%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL498+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 11:52:37 AM UTC 2026
% Result : Theorem 12.04s 3.03s
% Output : Refutation 14.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 113 ( 41 unt; 3 def)
% Number of atoms : 203 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 166 ( 76 ~; 68 |; 2 &)
% ( 10 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 165 ( 0 sgn 164 !; 1 ?)
% 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(f21,axiom,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
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(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(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
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(f45,conjecture,
cn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn3) ).
fof(f46,negated_conjecture,
~ cn3,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ cn3,
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] : is_a_theorem(implies(implies(not(X0),X0),X0))
=> cn3 ),
inference(unused_predicate_definition_removal,[],[f21]) ).
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(f58,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f55]) ).
fof(f59,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f58]) ).
fof(f61,plain,
( cn3
| ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(ennf_transformation,[],[f53]) ).
fof(f62,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(ennf_transformation,[],[f52]) ).
fof(f63,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f51]) ).
fof(f64,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f50]) ).
fof(f65,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(ennf_transformation,[],[f49]) ).
fof(f66,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f48]) ).
fof(f69,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f71,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f59]) ).
fof(f74,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f75,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f76,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f64]) ).
fof(f78,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f65]) ).
fof(f79,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f66]) ).
fof(f82,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f69]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
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(f96,plain,
~ cn3,
inference(cnf_transformation,[],[f47]) ).
fof(f98,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[],[f82,f84]) ).
fof(f101,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))),
inference(forward_subsumption_resolution,[],[f79,f92]) ).
fof(f102,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(forward_subsumption_resolution,[],[f78,f91]) ).
fof(f103,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[],[f77,f90]) ).
fof(f104,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(forward_subsumption_resolution,[],[f76,f89]) ).
fof(f105,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(forward_subsumption_resolution,[],[f75,f88]) ).
fof(f106,plain,
~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)),
inference(forward_subsumption_resolution,[],[f74,f96]) ).
fof(f108,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f72,f87]) ).
fof(f113,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X1))),
inference(superposition,[],[f104,f98]) ).
fof(f120,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X2,X0),or(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f108,f101]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[],[f120,f108]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(or(not(X0),X2)) ),
inference(superposition,[],[f121,f98]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(forward_demodulation,[],[f126,f98]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| is_a_theorem(implies(X0,or(X1,X3)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(resolution,[],[f127,f120]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,or(X1,X2)))
| is_a_theorem(or(X1,or(X0,X2))) ),
inference(resolution,[],[f102,f108]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| is_a_theorem(or(X1,or(not(X0),X2))) ),
inference(superposition,[],[f133,f98]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| is_a_theorem(or(X1,implies(X0,X2))) ),
inference(forward_demodulation,[],[f143,f98]) ).
fof(f146,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,X1))),
inference(resolution,[],[f144,f104]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,implies(X0,X1)))
| is_a_theorem(or(not(X0),implies(X2,X1))) ),
inference(superposition,[],[f144,f98]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,implies(X0,X1)))
| is_a_theorem(implies(X0,implies(X2,X1))) ),
inference(forward_demodulation,[],[f149,f98]) ).
fof(f151,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[],[f150,f113]) ).
fof(f155,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,X1)) ),
inference(resolution,[],[f151,f108]) ).
fof(f157,definition,
( spl1_1
<=> ! [X1] : is_a_theorem(implies(X1,X1)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f158,plain,
( ! [X1] : is_a_theorem(implies(X1,X1))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,definition,
( spl1_2
<=> ! [X0] : ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f161,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f162,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f155,f160,f157]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X0),X1))
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[],[f146,f121]) ).
fof(f173,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(or(X1,X0),X1))),
inference(resolution,[],[f103,f144]) ).
fof(f175,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f103,f108]) ).
fof(f176,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[],[f103,f98]) ).
fof(f177,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(superposition,[],[f103,f98]) ).
fof(f182,plain,
( $false
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f173,f161]) ).
fof(f183,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f182]) ).
fof(f243,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f175,f98]) ).
fof(f251,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[],[f243,f98]) ).
fof(f267,plain,
( ! [X0] : is_a_theorem(implies(X0,not(not(X0))))
| ~ spl1_1 ),
inference(resolution,[],[f251,f158]) ).
