%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL045+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:34:07 PM UTC 2026
% Result : Theorem 9.43s 2.39s
% Output : Refutation 10.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 19
% Syntax : Number of formulae : 105 ( 105 unt; 4 def)
% Number of atoms : 105 ( 104 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 151 ( 150 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
fof(f14,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dedekind_law) ).
fof(f17,conjecture,
! [X0] : join(X0,composition(composition(X0,converse(X0)),X0)) = composition(composition(X0,converse(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] : join(X0,composition(composition(X0,converse(X0)),X0)) = composition(composition(X0,converse(X0)),X0),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0] : composition(composition(X0,converse(X0)),X0) != join(X0,composition(composition(X0,converse(X0)),X0)),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
composition(composition(sK0,converse(sK0)),sK0) != join(sK0,composition(composition(sK0,converse(sK0)),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f19]) ).
fof(f21,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f22,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f27,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f28,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f29,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f30,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f32,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f33,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f34,plain,
! [X2,X0,X1] : composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) = join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))),
inference(cnf_transformation,[],[f14]) ).
fof(f37,plain,
composition(composition(sK0,converse(sK0)),sK0) != join(sK0,composition(composition(sK0,converse(sK0)),sK0)),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f33,f24]) ).
fof(f39,plain,
! [X2,X0,X1] : composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2))))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2)))))),
inference(definition_unfolding,[],[f34,f24,f24,f24,f24,f24]) ).
fof(f42,definition,
sF1 = converse(sK0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f43,plain,
converse(sK0) = sF1,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF2 = composition(sK0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f45,plain,
composition(sK0,sF1) = sF2,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF3 = composition(sF2,sK0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f47,plain,
composition(sF2,sK0) = sF3,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF4 = join(sK0,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f49,plain,
join(sK0,sF3) = sF4,
inference(reorient_equations,[],[f48]) ).
fof(f50,plain,
sF3 != sF4,
inference(definition_folding,[],[f37,f49,f47,f45,f43,f47,f45,f43]) ).
fof(f52,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f29,f28]) ).
fof(f66,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f30,f28]) ).
fof(f70,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f27,f30]) ).
fof(f91,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f21,f22]) ).
fof(f104,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f66,f26]) ).
fof(f112,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f104,f28]) ).
fof(f123,plain,
one = converse(one),
inference(superposition,[],[f26,f112]) ).
fof(f126,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f112,f123]) ).
fof(f188,plain,
! [X0] : composition(sK0,composition(sF1,X0)) = composition(sF2,X0),
inference(superposition,[],[f25,f45]) ).
fof(f198,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f22,f32]) ).
fof(f201,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f52,f32]) ).
fof(f235,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(superposition,[],[f31,f112]) ).
fof(f241,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f235,f126]) ).
fof(f257,plain,
! [X0,X1] : join(complement(X1),join(X0,X1)) = join(X0,top),
inference(superposition,[],[f91,f32]) ).
fof(f344,plain,
! [X2,X0,X1] : composition(complement(join(complement(X1),complement(composition(X0,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X0))))) = join(complement(join(complement(X0),complement(composition(X1,X2)))),composition(complement(join(complement(X1),complement(composition(X0,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X0)))))),
inference(superposition,[],[f39,f21]) ).
fof(f427,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f23,f21]) ).
fof(f442,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f22,f23]) ).
fof(f464,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[],[f198,f241]) ).
fof(f468,plain,
! [X0,X1] : join(top,X0) = join(X1,join(X0,complement(X1))),
inference(superposition,[],[f198,f21]) ).
fof(f493,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f464,f32]) ).
fof(f531,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f70,f30]) ).
fof(f548,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f531,f29]) ).
fof(f568,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f548,f29]) ).
fof(f578,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f568,f30]) ).
fof(f607,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f28,f578]) ).
fof(f626,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f607,f28]) ).
fof(f667,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(one,X1)),
inference(superposition,[],[f626,f26]) ).
fof(f811,plain,
! [X0] : join(X0,composition(X0,complement(one))) = composition(X0,top),
inference(superposition,[],[f667,f32]) ).
fof(f1696,plain,
! [X0,X1] : join(join(complement(X0),X1),X0) = join(top,complement(join(complement(X1),complement(X0)))),
inference(superposition,[],[f468,f427]) ).
