%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL026+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:33:51 PM UTC 2026
% Result : Theorem 9.88s 2.33s
% Output : Refutation 10.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 16
% Syntax : Number of formulae : 129 ( 110 unt; 2 def)
% Number of atoms : 152 ( 132 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 23 ~; 15 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 174 ( 0 sgn 172 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f14,conjecture,
! [X0,X1] :
( join(X0,one) = one
=> ( join(meet(composition(X0,top),X1),composition(X0,X1)) = composition(X0,X1)
& join(composition(X0,X1),meet(composition(X0,top),X1)) = meet(composition(X0,top),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( join(X0,one) = one
=> ( join(meet(composition(X0,top),X1),composition(X0,X1)) = composition(X0,X1)
& join(composition(X0,X1),meet(composition(X0,top),X1)) = meet(composition(X0,top),X1) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( ( composition(X0,X1) != join(meet(composition(X0,top),X1),composition(X0,X1))
| meet(composition(X0,top),X1) != join(composition(X0,X1),meet(composition(X0,top),X1)) )
& join(X0,one) = one ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( ( composition(sK0,sK1) != join(meet(composition(sK0,top),sK1),composition(sK0,sK1))
| meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1)) )
& one = join(sK0,one) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f18,plain,
one = join(sK0,one),
inference(cnf_transformation,[],[f17]) ).
fof(f19,plain,
( composition(sK0,sK1) != join(meet(composition(sK0,top),sK1),composition(sK0,sK1))
| meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f20,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f23,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f26,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f30,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f31,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
( composition(sK0,sK1) != join(complement(join(complement(composition(sK0,top)),complement(sK1))),composition(sK0,sK1))
| complement(join(complement(composition(sK0,top)),complement(sK1))) != join(composition(sK0,sK1),complement(join(complement(composition(sK0,top)),complement(sK1)))) ),
inference(definition_unfolding,[],[f19,f24,f24,f24]) ).
fof(f34,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f28,f24]) ).
fof(f35,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f25,f27]) ).
fof(f36,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(forward_demodulation,[],[f21,f27]) ).
fof(f37,plain,
( composition(sK0,sK1) != join(composition(sK0,sK1),complement(join(complement(composition(sK0,top)),complement(sK1))))
| complement(join(complement(composition(sK0,top)),complement(sK1))) != join(composition(sK0,sK1),complement(join(complement(composition(sK0,top)),complement(sK1)))) ),
inference(forward_demodulation,[],[f33,f27]) ).
fof(f38,plain,
( composition(sK0,sK1) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top)))))
| complement(join(complement(composition(sK0,top)),complement(sK1))) != join(composition(sK0,sK1),complement(join(complement(composition(sK0,top)),complement(sK1)))) ),
inference(forward_demodulation,[],[f37,f27]) ).
fof(f39,plain,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top)))))
| composition(sK0,sK1) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top))))) ),
inference(forward_demodulation,[],[f38,f27]) ).
fof(f41,definition,
( spl2_1
<=> composition(sK0,sK1) = join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top))))) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f42,plain,
( composition(sK0,sK1) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top)))))
| spl2_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,definition,
( spl2_2
<=> complement(join(complement(sK1),complement(composition(sK0,top)))) = join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top))))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f45,plain,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top)))))
| spl2_2 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f39,f44,f41]) ).
fof(f62,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f29,f32]) ).
fof(f64,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f23,f29]) ).
fof(f68,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(join(complement(join(complement(X0),X1)),join(complement(X0),complement(X1)))),complement(X0)),
inference(superposition,[],[f35,f35]) ).
fof(f70,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f35,f27]) ).
fof(f71,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),complement(join(complement(join(complement(X0),X1)),join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f68,f27]) ).
fof(f72,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),complement(join(join(complement(X0),complement(X1)),complement(join(complement(X0),X1))))),
inference(forward_demodulation,[],[f71,f27]) ).
fof(f73,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),complement(join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))))),
inference(forward_demodulation,[],[f72,f26]) ).
fof(f77,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f26,f35]) ).
fof(f93,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f36,f32]) ).
fof(f102,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f62,f30]) ).
fof(f112,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f102,f32]) ).
fof(f125,plain,
! [X0,X1] : composition(join(converse(one),X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f23,f112]) ).
