%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU053+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:47:08 PM UTC 2026
% Result : Theorem 3.21s 1.07s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 92 ( 31 unt; 2 def)
% Number of atoms : 250 ( 87 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 266 ( 108 ~; 111 |; 31 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 102 ( 1 sgn 96 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f8,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f10,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f14,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f18,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f34,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f35,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ! [X1,X2] : relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(relation_image(X0,X1),relation_image(X0,X2))
=> one_to_one(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ! [X1,X2] : relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(relation_image(X0,X1),relation_image(X0,X2))
=> one_to_one(X0) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,axiom,
! [X0] :
( relation(X0)
=> relation_image(X0,empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
fof(f38,axiom,
! [X0,X1] :
( X0 != X1
=> disjoint(singleton(X0),singleton(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(f40,axiom,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f48,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f18]) ).
fof(f52,plain,
( empty(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f10]) ).
fof(f58,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f58]) ).
fof(f73,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f74,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1,X2] : relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(relation_image(X0,X1),relation_image(X0,X2))
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f76,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1,X2] : relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(relation_image(X0,X1),relation_image(X0,X2))
& relation(X0)
& function(X0) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0] :
( relation_image(X0,empty_set) = empty_set
| ~ relation(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f78,plain,
! [X0,X1] :
( disjoint(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f38]) ).
fof(f92,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f93,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f59]) ).
fof(f94,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK1(X0) != sK2(X0)
& in(sK1(X0),relation_dom(X0))
& in(sK2(X0),relation_dom(X0))
& apply(X0,sK1(X0)) = apply(X0,sK2(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f94]) ).
fof(f108,plain,
( ~ one_to_one(sK14)
& ! [X1,X2] : relation_image(sK14,set_intersection2(X1,X2)) = set_intersection2(relation_image(sK14,X1),relation_image(sK14,X2))
& relation(sK14)
& function(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f76]) ).
fof(f115,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f120,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f92]) ).
fof(f123,plain,
! [X0] :
( apply(X0,sK1(X0)) = apply(X0,sK2(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f124,plain,
! [X0] :
( in(sK2(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f125,plain,
! [X0] :
( in(sK1(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f126,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f129,plain,
empty(empty_set),
inference(cnf_transformation,[],[f52]) ).
fof(f133,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f139,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f48]) ).
fof(f165,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f166,plain,
function(sK14),
inference(cnf_transformation,[],[f108]) ).
fof(f167,plain,
relation(sK14),
inference(cnf_transformation,[],[f108]) ).
fof(f168,plain,
! [X2,X1] : relation_image(sK14,set_intersection2(X1,X2)) = set_intersection2(relation_image(sK14,X1),relation_image(sK14,X2)),
inference(cnf_transformation,[],[f108]) ).
fof(f169,plain,
~ one_to_one(sK14),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
! [X0] :
( empty_set = relation_image(X0,empty_set)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f171,plain,
! [X0,X1] :
( disjoint(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f173,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f40]) ).
fof(f201,plain,
! [X0,X1] : relation_image(sK14,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK14,X1),relation_image(sK14,X0)),
inference(superposition,[],[f115,f168]) ).
fof(f209,plain,
! [X0,X1] : relation_image(sK14,set_intersection2(X0,X1)) = relation_image(sK14,set_intersection2(X1,X0)),
inference(superposition,[],[f201,f168]) ).
fof(f244,plain,
! [X0] :
( relation_image(sK14,set_intersection2(X0,empty_set)) = set_intersection2(relation_image(sK14,X0),empty_set)
| ~ relation(sK14) ),
inference(superposition,[],[f168,f170]) ).
fof(f247,plain,
! [X0] : relation_image(sK14,set_intersection2(X0,empty_set)) = set_intersection2(relation_image(sK14,X0),empty_set),
inference(forward_subsumption_resolution,[],[f244,f167]) ).
fof(f250,plain,
! [X0] : empty_set = relation_image(sK14,set_intersection2(X0,empty_set)),
inference(forward_demodulation,[],[f247,f173]) ).
fof(f253,plain,
empty_set = relation_image(sK14,empty_set),
inference(forward_demodulation,[],[f250,f173]) ).