fof(f274,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,not(X2))))
| is_a_theorem(implies(X0,implies(X2,X1))) ),
inference(resolution,[],[f177,f127]) ).
fof(f327,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X1)))),
inference(resolution,[],[f176,f163]) ).
fof(f346,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,not(X1)))),
inference(superposition,[],[f327,f98]) ).
fof(f362,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f105,f127]) ).
fof(f1375,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,or(X1,X2)))
| ~ is_a_theorem(implies(not(X1),X2)) ),
inference(resolution,[],[f131,f346]) ).
fof(f1389,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X2)))
| ~ is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f131,f103]) ).
fof(f1405,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1389,f362]) ).
fof(f1435,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f1405,f98]) ).
fof(f1664,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(not(X0),not(X1)))
| is_a_theorem(implies(X2,implies(X1,X0))) ),
inference(resolution,[],[f1375,f274]) ).
fof(f1760,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(not(X1)),X1)))
| ~ spl1_1 ),
inference(resolution,[],[f1664,f267]) ).
fof(f1778,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(not(not(X1)),X1)) )
| ~ spl1_1 ),
inference(resolution,[],[f1760,f108]) ).
fof(f1796,definition,
( spl1_16
<=> ! [X1] : is_a_theorem(implies(not(not(X1)),X1)) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f1797,plain,
( ! [X1] : is_a_theorem(implies(not(not(X1)),X1))
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f1796]) ).
fof(f1798,plain,
( spl1_16
| spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f1778,f157,f160,f1796]) ).
fof(f3703,plain,
~ is_a_theorem(implies(not(not(sK0)),sK0)),
inference(resolution,[],[f1435,f106]) ).
fof(f3733,plain,
( $false
| ~ spl1_16 ),
inference(forward_subsumption_resolution,[],[f3703,f1797]) ).
fof(f3734,plain,
~ spl1_16,
inference(avatar_contradiction_clause,[],[f3733]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f162]) ).
cnf(s4,plain,
~ spl1_2,
inference(sat_conversion,[],[f183]) ).
cnf(s29,plain,
( ~ spl1_1
| spl1_2
| spl1_16 ),
inference(sat_conversion,[],[f1798]) ).
cnf(s52,plain,
~ spl1_16,
inference(sat_conversion,[],[f3734]) ).
cnf(s53,plain,
( ~ spl1_1
| spl1_2 ),
inference(rat,[],[s29,s52]) ).
cnf(s57,plain,
~ spl1_1,
inference(rat,[],[s53,s4]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s1,s4,s57]) ).
fof(f3735,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL498+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n008.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 15:51:54 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 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
% 12.04/3.03 % (1412048)Detected formulas, will run a generic FOF schedule.
% 12.04/3.03 % (1412056)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3739972532:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.04/3.03 % (1412056)Refutation not found, incomplete strategy
% 12.04/3.03 % (1412056)------------------------------
% 12.04/3.03 % (1412056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412056)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412056)Termination reason: Refutation not found, incomplete strategy
% 12.04/3.03 % (1412056)Time elapsed: 0.001 s
% 12.04/3.03 % (1412056)Peak memory usage: 86 MB
% 12.04/3.03 % (1412059)dis-21_1_sil=8000:lcm=predicate:random_seed=2569808981: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)
% 12.04/3.03 % (1412059)Refutation not found, incomplete strategy
% 12.04/3.03 % (1412059)------------------------------
% 12.04/3.03 % (1412059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412059)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412059)Termination reason: Refutation not found, incomplete strategy
% 12.04/3.03 % (1412059)Time elapsed: 0.003 s
% 12.04/3.03 % (1412059)Peak memory usage: 88 MB
% 12.04/3.03 % (1412053)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=984369168:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.04/3.03 % (1412054)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=2273790258:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.04/3.03 % (1412055)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=880586660:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.04/3.03 % (1412057)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2812272029:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.04/3.03 % (1412058)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=101693780:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.04/3.03 % (1412057)Refutation not found, incomplete strategy
% 12.04/3.03 % (1412057)------------------------------
% 12.04/3.03 % (1412057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412057)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412057)Termination reason: Refutation not found, incomplete strategy
% 12.04/3.03 % (1412057)Time elapsed: 0.001 s
% 12.04/3.03 % (1412057)Peak memory usage: 86 MB
% 12.04/3.03 % (1412058)Instruction limit reached!