fof(f126,plain,
one = converse(one),
inference(superposition,[],[f30,f112]) ).
fof(f127,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(forward_demodulation,[],[f125,f126]) ).
fof(f138,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f64,f29]) ).
fof(f146,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f138,f22]) ).
fof(f154,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f146,f22]) ).
fof(f159,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f154,f29]) ).
fof(f175,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f32,f159]) ).
fof(f180,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f175,f32]) ).
fof(f208,plain,
! [X0,X1] : composition(X0,join(X1,one)) = join(composition(X0,X1),X0),
inference(superposition,[],[f180,f30]) ).
fof(f219,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(X1,one)),
inference(forward_demodulation,[],[f208,f27]) ).
fof(f472,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f112,f126]) ).
fof(f548,plain,
zero = complement(top),
inference(superposition,[],[f34,f20]) ).
fof(f633,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,sK0)),
inference(superposition,[],[f219,f18]) ).
fof(f672,plain,
! [X0] : join(X0,composition(X0,sK0)) = X0,
inference(forward_demodulation,[],[f633,f30]) ).
fof(f710,plain,
! [X0] : composition(one,X0) = join(X0,composition(composition(one,sK0),X0)),
inference(superposition,[],[f127,f672]) ).
fof(f725,plain,
! [X0] : composition(one,X0) = join(X0,composition(one,composition(sK0,X0))),
inference(forward_demodulation,[],[f710,f31]) ).
fof(f739,plain,
! [X0] : composition(one,X0) = join(X0,composition(sK0,X0)),
inference(forward_demodulation,[],[f725,f472]) ).
fof(f748,plain,
! [X0] : join(X0,composition(sK0,X0)) = X0,
inference(forward_demodulation,[],[f739,f472]) ).
fof(f766,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(composition(sK0,X0),X1)),
inference(superposition,[],[f26,f748]) ).
fof(f801,plain,
! [X0,X1] : join(X0,composition(sK0,X1)) = join(X0,composition(sK0,join(X0,X1))),
inference(superposition,[],[f766,f180]) ).
fof(f807,plain,
! [X0] : join(X0,top) = join(X0,complement(composition(sK0,X0))),
inference(superposition,[],[f766,f20]) ).
fof(f868,plain,
! [X0] : join(X0,composition(sK0,complement(X0))) = join(X0,composition(sK0,top)),
inference(superposition,[],[f801,f20]) ).
fof(f1039,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(converse(one),X0))),
inference(superposition,[],[f93,f472]) ).
fof(f1060,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f1039,f112]) ).
fof(f1080,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(X0,complement(join(complement(X0),complement(X1)))),
inference(superposition,[],[f77,f1060]) ).
fof(f1081,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f1080,f35]) ).
fof(f1115,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f1081,f27]) ).
fof(f1116,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f1081,f34]) ).
fof(f1168,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f27,f1116]) ).
fof(f1221,plain,
! [X0] : join(zero,X0) = join(zero,complement(join(zero,join(complement(X0),complement(join(zero,X0)))))),
inference(superposition,[],[f73,f548]) ).
fof(f1250,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(superposition,[],[f1081,f73]) ).
fof(f1289,plain,
! [X0] : join(zero,X0) = complement(join(zero,join(complement(X0),complement(join(zero,X0))))),
inference(forward_demodulation,[],[f1221,f1168]) ).
fof(f1306,plain,
! [X0] : join(zero,X0) = complement(join(complement(X0),complement(join(zero,X0)))),
inference(forward_demodulation,[],[f1289,f1168]) ).
fof(f1314,plain,
! [X0] : complement(join(complement(X0),complement(X0))) = X0,
inference(forward_demodulation,[],[f1306,f1168]) ).
fof(f1322,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f1314,f1060]) ).
fof(f1334,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f35,f1322]) ).
fof(f1344,plain,
! [X0] : join(complement(X0),composition(sK0,top)) = join(complement(X0),composition(sK0,X0)),
inference(superposition,[],[f868,f1322]) ).
fof(f1345,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f1060,f1322]) ).
fof(f1358,plain,
! [X0] : top = join(top,complement(join(zero,X0))),
inference(superposition,[],[f1250,f548]) ).
fof(f1368,plain,
! [X0,X1] : join(X1,complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f1250,f27]) ).
