%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL539+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 : n004.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 11:52:53 AM UTC 2026
% Result : Theorem 6.53s 1.96s
% Output : Refutation 8.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 103 ( 44 unt; 1 def)
% Number of atoms : 183 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 135 ( 55 ~; 51 |; 4 &)
% ( 9 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 108 !; 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(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
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(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(f53,axiom,
( substitution_strict_equiv
<=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_strict_equiv) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_M) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f76,axiom,
( op_strict_equiv
=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_equiv) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_axiom_M) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f89,conjecture,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f90,negated_conjecture,
~ substitution_strict_equiv,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ substitution_strict_equiv,
inference(flattening,[],[f90]) ).
fof(f94,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f96,plain,
( ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 )
=> substitution_strict_equiv ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f98,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f99,plain,
( equivalence_2
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f105,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f106,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f111,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f112,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(f117,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f112]) ).
fof(f118,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f111]) ).
fof(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f106]) ).
fof(f125,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f105]) ).
fof(f131,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f99]) ).
fof(f132,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f98]) ).
fof(f137,plain,
( substitution_strict_equiv
| ? [X0,X1] :
( X0 != X1
& is_a_theorem(strict_equiv(X0,X1)) ) ),
inference(ennf_transformation,[],[f96]) ).
fof(f139,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f94]) ).
fof(f143,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f144,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f76]) ).
fof(f145,plain,
( substitution_strict_equiv
| ( sK0 != sK1
& is_a_theorem(strict_equiv(sK0,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f137]) ).
fof(f146,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f118]) ).
fof(f147,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f119]) ).
fof(f152,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f153,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f159,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f131]) ).
fof(f160,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f132]) ).
fof(f167,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f172,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f173,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f179,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f180,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f181,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f183,plain,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(sK0,sK1)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f184,plain,
( substitution_strict_equiv
| sK0 != sK1 ),
inference(cnf_transformation,[],[f145]) ).
fof(f186,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f139]) ).
fof(f190,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f143]) ).
fof(f191,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f144]) ).
fof(f195,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f200,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f202,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f88]) ).
fof(f203,plain,
~ substitution_strict_equiv,
inference(cnf_transformation,[],[f91]) ).
fof(f204,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f191,f202]) ).
fof(f205,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f190,f200]) ).
fof(f209,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(forward_subsumption_resolution,[],[f186,f195]) ).
fof(f211,plain,
is_a_theorem(strict_equiv(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f183,f203]) ).
fof(f212,plain,
sK0 != sK1,
inference(forward_subsumption_resolution,[],[f184,f203]) ).
fof(f217,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(forward_subsumption_resolution,[],[f160,f180]) ).
fof(f218,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(forward_subsumption_resolution,[],[f159,f179]) ).
fof(f224,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(forward_subsumption_resolution,[],[f153,f173]) ).
fof(f225,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f152,f172]) ).
fof(f230,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f147,f181]) ).
fof(f231,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f146,f167]) ).
fof(f238,plain,
! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f209,f231]) ).
fof(f295,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f217,f231]) ).
fof(f300,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f295,f231]) ).
fof(f307,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| is_a_theorem(equiv(equiv(X0,X1),implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f300,f295]) ).
fof(f313,plain,
! [X0,X1] :
( is_a_theorem(equiv(equiv(X0,X1),implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f307,f218]) ).
fof(f317,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| equiv(X0,X1) = implies(X1,X0) ),
inference(resolution,[],[f313,f230]) ).
fof(f334,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f238,f205]) ).
fof(f452,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X0,X1))),
inference(superposition,[],[f225,f204]) ).
fof(f457,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f452,f231]) ).
fof(f459,plain,
is_a_theorem(strict_implies(sK0,sK1)),
inference(resolution,[],[f457,f211]) ).
fof(f460,plain,
is_a_theorem(implies(sK0,sK1)),
inference(resolution,[],[f459,f334]) ).
fof(f461,plain,
equiv(sK0,sK1) = implies(sK1,sK0),
inference(resolution,[],[f460,f317]) ).
fof(f480,definition,
( spl2_4
<=> is_a_theorem(implies(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f481,plain,
( is_a_theorem(implies(sK1,sK0))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f482,plain,
( ~ is_a_theorem(implies(sK1,sK0))
| spl2_4 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f487,plain,
( ~ is_a_theorem(implies(sK1,sK0))
| sK0 = sK1 ),
inference(superposition,[],[f230,f461]) ).
fof(f494,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X1,X0))),
inference(superposition,[],[f224,f204]) ).