% 12.04/3.03 % (1412058)------------------------------
% 12.04/3.03 % (1412058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412058)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412058)Termination reason: Instruction limit
% 12.04/3.03 % (1412058)Termination phase: Saturation
% 12.04/3.03 % (1412058)Time elapsed: 0.144 s
% 12.04/3.03 % (1412058)Peak memory usage: 90 MB
% 12.04/3.03 % (1412058)Instructions burned: 139 (million)
% 12.04/3.03 % (1412056)------------------------------
% 12.04/3.03 % (1412056)------------------------------
% 12.04/3.03 % (1412059)------------------------------
% 12.04/3.03 % (1412059)------------------------------
% 12.04/3.03 % (1412057)------------------------------
% 12.04/3.03 % (1412057)------------------------------
% 12.04/3.03 % (1412070)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3448160260:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 12.04/3.03 % (1412069)lrs+10_1_sil=8000:sp=occurrence:random_seed=1060099297:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 12.04/3.03 % (1412070)Refutation not found, incomplete strategy
% 12.04/3.03 % (1412070)------------------------------
% 12.04/3.03 % (1412070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412070)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412070)Termination reason: Refutation not found, incomplete strategy
% 12.04/3.03 % (1412070)Time elapsed: 0.002 s
% 12.04/3.03 % (1412070)Peak memory usage: 87 MB
% 12.04/3.03 % (1412071)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1055795983:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 12.04/3.03 % (1412072)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=1734635868:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 12.04/3.03 % (1412071)Refutation not found, incomplete strategy
% 12.04/3.03 % (1412071)------------------------------
% 12.04/3.03 % (1412071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412071)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412071)Termination reason: Refutation not found, incomplete strategy
% 12.04/3.03 % (1412071)Time elapsed: 0.001 s
% 12.04/3.03 % (1412071)Peak memory usage: 86 MB
% 12.04/3.03 % (1412069)Instruction limit reached!
% 12.04/3.03 % (1412069)------------------------------
% 12.04/3.03 % (1412069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412069)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412069)Termination reason: Instruction limit
% 12.04/3.03 % (1412069)Termination phase: Saturation
% 12.04/3.03 % (1412069)Time elapsed: 0.271 s
% 12.04/3.03 % (1412069)Peak memory usage: 91 MB
% 12.04/3.03 % (1412069)Instructions burned: 286 (million)
% 12.04/3.03 % (1412072)Instruction limit reached!
% 12.04/3.03 % (1412072)------------------------------
% 12.04/3.03 % (1412072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412072)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412072)Termination reason: Instruction limit
% 12.04/3.03 % (1412072)Termination phase: Saturation
% 12.04/3.03 % (1412072)Time elapsed: 0.221 s
% 12.04/3.03 % (1412072)Peak memory usage: 92 MB
% 12.04/3.03 % (1412072)Instructions burned: 248 (million)
% 12.04/3.03 % (1412071)------------------------------
% 12.04/3.03 % (1412071)------------------------------
% 12.04/3.03 % (1412070)------------------------------
% 12.04/3.03 % (1412070)------------------------------
% 12.04/3.03 % (1412055)Refutation not found, incomplete strategy
% 12.04/3.03 % (1412055)------------------------------
% 12.04/3.03 % (1412055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412055)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412055)Termination reason: Refutation not found, incomplete strategy
% 12.04/3.03 % (1412055)Time elapsed: 0.927 s
% 12.04/3.03 % (1412055)Peak memory usage: 127 MB
% 12.04/3.03 % (1412055)Instructions burned: 829 (million)
% 12.04/3.03 % (1412077)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1816780428:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2990 on theBenchmark for (2990ds/294Mi)
% 12.04/3.03 % (1412077)Refutation not found, incomplete strategy
% 12.04/3.03 % (1412077)------------------------------
% 12.04/3.03 % (1412077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412077)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412077)Termination reason: Refutation not found, incomplete strategy
% 12.04/3.03 % (1412077)Time elapsed: 0.001 s
% 12.04/3.03 % (1412077)Peak memory usage: 87 MB
% 12.04/3.03 % (1412078)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2980222276:i=2350_2989 on theBenchmark for (2989ds/2350Mi)
% 12.04/3.03 % (1412079)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3792613655:cts=off:i=113:fsr=off:ss=included:sgt=4_2989 on theBenchmark for (2989ds/113Mi)
% 12.04/3.03 % (1412079)Refutation not found, incomplete strategy
% 12.04/3.03 % (1412079)------------------------------
% 12.04/3.03 % (1412079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412079)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412079)Termination reason: Refutation not found, incomplete strategy
% 12.04/3.03 % (1412079)Time elapsed: 0.002 s
% 12.04/3.03 % (1412079)Peak memory usage: 88 MB
% 12.04/3.03 % (1412080)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1105449687:i=127:av=off:fsr=off:sup=off_2989 on theBenchmark for (2989ds/127Mi)
% 12.04/3.03 % (1412080)Instruction limit reached!