fof(f1423,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f1358,f1168]) ).
fof(f1442,plain,
! [X0] : top = join(top,X0),
inference(superposition,[],[f1423,f1322]) ).
fof(f1581,plain,
! [X0] : top = join(X0,top),
inference(superposition,[],[f27,f1442]) ).
fof(f1661,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(join(complement(join(X0,complement(X1))),join(X0,X1))),complement(complement(X0))),
inference(superposition,[],[f70,f1334]) ).
fof(f1683,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(complement(X0)),complement(join(complement(join(X0,complement(X1))),join(X0,X1)))),
inference(forward_demodulation,[],[f1661,f27]) ).
fof(f1721,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(complement(X0)),complement(join(join(X0,X1),complement(join(X0,complement(X1)))))),
inference(forward_demodulation,[],[f1683,f27]) ).
fof(f1742,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(complement(X0)),complement(join(X0,join(X1,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f1721,f26]) ).
fof(f1757,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1742,f1368]) ).
fof(f1768,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1757,f1322]) ).
fof(f1796,plain,
! [X0] : join(X0,complement(composition(sK0,complement(X0)))) = join(X0,complement(join(X0,composition(sK0,top)))),
inference(superposition,[],[f1768,f868]) ).
fof(f1806,plain,
! [X0] : join(complement(X0),complement(composition(sK0,X0))) = join(complement(X0),complement(join(complement(X0),composition(sK0,top)))),
inference(superposition,[],[f1768,f1344]) ).
fof(f1869,plain,
! [X0] : join(complement(X0),complement(composition(sK0,top))) = join(complement(X0),complement(composition(sK0,X0))),
inference(forward_demodulation,[],[f1806,f1768]) ).
fof(f1879,plain,
! [X0] : join(X0,complement(composition(sK0,complement(X0)))) = join(X0,complement(composition(sK0,top))),
inference(forward_demodulation,[],[f1796,f1768]) ).
fof(f1948,plain,
! [X0] : composition(sK0,complement(complement(X0))) = join(complement(join(complement(composition(sK0,complement(complement(X0)))),X0)),complement(join(complement(X0),complement(composition(sK0,top))))),
inference(superposition,[],[f70,f1879]) ).
fof(f1981,plain,
! [X0] : composition(sK0,complement(complement(X0))) = join(complement(join(complement(X0),complement(composition(sK0,top)))),complement(join(complement(composition(sK0,complement(complement(X0)))),X0))),
inference(forward_demodulation,[],[f1948,f27]) ).
fof(f1995,plain,
! [X0] : composition(sK0,complement(complement(X0))) = join(complement(join(complement(X0),complement(composition(sK0,top)))),complement(join(X0,complement(composition(sK0,complement(complement(X0))))))),
inference(forward_demodulation,[],[f1981,f27]) ).
fof(f2006,plain,
! [X0] : composition(sK0,X0) = join(complement(join(complement(X0),complement(composition(sK0,top)))),complement(join(X0,complement(composition(sK0,X0))))),
inference(forward_demodulation,[],[f1995,f1322]) ).
fof(f2011,plain,
! [X0] : composition(sK0,X0) = join(complement(join(complement(X0),complement(composition(sK0,top)))),complement(join(X0,top))),
inference(forward_demodulation,[],[f2006,f807]) ).
fof(f2013,plain,
! [X0] : composition(sK0,X0) = join(complement(join(X0,top)),complement(join(complement(X0),complement(composition(sK0,top))))),
inference(forward_demodulation,[],[f2011,f27]) ).
fof(f2014,plain,
! [X0] : composition(sK0,X0) = join(complement(top),complement(join(complement(X0),complement(composition(sK0,top))))),
inference(forward_demodulation,[],[f2013,f1581]) ).
fof(f2015,plain,
! [X0] : composition(sK0,X0) = join(zero,complement(join(complement(X0),complement(composition(sK0,top))))),
inference(forward_demodulation,[],[f2014,f548]) ).
fof(f2016,plain,
! [X0] : composition(sK0,X0) = complement(join(complement(X0),complement(composition(sK0,top)))),
inference(forward_demodulation,[],[f2015,f1168]) ).
fof(f2024,plain,
( composition(sK0,sK1) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,sK1)))))
| spl2_1 ),
inference(superposition,[],[f42,f1869]) ).
fof(f2084,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f2024,f1115]) ).
fof(f2085,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f2084]) ).
fof(f2116,plain,
( composition(sK0,sK1) != join(composition(sK0,sK1),composition(sK0,sK1))
| spl2_2 ),
inference(forward_demodulation,[],[f45,f2016]) ).
fof(f2117,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f2116,f1345]) ).
fof(f2118,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f2117]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f46]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f2085]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f2118]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f2119,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL026+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.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 22:52:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 9.88/2.33 % (3418596)Detected formulas, will run a generic FOF schedule.