fof(f499,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(resolution,[],[f494,f231]) ).
fof(f501,plain,
is_a_theorem(strict_implies(sK1,sK0)),
inference(resolution,[],[f499,f211]) ).
fof(f502,plain,
is_a_theorem(implies(sK1,sK0)),
inference(resolution,[],[f501,f334]) ).
fof(f503,plain,
( $false
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f502,f482]) ).
fof(f504,plain,
spl2_4,
inference(avatar_contradiction_clause,[],[f503]) ).
fof(f505,plain,
( sK0 = sK1
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f487,f481]) ).
fof(f506,plain,
( $false
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f505,f212]) ).
fof(f507,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f506]) ).
cnf(s3,plain,
spl2_4,
inference(sat_conversion,[],[f504]) ).
cnf(s4,plain,
~ spl2_4,
inference(sat_conversion,[],[f507]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s3,s4]) ).
fof(f508,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL539+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.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 : Sun Sep 27 15:58:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 6.53/1.96 % (3695931)Detected formulas, will run a generic FOF schedule.
% 6.53/1.96 % (3695938)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=1275557926:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.53/1.96 % (3695941)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3301409345:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.53/1.96 % (3695940)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2421904367:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.53/1.96 % (3695936)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=2611816875:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.53/1.96 % (3695939)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=327414952:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.53/1.96 % (3695942)dis-21_1_sil=8000:lcm=predicate:random_seed=1485126591: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)
% 6.53/1.96 % (3695937)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=1699534490:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.53/1.96 % (3695940)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695940)------------------------------
% 6.53/1.96 % (3695940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695939)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695939)------------------------------
% 6.53/1.96 % (3695939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695940)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695939)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695940)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695940)Time elapsed: 0.001 s
% 6.53/1.96 % (3695939)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695939)Time elapsed: 0.001 s
% 6.53/1.96 % (3695940)Peak memory usage: 88 MB
% 6.53/1.96 % (3695939)Peak memory usage: 88 MB
% 6.53/1.96 % (3695942)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695942)------------------------------
% 6.53/1.96 % (3695942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695942)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695942)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695942)Time elapsed: 0.002 s
% 6.53/1.96 % (3695942)Peak memory usage: 88 MB
% 6.53/1.96 % (3695942)Instructions burned: 1 (million)
% 6.53/1.96 % (3695941)Instruction limit reached!
% 6.53/1.96 % (3695941)------------------------------
% 6.53/1.96 % (3695941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695941)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695941)Termination reason: Instruction limit
% 6.53/1.96 % (3695941)Termination phase: Saturation
% 6.53/1.96 % (3695941)Time elapsed: 0.094 s
% 6.53/1.96 % (3695941)Peak memory usage: 90 MB
% 6.53/1.96 % (3695941)Instructions burned: 141 (million)
% 6.53/1.96 % (3695950)lrs+10_1_sil=8000:sp=occurrence:random_seed=650540218:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.53/1.96 % (3695950)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695950)------------------------------
% 6.53/1.96 % (3695950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695950)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695950)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695950)Time elapsed: 0.001 s
% 6.53/1.96 % (3695950)Peak memory usage: 88 MB
% 6.53/1.96 % (3695940)------------------------------
% 6.53/1.96 % (3695940)------------------------------
% 6.53/1.96 % (3695942)------------------------------
% 6.53/1.96 % (3695942)------------------------------
% 6.53/1.96 % (3695939)------------------------------
% 6.53/1.96 % (3695939)------------------------------
% 6.53/1.96 % (3695938)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695938)------------------------------
% 6.53/1.96 % (3695938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695938)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695938)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695938)Time elapsed: 0.327 s
% 6.53/1.96 % (3695938)Peak memory usage: 128 MB
% 6.53/1.96 % (3695938)Instructions burned: 894 (million)
% 6.53/1.96 % (3695952)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3522968901:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 6.53/1.96 % (3695954)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=395024201:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.53/1.96 % (3695953)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3917472322:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 6.53/1.96 % (3695953)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695953)------------------------------
% 6.53/1.96 % (3695953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695953)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695953)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695953)Time elapsed: 0.001 s
% 6.53/1.96 % (3695953)Peak memory usage: 88 MB
% 6.53/1.96 % (3695952)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695952)------------------------------
% 6.53/1.96 % (3695952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695952)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695952)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695952)Time elapsed: 0.001 s
% 6.53/1.96 % (3695952)Peak memory usage: 88 MB
% 6.53/1.96 % (3695952)Instructions burned: 1 (million)
% 6.53/1.96 % (3695938)------------------------------
% 6.53/1.96 % (3695938)------------------------------
% 6.53/1.96 % (3695950)------------------------------
% 6.53/1.96 % (3695950)------------------------------
% 6.53/1.96 % (3695954)Instruction limit reached!