% 12.04/3.03 % (1412080)------------------------------
% 12.04/3.03 % (1412080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412080)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412080)Termination reason: Instruction limit
% 12.04/3.03 % (1412080)Termination phase: Saturation
% 12.04/3.03 % (1412080)Time elapsed: 0.118 s
% 12.04/3.03 % (1412080)Peak memory usage: 88 MB
% 12.04/3.03 % (1412080)Instructions burned: 128 (million)
% 12.04/3.03 % (1412055)------------------------------
% 12.04/3.03 % (1412055)------------------------------
% 12.04/3.03 % (1412077)------------------------------
% 12.04/3.03 % (1412077)------------------------------
% 12.04/3.03 % (1412053)First to succeed.
% 12.04/3.03 % (1412053)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1412048"
% 12.04/3.03 % (1412085)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1761054107:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2985 on theBenchmark for (2985ds/114Mi)
% 12.04/3.03 % (1412085)Refutation not found, incomplete strategy
% 12.04/3.03 % (1412085)------------------------------
% 12.04/3.03 % (1412085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412085)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412085)Termination reason: Refutation not found, incomplete strategy
% 12.04/3.03 % (1412085)Time elapsed: 0.002 s
% 12.04/3.03 % (1412085)Peak memory usage: 87 MB
% 12.04/3.03 % (1412079)------------------------------
% 12.04/3.03 % (1412079)------------------------------
% 12.04/3.03 % (1412086)lrs+10_1_sil=8000:sp=occurrence:random_seed=752709026:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2984 on theBenchmark for (2984ds/907Mi)
% 12.04/3.03 % (1412087)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1779211144:i=437:sd=1:aac=none:ss=included_2983 on theBenchmark for (2983ds/437Mi)
% 12.04/3.03 % (1412087)Refutation not found, incomplete strategy
% 12.04/3.03 % (1412087)------------------------------
% 12.04/3.03 % (1412087)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.04/3.03 % (1412087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.04/3.03 % (1412087)CaDiCaL version: 2.1.3
% 12.04/3.03 % (1412087)Termination reason: Refutation not found, incomplete strategy
% 12.04/3.03 % (1412087)Time elapsed: 0.002 s
% 12.04/3.03 % (1412087)Peak memory usage: 88 MB
% 12.04/3.03 % (1412053)Refutation found. Thanks to Tanya!
% 12.04/3.03 % SZS status Theorem for theBenchmark
% 12.04/3.03 % SZS output start Proof for theBenchmark
% See solution above
% 14.66/3.23 % (1412053)------------------------------
% 14.66/3.23 % (1412053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.23 % (1412053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.23 % (1412053)CaDiCaL version: 2.1.3
% 14.66/3.23 % (1412053)Termination reason: Refutation
% 14.66/3.23 % (1412053)Time elapsed: 1.446 s
% 14.66/3.23 % (1412053)Peak memory usage: 136 MB
% 14.66/3.23 % (1412053)Instructions burned: 1769 (million)
% 14.66/3.23 % (1412053)------------------------------
% 14.66/3.23 % (1412053)------------------------------
% 14.66/3.23 % (1412048)Success in time 1.956 s
% 14.66/3.23 % Vampire exiting
%------------------------------------------------------------------------------