy
% 11.96/2.39 % (2208542)Time elapsed: 0.0000 s
% 11.96/2.39 % (2208542)Peak memory usage: 87 MB
% 11.96/2.39 % (2208541)Instruction limit reached!
% 11.96/2.39 % (2208541)------------------------------
% 11.96/2.39 % (2208541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208541)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208541)Termination reason: Instruction limit
% 11.96/2.39 % (2208541)Termination phase: Saturation
% 11.96/2.39 % (2208541)Time elapsed: 0.150 s
% 11.96/2.39 % (2208541)Peak memory usage: 92 MB
% 11.96/2.39 % (2208541)Instructions burned: 249 (million)
% 11.96/2.39 % (2208525)Refutation not found, incomplete strategy
% 11.96/2.39 % (2208525)------------------------------
% 11.96/2.39 % (2208525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208525)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208525)Termination reason: Refutation not found, incomplete strategy
% 11.96/2.39 % (2208525)Time elapsed: 0.565 s
% 11.96/2.39 % (2208525)Peak memory usage: 125 MB
% 11.96/2.39 % (2208525)Instructions burned: 828 (million)
% 11.96/2.39 % (2208542)------------------------------
% 11.96/2.39 % (2208542)------------------------------
% 11.96/2.39 % (2208540)------------------------------
% 11.96/2.39 % (2208540)------------------------------
% 11.96/2.39 % (2208539)------------------------------
% 11.96/2.39 % (2208539)------------------------------
% 11.96/2.39 % (2208547)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2324875536:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 11.96/2.39 % (2208548)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=810136929:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 11.96/2.39 % (2208548)Refutation not found, incomplete strategy
% 11.96/2.39 % (2208548)------------------------------
% 11.96/2.39 % (2208548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208548)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208548)Termination reason: Refutation not found, incomplete strategy
% 11.96/2.39 % (2208548)Time elapsed: 0.001 s
% 11.96/2.39 % (2208548)Peak memory usage: 88 MB
% 11.96/2.39 % (2208525)------------------------------
% 11.96/2.39 % (2208525)------------------------------
% 11.96/2.39 % (2208550)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1774192626:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 11.96/2.39 % (2208549)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1949803659:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 11.96/2.39 % (2208550)Refutation not found, incomplete strategy
% 11.96/2.39 % (2208550)------------------------------
% 11.96/2.39 % (2208550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208550)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208550)Termination reason: Refutation not found, incomplete strategy
% 11.96/2.39 % (2208550)Time elapsed: 0.001 s
% 11.96/2.39 % (2208550)Peak memory usage: 87 MB
% 11.96/2.39 % (2208548)------------------------------
% 11.96/2.39 % (2208548)------------------------------
% 11.96/2.39 % (2208549)Instruction limit reached!
% 11.96/2.39 % (2208549)------------------------------
% 11.96/2.39 % (2208549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208549)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208549)Termination reason: Instruction limit
% 11.96/2.39 % (2208549)Termination phase: Saturation
% 11.96/2.39 % (2208549)Time elapsed: 0.068 s
% 11.96/2.39 % (2208549)Peak memory usage: 88 MB
% 11.96/2.39 % (2208549)Instructions burned: 128 (million)
% 11.96/2.39 % (2208555)lrs+10_1_sil=8000:sp=occurrence:random_seed=2214287285:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 11.96/2.39 % (2208556)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=744305256:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 11.96/2.39 % (2208556)Refutation not found, incomplete strategy
% 11.96/2.39 % (2208556)------------------------------
% 11.96/2.39 % (2208556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208556)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208556)Termination reason: Refutation not found, incomplete strategy
% 11.96/2.39 % (2208556)Time elapsed: 0.001 s
% 11.96/2.39 % (2208556)Peak memory usage: 88 MB
% 11.96/2.39 % (2208557)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2793181769:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 11.96/2.39 % (2208550)------------------------------
% 11.96/2.39 % (2208550)------------------------------
% 11.96/2.39 % (2208556)------------------------------
% 11.96/2.39 % (2208556)------------------------------
% 11.96/2.39 % (2208561)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2331110263:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 11.96/2.39 % (2208561)Refutation not found, incomplete strategy
% 11.96/2.39 % (2208561)------------------------------
% 11.96/2.39 % (2208561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208561)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208561)Termination reason: Refutation not found, incomplete strategy
% 11.96/2.39 % (2208561)Time elapsed: 0.002 s
% 11.96/2.39 % (2208561)Peak memory usage: 89 MB
% 11.96/2.39 % (2208562)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3191481444:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 11.96/2.39 % (2208562)Refutation not found, incomplete strategy
% 11.96/2.39 % (2208562)------------------------------
% 11.96/2.39 % (2208562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208562)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208562)Termination reason: Refutation not found, incomplete strategy
% 11.96/2.39 % (2208562)Time elapsed: 0.001 s
% 11.96/2.39 % (2208562)Peak memory usage: 88 MB
% 11.96/2.39 % (2208523)First to succeed.
% 11.96/2.39 % (2208523)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2208518"
% 11.96/2.39 % (2208562)------------------------------
% 11.96/2.39 % (2208562)------------------------------
% 11.96/2.39 % (2208561)------------------------------
% 11.96/2.39 % (2208561)------------------------------
% 11.96/2.39 % (2208555)Instruction limit reached!
% 11.96/2.39 % (2208555)------------------------------
% 11.96/2.39 % (2208555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.39 % (2208555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.39 % (2208555)CaDiCaL version: 2.1.3
% 11.96/2.39 % (2208555)Termination reason: Instruction limit
% 11.96/2.39 % (2208555)Termination phase: Saturation
% 11.96/2.39 % (2208555)Time elapsed: 0.552 s
% 11.96/2.39 % (2208555)Peak memory usage: 102 MB
% 11.96/2.39 % (2208555)Instructions burned: 908 (million)
% 11.96/2.39 % (2208565)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=617842167:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 11.96/2.39 % (2208523)Refutation found. Thanks to Tanya!
% 11.96/2.39 % SZS status Theorem for theBenchmark
% 11.96/2.39 % SZS output start Proof for theBenchmark
% See solution above
% 12.83/2.59 % (2208523)------------------------------
% 12.83/2.59 % (2208523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.83/2.59 % (2208523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.83/2.59 % (2208523)CaDiCaL version: 2.1.3
% 12.83/2.59 % (2208523)Termination reason: Refutation
% 12.83/2.59 % (2208523)Time elapsed: 1.340 s
% 12.83/2.59 % (2208523)Peak memory usage: 138 MB
% 12.83/2.59 % (2208523)Instructions burned: 2055 (million)
% 12.83/2.59 % (2208523)------------------------------
% 12.83/2.59 % (2208523)------------------------------
% 12.83/2.59 % (2208518)Success in time 1.771 s
% 12.83/2.59 % Vampire exiting
%------------------------------------------------------------------------------