fof(f313,plain,
! [X0,X1] :
( empty_set = set_intersection2(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(resolution,[],[f171,f120]) ).
fof(f369,plain,
! [X0] :
( relation_image(X0,singleton(sK2(X0))) = singleton(apply(X0,sK2(X0)))
| ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[],[f165,f124]) ).
fof(f370,plain,
! [X0] :
( relation_image(X0,singleton(sK1(X0))) = singleton(apply(X0,sK1(X0)))
| ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[],[f165,f125]) ).
fof(f371,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| relation_image(X0,singleton(sK1(X0))) = singleton(apply(X0,sK1(X0))) ),
inference(duplicate_literal_removal,[],[f370]) ).
fof(f372,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| relation_image(X0,singleton(sK2(X0))) = singleton(apply(X0,sK2(X0))) ),
inference(duplicate_literal_removal,[],[f369]) ).
fof(f611,plain,
! [X0,X1] :
( relation_image(sK14,empty_set) = relation_image(sK14,set_intersection2(singleton(X1),singleton(X0)))
| X0 = X1 ),
inference(superposition,[],[f209,f313]) ).
fof(f614,plain,
! [X0,X1] :
( empty_set = relation_image(sK14,set_intersection2(singleton(X1),singleton(X0)))
| X0 = X1 ),
inference(forward_demodulation,[],[f611,f253]) ).
fof(f638,plain,
( ~ relation(sK14)
| ~ function(sK14)
| relation_image(sK14,singleton(sK1(sK14))) = singleton(apply(sK14,sK1(sK14))) ),
inference(resolution,[],[f371,f169]) ).
fof(f641,plain,
( ~ function(sK14)
| relation_image(sK14,singleton(sK1(sK14))) = singleton(apply(sK14,sK1(sK14))) ),
inference(forward_subsumption_resolution,[],[f638,f167]) ).
fof(f642,plain,
relation_image(sK14,singleton(sK1(sK14))) = singleton(apply(sK14,sK1(sK14))),
inference(forward_subsumption_resolution,[],[f641,f166]) ).
fof(f645,plain,
! [X0] : relation_image(sK14,set_intersection2(singleton(sK1(sK14)),X0)) = set_intersection2(relation_image(sK14,X0),singleton(apply(sK14,sK1(sK14)))),
inference(superposition,[],[f201,f642]) ).
fof(f657,plain,
( ~ relation(sK14)
| ~ function(sK14)
| relation_image(sK14,singleton(sK2(sK14))) = singleton(apply(sK14,sK2(sK14))) ),
inference(resolution,[],[f372,f169]) ).
fof(f660,plain,
( ~ function(sK14)
| relation_image(sK14,singleton(sK2(sK14))) = singleton(apply(sK14,sK2(sK14))) ),
inference(forward_subsumption_resolution,[],[f657,f167]) ).
fof(f661,plain,
relation_image(sK14,singleton(sK2(sK14))) = singleton(apply(sK14,sK2(sK14))),
inference(forward_subsumption_resolution,[],[f660,f166]) ).
fof(f668,plain,
! [X0] : relation_image(sK14,set_intersection2(singleton(sK2(sK14)),X0)) = set_intersection2(relation_image(sK14,X0),singleton(apply(sK14,sK2(sK14)))),
inference(superposition,[],[f201,f661]) ).
fof(f2026,plain,
! [X0] :
( set_intersection2(relation_image(sK14,X0),singleton(apply(sK14,sK1(sK14)))) = relation_image(sK14,set_intersection2(singleton(sK2(sK14)),X0))
| one_to_one(sK14)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(superposition,[],[f668,f123]) ).
fof(f2042,plain,
! [X0] :
( set_intersection2(relation_image(sK14,X0),singleton(apply(sK14,sK1(sK14)))) = relation_image(sK14,set_intersection2(singleton(sK2(sK14)),X0))
| ~ relation(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f2026,f169]) ).
fof(f2067,plain,
! [X0] :
( set_intersection2(relation_image(sK14,X0),singleton(apply(sK14,sK1(sK14)))) = relation_image(sK14,set_intersection2(singleton(sK2(sK14)),X0))
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f2042,f167]) ).