fof(f1727,plain,
! [X0,X1] : top = join(join(complement(X0),X1),X0),
inference(forward_demodulation,[],[f1696,f493]) ).
fof(f1733,plain,
! [X0,X1] : top = join(complement(X0),join(X1,X0)),
inference(forward_demodulation,[],[f1727,f22]) ).
fof(f1737,plain,
! [X1] : top = join(X1,top),
inference(forward_demodulation,[],[f1733,f257]) ).
fof(f1746,plain,
! [X0] : top = join(top,X0),
inference(superposition,[],[f21,f1737]) ).
fof(f1792,plain,
top = converse(top),
inference(superposition,[],[f201,f1746]) ).
fof(f1826,plain,
zero = complement(top),
inference(superposition,[],[f38,f32]) ).
fof(f1829,plain,
! [X0] : complement(X0) = join(zero,complement(join(complement(complement(X0)),X0))),
inference(superposition,[],[f427,f38]) ).
fof(f3188,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X0),X1))),
inference(superposition,[],[f442,f241]) ).
fof(f3236,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f3188,f23]) ).
fof(f3301,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f3236,f38]) ).
fof(f3312,plain,
! [X0,X1] : join(complement(complement(X0)),complement(join(complement(X0),join(complement(complement(X0)),X1)))) = X0,
inference(superposition,[],[f23,f3236]) ).
fof(f3349,plain,
! [X0,X1] : join(complement(complement(X0)),complement(join(top,X1))) = X0,
inference(forward_demodulation,[],[f3312,f198]) ).
fof(f3369,plain,
! [X0] : join(complement(complement(X0)),complement(top)) = X0,
inference(forward_demodulation,[],[f3349,f1746]) ).
fof(f3377,plain,
! [X0] : join(complement(complement(X0)),zero) = X0,
inference(forward_demodulation,[],[f3369,f1826]) ).
fof(f3381,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f3377,f3301]) ).
fof(f3384,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(superposition,[],[f1829,f3381]) ).
fof(f3397,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f241,f3381]) ).
fof(f3412,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f3236,f3381]) ).
fof(f3418,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f3384,f3397]) ).
fof(f3931,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(X0,top))),
inference(superposition,[],[f3412,f811]) ).
fof(f4061,plain,
! [X0] : composition(complement(join(complement(X0),complement(composition(X0,converse(top))))),complement(join(complement(top),complement(composition(converse(X0),X0))))) = join(complement(complement(X0)),composition(complement(join(complement(X0),complement(composition(X0,converse(top))))),complement(join(complement(top),complement(composition(converse(X0),X0)))))),
inference(superposition,[],[f344,f3931]) ).
fof(f4105,plain,
! [X0] : composition(complement(join(complement(X0),complement(composition(X0,converse(top))))),complement(join(zero,complement(composition(converse(X0),X0))))) = join(complement(complement(X0)),composition(complement(join(complement(X0),complement(composition(X0,converse(top))))),complement(join(zero,complement(composition(converse(X0),X0)))))),
inference(forward_demodulation,[],[f4061,f1826]) ).
fof(f4124,plain,
! [X0] : composition(complement(join(complement(X0),complement(composition(X0,converse(top))))),complement(complement(composition(converse(X0),X0)))) = join(complement(complement(X0)),composition(complement(join(complement(X0),complement(composition(X0,converse(top))))),complement(complement(composition(converse(X0),X0))))),
inference(forward_demodulation,[],[f4105,f3418]) ).
fof(f4138,plain,
! [X0] : composition(complement(join(complement(X0),complement(composition(X0,converse(top))))),composition(converse(X0),X0)) = join(complement(complement(X0)),composition(complement(join(complement(X0),complement(composition(X0,converse(top))))),composition(converse(X0),X0))),
inference(forward_demodulation,[],[f4124,f3381]) ).
fof(f4148,plain,
! [X0] : composition(complement(join(complement(X0),complement(composition(X0,top)))),composition(converse(X0),X0)) = join(complement(complement(X0)),composition(complement(join(complement(X0),complement(composition(X0,top)))),composition(converse(X0),X0))),
inference(forward_demodulation,[],[f4138,f1792]) ).
fof(f4154,plain,
! [X0] : composition(complement(complement(X0)),composition(converse(X0),X0)) = join(complement(complement(X0)),composition(complement(complement(X0)),composition(converse(X0),X0))),
inference(forward_demodulation,[],[f4148,f3931]) ).