% 6.53/1.96 % (3695954)------------------------------
% 6.53/1.96 % (3695954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695954)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695954)Termination reason: Instruction limit
% 6.53/1.96 % (3695954)Termination phase: Saturation
% 6.53/1.96 % (3695954)Time elapsed: 0.152 s
% 6.53/1.96 % (3695954)Peak memory usage: 93 MB
% 6.53/1.96 % (3695954)Instructions burned: 249 (million)
% 6.53/1.96 % (3695958)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2838756513:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 6.53/1.96 % (3695958)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695958)------------------------------
% 6.53/1.96 % (3695958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695958)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695958)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695958)Time elapsed: 0.001 s
% 6.53/1.96 % (3695958)Peak memory usage: 88 MB
% 6.53/1.96 % (3695959)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1651249428:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 6.53/1.96 % (3695952)------------------------------
% 6.53/1.96 % (3695952)------------------------------
% 6.53/1.96 % (3695953)------------------------------
% 6.53/1.96 % (3695953)------------------------------
% 6.53/1.96 % (3695960)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2740889246:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.53/1.96 % (3695960)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695960)------------------------------
% 6.53/1.96 % (3695960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695960)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695960)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695960)Time elapsed: 0.001 s
% 6.53/1.96 % (3695960)Peak memory usage: 88 MB
% 6.53/1.96 % (3695960)Instructions burned: 1 (million)
% 6.53/1.96 % (3695958)------------------------------
% 6.53/1.96 % (3695958)------------------------------
% 6.53/1.96 % (3695936)First to succeed.
% 6.53/1.96 % (3695936)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3695931"
% 6.53/1.96 % (3695963)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1415103294:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.53/1.96 % (3695964)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=72880769:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.53/1.96 % (3695964)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695964)------------------------------
% 6.53/1.96 % (3695964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695964)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695964)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695964)Time elapsed: 0.001 s
% 6.53/1.96 % (3695964)Peak memory usage: 88 MB
% 6.53/1.96 % (3695964)Instructions burned: 1 (million)
% 6.53/1.96 % (3695966)lrs+10_1_sil=8000:sp=occurrence:random_seed=2973969299:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.53/1.96 % (3695963)Instruction limit reached!
% 6.53/1.96 % (3695963)------------------------------
% 6.53/1.96 % (3695963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695963)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695963)Termination reason: Instruction limit
% 6.53/1.96 % (3695963)Termination phase: Saturation
% 6.53/1.96 % (3695963)Time elapsed: 0.064 s
% 6.53/1.96 % (3695963)Peak memory usage: 89 MB
% 6.53/1.96 % (3695963)Instructions burned: 127 (million)
% 6.53/1.96 % (3695960)------------------------------
% 6.53/1.96 % (3695960)------------------------------
% 6.53/1.96 % (3695970)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1744126375:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 6.53/1.96 % (3695970)Refutation not found, incomplete strategy
% 6.53/1.96 % (3695970)------------------------------
% 6.53/1.96 % (3695970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.53/1.96 % (3695970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.53/1.96 % (3695970)CaDiCaL version: 2.1.3
% 6.53/1.96 % (3695970)Termination reason: Refutation not found, incomplete strategy
% 6.53/1.96 % (3695970)Time elapsed: 0.001 s
% 6.53/1.96 % (3695970)Peak memory usage: 88 MB
% 6.53/1.96 % (3695936)Refutation found. Thanks to Tanya!
% 6.53/1.96 % SZS status Theorem for theBenchmark
% 6.53/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 8.46/2.15 % (3695936)------------------------------
% 8.46/2.15 % (3695936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.46/2.15 % (3695936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.46/2.15 % (3695936)CaDiCaL version: 2.1.3
% 8.46/2.15 % (3695936)Termination reason: Refutation
% 8.46/2.15 % (3695936)Time elapsed: 0.701 s
% 8.46/2.15 % (3695936)Peak memory usage: 129 MB
% 8.46/2.15 % (3695936)Instructions burned: 999 (million)
% 8.46/2.15 % (3695936)------------------------------
% 8.46/2.15 % (3695936)------------------------------
% 8.46/2.15 % (3695931)Success in time 1.111 s
% 8.46/2.15 % Vampire exiting
%------------------------------------------------------------------------------