% 9.88/2.33 % (3418708)dis-21_1_sil=8000:lcm=predicate:random_seed=1756546423: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)
% 9.88/2.33 % (3418708)Refutation not found, incomplete strategy
% 9.88/2.33 % (3418708)------------------------------
% 9.88/2.33 % (3418708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418708)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418708)Termination reason: Refutation not found, incomplete strategy
% 9.88/2.33 % (3418708)Time elapsed: 0.001 s
% 9.88/2.33 % (3418708)Peak memory usage: 88 MB
% 9.88/2.33 % (3418708)Instructions burned: 1 (million)
% 9.88/2.33 % (3418705)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3124307407:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.88/2.33 % (3418707)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1972255676:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.88/2.33 % (3418702)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=1859019737:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.88/2.33 % (3418703)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=3488480745:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.88/2.33 % (3418704)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=378985759:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.88/2.33 % (3418706)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=213493966:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.88/2.33 % (3418706)Instruction limit reached!
% 9.88/2.33 % (3418706)------------------------------
% 9.88/2.33 % (3418706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418706)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418706)Termination reason: Instruction limit
% 9.88/2.33 % (3418706)Termination phase: Saturation
% 9.88/2.33 % (3418706)Time elapsed: 0.067 s
% 9.88/2.33 % (3418706)Peak memory usage: 88 MB
% 9.88/2.33 % (3418706)Instructions burned: 120 (million)
% 9.88/2.33 % (3418705)Instruction limit reached!
% 9.88/2.33 % (3418705)------------------------------
% 9.88/2.33 % (3418705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418705)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418705)Termination reason: Instruction limit
% 9.88/2.33 % (3418705)Termination phase: Saturation
% 9.88/2.33 % (3418705)Time elapsed: 0.072 s
% 9.88/2.33 % (3418705)Peak memory usage: 89 MB
% 9.88/2.33 % (3418705)Instructions burned: 109 (million)
% 9.88/2.33 % (3418707)Instruction limit reached!
% 9.88/2.33 % (3418707)------------------------------
% 9.88/2.33 % (3418707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418707)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418707)Termination reason: Instruction limit
% 9.88/2.33 % (3418707)Termination phase: Saturation
% 9.88/2.33 % (3418707)Time elapsed: 0.082 s
% 9.88/2.33 % (3418707)Peak memory usage: 90 MB
% 9.88/2.33 % (3418707)Instructions burned: 139 (million)
% 9.88/2.33 % (3418708)------------------------------
% 9.88/2.33 % (3418708)------------------------------
% 9.88/2.33 % (3418721)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3366617825:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.88/2.33 % (3418720)lrs+10_1_sil=8000:sp=occurrence:random_seed=1879777592:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.88/2.33 % (3418739)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=2278637725:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 9.88/2.33 % (3418724)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3697565168:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.88/2.33 % (3418721)Instruction limit reached!
% 9.88/2.33 % (3418721)------------------------------
% 9.88/2.33 % (3418721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418721)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418721)Termination reason: Instruction limit
% 9.88/2.33 % (3418721)Termination phase: Saturation
% 9.88/2.33 % (3418721)Time elapsed: 0.113 s
% 9.88/2.33 % (3418721)Peak memory usage: 90 MB
% 9.88/2.33 % (3418721)Instructions burned: 157 (million)
% 9.88/2.33 % (3418739)Instruction limit reached!
% 9.88/2.33 % (3418739)------------------------------
% 9.88/2.33 % (3418739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418739)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418739)Termination reason: Instruction limit
% 9.88/2.33 % (3418739)Termination phase: Saturation
% 9.88/2.33 % (3418739)Time elapsed: 0.129 s
% 9.88/2.33 % (3418739)Peak memory usage: 91 MB
% 9.88/2.33 % (3418739)Instructions burned: 249 (million)
% 9.88/2.33 % (3418720)Instruction limit reached!