fof(f4158,plain,
! [X0] : composition(X0,composition(converse(X0),X0)) = join(X0,composition(X0,composition(converse(X0),X0))),
inference(forward_demodulation,[],[f4154,f3381]) ).
fof(f4312,plain,
composition(sK0,composition(sF1,sK0)) = join(sK0,composition(sK0,composition(sF1,sK0))),
inference(superposition,[],[f4158,f43]) ).
fof(f4382,plain,
composition(sF2,sK0) = join(sK0,composition(sF2,sK0)),
inference(forward_demodulation,[],[f4312,f188]) ).
fof(f4414,plain,
sF3 = join(sK0,sF3),
inference(forward_demodulation,[],[f4382,f47]) ).
fof(f4440,plain,
sF3 = sF4,
inference(forward_demodulation,[],[f4414,f49]) ).
fof(f4457,plain,
$false,
inference(forward_subsumption_resolution,[],[f4440,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL045+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n013.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 22:56:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 9.43/2.39 % (643368)Detected formulas, will run a generic FOF schedule.
% 9.43/2.39 % (643390)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=128619984:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.43/2.39 % (643396)dis-21_1_sil=8000:lcm=predicate:random_seed=362426652:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 9.43/2.39 % (643396)Refutation not found, incomplete strategy
% 9.43/2.39 % (643396)------------------------------
% 9.43/2.39 % (643396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643396)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643396)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.39 % (643396)Time elapsed: 0.003 s
% 9.43/2.39 % (643396)Peak memory usage: 88 MB
% 9.43/2.39 % (643396)Instructions burned: 1 (million)
% 9.43/2.39 % (643392)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=591102616:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.43/2.39 % (643393)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=782277046:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.43/2.39 % (643394)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2258176542:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.43/2.39 % (643391)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=3808800970:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.43/2.39 % (643393)Refutation not found, incomplete strategy
% 9.43/2.39 % (643393)------------------------------
% 9.43/2.39 % (643393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643393)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643393)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.39 % (643393)Time elapsed: 0.002 s
% 9.43/2.39 % (643393)Peak memory usage: 88 MB
% 9.43/2.39 % (643395)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2036322508:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.43/2.39 % (643394)Instruction limit reached!
% 9.43/2.39 % (643394)------------------------------
% 9.43/2.39 % (643394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643394)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643394)Termination reason: Instruction limit
% 9.43/2.39 % (643394)Termination phase: Saturation
% 9.43/2.39 % (643394)Time elapsed: 0.108 s
% 9.43/2.39 % (643394)Peak memory usage: 88 MB
% 9.43/2.39 % (643394)Instructions burned: 119 (million)
% 9.43/2.39 % (643395)Instruction limit reached!
% 9.43/2.39 % (643395)------------------------------
% 9.43/2.39 % (643395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643395)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643395)Termination reason: Instruction limit
% 9.43/2.39 % (643395)Termination phase: Saturation
% 9.43/2.39 % (643395)Time elapsed: 0.139 s
% 9.43/2.39 % (643395)Peak memory usage: 90 MB
% 9.43/2.39 % (643395)Instructions burned: 139 (million)
% 9.43/2.39 % (643393)------------------------------
% 9.43/2.39 % (643393)------------------------------
% 9.43/2.39 % (643396)------------------------------
% 9.43/2.39 % (643396)------------------------------
% 9.43/2.39 % (643406)lrs+10_1_sil=8000:sp=occurrence:random_seed=3172559974:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 9.43/2.39 % (643408)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2572760341:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 9.43/2.39 % (643410)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2905397816:i=325:sd=1:ss=axioms:sgt=32_2994 on theBenchmark for (2994ds/325Mi)
% 9.43/2.39 % (643408)Instruction limit reached!
% 9.43/2.39 % (643408)------------------------------
% 9.43/2.39 % (643408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643408)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643408)Termination reason: Instruction limit
% 9.43/2.39 % (643408)Termination phase: Saturation
% 9.43/2.39 % (643408)Time elapsed: 0.152 s
% 9.43/2.39 % (643408)Peak memory usage: 90 MB
% 9.43/2.39 % (643408)Instructions burned: 157 (million)
% 9.43/2.39 % (643412)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=2497001454:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 9.43/2.39 % (643406)Instruction limit reached!