fof(f2075,plain,
! [X0] : set_intersection2(relation_image(sK14,X0),singleton(apply(sK14,sK1(sK14)))) = relation_image(sK14,set_intersection2(singleton(sK2(sK14)),X0)),
inference(forward_subsumption_resolution,[],[f2067,f166]) ).
fof(f2079,plain,
! [X0] : relation_image(sK14,set_intersection2(singleton(sK1(sK14)),X0)) = relation_image(sK14,set_intersection2(singleton(sK2(sK14)),X0)),
inference(forward_demodulation,[],[f2075,f645]) ).
fof(f3461,plain,
! [X0] :
( empty_set = relation_image(sK14,set_intersection2(singleton(sK1(sK14)),singleton(X0)))
| sK2(sK14) = X0 ),
inference(superposition,[],[f2079,f614]) ).
fof(f3539,plain,
( empty_set = relation_image(sK14,singleton(sK1(sK14)))
| sK1(sK14) = sK2(sK14) ),
inference(superposition,[],[f3461,f139]) ).
fof(f3586,plain,
( empty_set = singleton(apply(sK14,sK1(sK14)))
| sK1(sK14) = sK2(sK14) ),
inference(forward_demodulation,[],[f3539,f642]) ).
fof(f3594,definition,
( spl15_34
<=> sK1(sK14) = sK2(sK14) ),
introduced(definition,[new_symbols(definition,[spl15_34])],[avatar_definition]) ).
fof(f3596,plain,
( sK1(sK14) = sK2(sK14)
| ~ spl15_34 ),
inference(avatar_component_clause,[],[f3594]) ).
fof(f3598,definition,
( spl15_35
<=> empty_set = singleton(apply(sK14,sK1(sK14))) ),
introduced(definition,[new_symbols(definition,[spl15_35])],[avatar_definition]) ).
fof(f3600,plain,
( empty_set = singleton(apply(sK14,sK1(sK14)))
| ~ spl15_35 ),
inference(avatar_component_clause,[],[f3598]) ).
fof(f3601,plain,
( spl15_34
| spl15_35 ),
inference(avatar_split_clause,[],[f3586,f3598,f3594]) ).
fof(f3716,plain,
( sK1(sK14) != sK1(sK14)
| one_to_one(sK14)
| ~ relation(sK14)
| ~ function(sK14)
| ~ spl15_34 ),
inference(superposition,[],[f126,f3596]) ).
fof(f3718,plain,
( one_to_one(sK14)
| ~ relation(sK14)
| ~ function(sK14)
| ~ spl15_34 ),
inference(trivial_inequality_removal,[],[f3716]) ).
fof(f3719,plain,
( ~ relation(sK14)
| ~ function(sK14)
| ~ spl15_34 ),
inference(forward_subsumption_resolution,[],[f3718,f169]) ).
fof(f3720,plain,
( ~ function(sK14)
| ~ spl15_34 ),
inference(forward_subsumption_resolution,[],[f3719,f167]) ).
fof(f3721,plain,
( $false
| ~ spl15_34 ),
inference(forward_subsumption_resolution,[],[f3720,f166]) ).
fof(f3722,plain,
~ spl15_34,
inference(avatar_contradiction_clause,[],[f3721]) ).
fof(f3728,plain,
( ~ empty(empty_set)
| ~ spl15_35 ),
inference(superposition,[],[f133,f3600]) ).
fof(f3753,plain,
( $false
| ~ spl15_35 ),
inference(forward_subsumption_resolution,[],[f3728,f129]) ).
fof(f3754,plain,
~ spl15_35,
inference(avatar_contradiction_clause,[],[f3753]) ).
cnf(s40,plain,
( spl15_34
| spl15_35 ),
inference(sat_conversion,[],[f3601]) ).
cnf(s41,plain,
~ spl15_34,
inference(sat_conversion,[],[f3722]) ).
cnf(s43,plain,
~ spl15_35,
inference(sat_conversion,[],[f3754]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s40,s43,s41]) ).
fof(f3762,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU053+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:32:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.21/1.07 % (3233112)Detected formulas, will run a generic FOF schedule.