% 9.88/2.33 % (3418720)------------------------------
% 9.88/2.33 % (3418720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418720)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418720)Termination reason: Instruction limit
% 9.88/2.33 % (3418720)Termination phase: Saturation
% 9.88/2.33 % (3418720)Time elapsed: 0.287 s
% 9.88/2.33 % (3418720)Peak memory usage: 91 MB
% 9.88/2.33 % (3418720)Instructions burned: 285 (million)
% 9.88/2.33 % (3418763)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2274744838:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 9.88/2.33 % (3418761)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=709525610:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 9.88/2.33 % (3418724)Instruction limit reached!
% 9.88/2.33 % (3418724)------------------------------
% 9.88/2.33 % (3418724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418724)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418724)Termination reason: Instruction limit
% 9.88/2.33 % (3418724)Termination phase: Saturation
% 9.88/2.33 % (3418724)Time elapsed: 0.311 s
% 9.88/2.33 % (3418724)Peak memory usage: 92 MB
% 9.88/2.33 % (3418724)Instructions burned: 325 (million)
% 9.88/2.33 % (3418767)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1967329723:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 9.88/2.33 % (3418770)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3747896427:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 9.88/2.33 % (3418761)Instruction limit reached!
% 9.88/2.33 % (3418761)------------------------------
% 9.88/2.33 % (3418761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418761)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418761)Termination reason: Instruction limit
% 9.88/2.33 % (3418761)Termination phase: Saturation
% 9.88/2.33 % (3418761)Time elapsed: 0.246 s
% 9.88/2.33 % (3418761)Peak memory usage: 91 MB
% 9.88/2.33 % (3418761)Instructions burned: 295 (million)
% 9.88/2.33 % (3418770)Refutation not found, incomplete strategy
% 9.88/2.33 % (3418770)------------------------------
% 9.88/2.33 % (3418770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418770)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418770)Termination reason: Refutation not found, incomplete strategy
% 9.88/2.33 % (3418770)Time elapsed: 0.002 s
% 9.88/2.33 % (3418770)Peak memory usage: 87 MB
% 9.88/2.33 % (3418767)Instruction limit reached!
% 9.88/2.33 % (3418767)------------------------------
% 9.88/2.33 % (3418767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.33 % (3418767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.33 % (3418767)CaDiCaL version: 2.1.3
% 9.88/2.33 % (3418767)Termination reason: Instruction limit
% 9.88/2.33 % (3418767)Termination phase: Saturation
% 9.88/2.33 % (3418767)Time elapsed: 0.108 s
% 9.88/2.33 % (3418767)Peak memory usage: 89 MB
% 9.88/2.33 % (3418767)Instructions burned: 114 (million)
% 9.88/2.33 % (3418703)First to succeed.
% 9.88/2.33 % (3418703)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3418596"
% 9.88/2.33 % (3418777)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1058455684:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2989 on theBenchmark for (2989ds/114Mi)
% 9.88/2.33 % (3418780)lrs+10_1_sil=8000:sp=occurrence:random_seed=1280108921:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 9.88/2.33 % (3418770)------------------------------
% 9.88/2.33 % (3418770)------------------------------
% 9.88/2.33 % (3418703)Refutation found. Thanks to Tanya!
% 9.88/2.33 % SZS status Theorem for theBenchmark
% 9.88/2.33 % SZS output start Proof for theBenchmark
% See solution above
% 10.92/2.59 % (3418703)------------------------------
% 10.92/2.59 % (3418703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.92/2.59 % (3418703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.92/2.59 % (3418703)CaDiCaL version: 2.1.3
% 10.92/2.59 % (3418703)Termination reason: Refutation
% 10.92/2.59 % (3418703)Time elapsed: 1.031 s
% 10.92/2.59 % (3418703)Peak memory usage: 132 MB
% 10.92/2.59 % (3418703)Instructions burned: 1273 (million)
% 10.92/2.59 % (3418703)------------------------------
% 10.92/2.59 % (3418703)------------------------------
% 10.92/2.59 % (3418596)Success in time 1.475 s
% 10.92/2.59 % Vampire exiting
%------------------------------------------------------------------------------