% 9.43/2.39 % (643406)------------------------------
% 9.43/2.39 % (643406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643406)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643406)Termination reason: Instruction limit
% 9.43/2.39 % (643406)Termination phase: Saturation
% 9.43/2.39 % (643406)Time elapsed: 0.267 s
% 9.43/2.39 % (643406)Peak memory usage: 91 MB
% 9.43/2.39 % (643406)Instructions burned: 285 (million)
% 9.43/2.39 % (643410)Instruction limit reached!
% 9.43/2.39 % (643410)------------------------------
% 9.43/2.39 % (643410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643410)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643410)Termination reason: Instruction limit
% 9.43/2.39 % (643410)Termination phase: Saturation
% 9.43/2.39 % (643410)Time elapsed: 0.232 s
% 9.43/2.39 % (643410)Peak memory usage: 92 MB
% 9.43/2.39 % (643410)Instructions burned: 326 (million)
% 9.43/2.39 % (643418)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3370716363:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 9.43/2.39 % (643418)Refutation not found, incomplete strategy
% 9.43/2.39 % (643418)------------------------------
% 9.43/2.39 % (643418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643418)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643418)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.39 % (643418)Time elapsed: 0.003 s
% 9.43/2.39 % (643418)Peak memory usage: 88 MB
% 9.43/2.39 % (643418)Instructions burned: 1 (million)
% 9.43/2.39 % (643412)Instruction limit reached!
% 9.43/2.39 % (643412)------------------------------
% 9.43/2.39 % (643412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643412)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643412)Termination reason: Instruction limit
% 9.43/2.39 % (643412)Termination phase: Saturation
% 9.43/2.39 % (643412)Time elapsed: 0.249 s
% 9.43/2.39 % (643412)Peak memory usage: 92 MB
% 9.43/2.39 % (643412)Instructions burned: 248 (million)
% 9.43/2.39 % (643420)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3838258486:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 9.43/2.39 % (643421)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1644058362:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 9.43/2.39 % (643421)Refutation not found, incomplete strategy
% 9.43/2.39 % (643421)------------------------------
% 9.43/2.39 % (643421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643421)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643421)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.39 % (643421)Time elapsed: 0.002 s
% 9.43/2.39 % (643421)Peak memory usage: 88 MB
% 9.43/2.39 % (643390)First to succeed.
% 9.43/2.39 % (643390)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-643368"
% 9.43/2.39 % (643392)Refutation not found, incomplete strategy
% 9.43/2.39 % (643392)------------------------------
% 9.43/2.39 % (643392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643392)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643392)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.39 % (643392)Time elapsed: 0.961 s
% 9.43/2.39 % (643392)Peak memory usage: 128 MB
% 9.43/2.39 % (643392)Instructions burned: 893 (million)
% 9.43/2.39 % (643425)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3055841014:i=127:av=off:fsr=off:sup=off_2989 on theBenchmark for (2989ds/127Mi)
% 9.43/2.39 % (643425)Refutation not found, incomplete strategy
% 9.43/2.39 % (643425)------------------------------
% 9.43/2.39 % (643425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.39 % (643425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.39 % (643425)CaDiCaL version: 2.1.3
% 9.43/2.39 % (643425)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.39 % (643425)Time elapsed: 0.002 s
% 9.43/2.39 % (643425)Peak memory usage: 87 MB
% 9.43/2.39 % (643425)Instructions burned: 1 (million)
% 9.43/2.39 % (643390)Refutation found. Thanks to Tanya!
% 9.43/2.39 % SZS status Theorem for theBenchmark
% 9.43/2.39 % SZS output start Proof for theBenchmark
% See solution above
% 10.44/2.55 % (643390)------------------------------
% 10.44/2.55 % (643390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.44/2.55 % (643390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.44/2.55 % (643390)CaDiCaL version: 2.1.3
% 10.44/2.55 % (643390)Termination reason: Refutation
% 10.44/2.55 % (643390)Time elapsed: 1.004 s
% 10.44/2.55 % (643390)Peak memory usage: 138 MB
% 10.44/2.55 % (643390)Instructions burned: 1828 (million)
% 10.44/2.55 % (643390)------------------------------
% 10.44/2.55 % (643390)------------------------------
% 10.44/2.55 % (643368)Success in time 1.384 s
% 10.44/2.55 % Vampire exiting
%------------------------------------------------------------------------------