% 3.21/1.07 % (3233122)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2195920056:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.21/1.07 % (3233121)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=770185326:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.21/1.07 % (3233120)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3894939812:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.21/1.07 % (3233123)dis-21_1_sil=8000:lcm=predicate:random_seed=3368804214: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)
% 3.21/1.07 % (3233118)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=802475387:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.21/1.07 % (3233117)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=2674528015:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.21/1.07 % (3233119)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=3931262575:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.21/1.07 % (3233123)Instruction limit reached!
% 3.21/1.07 % (3233123)------------------------------
% 3.21/1.07 % (3233123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.07 % (3233123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.07 % (3233123)CaDiCaL version: 2.1.3
% 3.21/1.07 % (3233123)Termination reason: Instruction limit
% 3.21/1.07 % (3233123)Termination phase: Saturation
% 3.21/1.07 % (3233123)Time elapsed: 0.056 s
% 3.21/1.07 % (3233123)Peak memory usage: 90 MB
% 3.21/1.07 % (3233123)Instructions burned: 129 (million)
% 3.21/1.07 % (3233120)Instruction limit reached!
% 3.21/1.07 % (3233120)------------------------------
% 3.21/1.07 % (3233120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.07 % (3233120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.07 % (3233120)CaDiCaL version: 2.1.3
% 3.21/1.07 % (3233120)Termination reason: Instruction limit
% 3.21/1.07 % (3233120)Termination phase: Saturation
% 3.21/1.07 % (3233120)Time elapsed: 0.060 s
% 3.21/1.07 % (3233120)Peak memory usage: 89 MB
% 3.21/1.07 % (3233120)Instructions burned: 109 (million)
% 3.21/1.07 % (3233121)Instruction limit reached!
% 3.21/1.07 % (3233121)------------------------------
% 3.21/1.07 % (3233121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.07 % (3233121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.07 % (3233121)CaDiCaL version: 2.1.3
% 3.21/1.07 % (3233121)Termination reason: Instruction limit
% 3.21/1.07 % (3233121)Termination phase: Saturation
% 3.21/1.07 % (3233121)Time elapsed: 0.062 s
% 3.21/1.07 % (3233121)Peak memory usage: 88 MB
% 3.21/1.07 % (3233121)Instructions burned: 119 (million)
% 3.21/1.07 % (3233122)First to succeed.
% 3.21/1.07 % (3233122)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3233112"
% 3.21/1.07 % (3233131)lrs+10_1_sil=8000:sp=occurrence:random_seed=4159401655:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.21/1.07 % (3233132)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3375663349:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 3.21/1.07 % (3233133)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3545590185:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 3.21/1.07 % (3233131)Also succeeded, but the first one will report.
% 3.21/1.07 % (3233132)Instruction limit reached!
% 3.21/1.07 % (3233132)------------------------------
% 3.21/1.07 % (3233132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.07 % (3233132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.07 % (3233132)CaDiCaL version: 2.1.3
% 3.21/1.07 % (3233132)Termination reason: Instruction limit
% 3.21/1.07 % (3233132)Termination phase: Saturation
% 3.21/1.07 % (3233132)Time elapsed: 0.077 s
% 3.21/1.07 % (3233132)Peak memory usage: 90 MB
% 3.21/1.07 % (3233132)Instructions burned: 158 (million)
% 3.21/1.07 % (3233122)Refutation found. Thanks to Tanya!
% 3.21/1.07 % SZS status Theorem for theBenchmark
% 3.21/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.26 % (3233122)------------------------------
% 3.69/1.26 % (3233122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.26 % (3233122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.26 % (3233122)CaDiCaL version: 2.1.3
% 3.69/1.26 % (3233122)Termination reason: Refutation
% 3.69/1.26 % (3233122)Time elapsed: 0.082 s
% 3.69/1.26 % (3233122)Peak memory usage: 90 MB
% 3.69/1.26 % (3233122)Instructions burned: 134 (million)
% 3.69/1.26 % (3233122)------------------------------
% 3.69/1.26 % (3233122)------------------------------
% 3.69/1.26 % (3233112)Success in time 0.469 s
% 3.69/1.26 % Vampire exiting
%------------------------------------------------------------------------------