%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL030+3 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:33:57 PM UTC 2026
% Result : Theorem 16.08s 3.28s
% Output : Refutation 17.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 12
% Syntax : Number of formulae : 130 ( 126 unt; 0 def)
% Number of atoms : 134 ( 133 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 217 ( 214 !; 3 ?)
% 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(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(f17,conjecture,
! [X0,X1,X2] :
( join(X0,one) = one
=> meet(composition(X0,X1),complement(X2)) = meet(composition(X0,X1),complement(composition(X0,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( join(X0,one) = one
=> meet(composition(X0,X1),complement(X2)) = meet(composition(X0,X1),complement(composition(X0,X2))) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( meet(composition(X0,X1),complement(X2)) != meet(composition(X0,X1),complement(composition(X0,X2)))
& join(X0,one) = one ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
( meet(composition(sK0,sK1),complement(sK2)) != meet(composition(sK0,sK1),complement(composition(sK0,sK2)))
& one = join(sK0,one) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
fof(f21,plain,
one = join(sK0,one),
inference(cnf_transformation,[],[f20]) ).
fof(f22,plain,
meet(composition(sK0,sK1),complement(sK2)) != meet(composition(sK0,sK1),complement(composition(sK0,sK2))),
inference(cnf_transformation,[],[f20]) ).
fof(f23,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f28,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f34,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f35,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f38,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f39,plain,
complement(join(complement(composition(sK0,sK1)),complement(complement(sK2)))) != complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))),
inference(definition_unfolding,[],[f22,f28,f28]) ).
fof(f45,plain,
complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),
inference(forward_demodulation,[],[f39,f24]) ).
fof(f46,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f37,f38]) ).
fof(f53,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f33,f38]) ).
fof(f55,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f34,f33]) ).
fof(f67,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f29,f24]) ).
fof(f75,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(superposition,[],[f24,f29]) ).
fof(f80,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(forward_demodulation,[],[f67,f24]) ).
fof(f90,plain,
! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)),
inference(superposition,[],[f27,f38]) ).
fof(f101,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(forward_demodulation,[],[f90,f24]) ).
fof(f113,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f23,f29]) ).
fof(f122,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f24,f23]) ).
fof(f125,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f113,f122]) ).
fof(f241,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f53,f35]) ).
fof(f251,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f241,f38]) ).
fof(f263,plain,
one = converse(one),
inference(superposition,[],[f35,f251]) ).
fof(f328,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f55,f33]) ).
fof(f338,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f328,f37]) ).
fof(f345,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f338,f37]) ).
fof(f350,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f345,f33]) ).
fof(f374,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(complement(join(complement(X1),X0)),X0),
inference(superposition,[],[f125,f80]) ).
fof(f379,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f374,f24]) ).
fof(f591,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f251,f263]) ).
fof(f614,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(converse(one),X0))),
inference(superposition,[],[f101,f591]) ).
fof(f617,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f614,f251]) ).
fof(f640,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,[],[f125,f617]) ).
fof(f644,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f640,f75]) ).
fof(f687,plain,
! [X0] : join(X0,complement(complement(X0))) = X0,
inference(superposition,[],[f644,f644]) ).
fof(f689,plain,
! [X0,X1] : join(X1,complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f644,f24]) ).
fof(f691,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,X0),
inference(superposition,[],[f125,f644]) ).
fof(f715,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,X0),
inference(forward_demodulation,[],[f691,f24]) ).
fof(f735,plain,
! [X0,X1] : join(X1,X1) = join(X1,complement(join(X0,complement(X1)))),
inference(superposition,[],[f715,f24]) ).
fof(f747,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f644,f715]) ).
fof(f785,plain,
! [X0,X1] : join(X1,complement(join(X0,complement(X1)))) = X1,
inference(forward_demodulation,[],[f735,f747]) ).
fof(f835,plain,
! [X0,X1] : join(X1,X0) = join(complement(join(complement(X1),X0)),X0),
inference(superposition,[],[f125,f785]) ).
fof(f862,plain,
! [X0,X1] : join(X1,X0) = join(X0,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f835,f24]) ).
fof(f905,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(complement(X1),X0))),
inference(superposition,[],[f379,f862]) ).
fof(f914,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(complement(join(complement(X0),complement(X1))),X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f80,f862]) ).
fof(f931,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(X0,complement(X1))),complement(join(complement(join(complement(X0),complement(X1))),X1))),
inference(forward_demodulation,[],[f914,f24]) ).
fof(f957,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(X0,complement(X1))),complement(join(X1,complement(join(complement(X0),complement(X1)))))),
inference(forward_demodulation,[],[f931,f24]) ).
fof(f972,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(X0,complement(X1))),complement(X1)),
inference(forward_demodulation,[],[f957,f689]) ).
fof(f980,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X1),complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f972,f24]) ).
fof(f1113,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),join(complement(X0),X1)) = join(complement(join(complement(X1),complement(X0))),complement(X0)),
inference(superposition,[],[f905,f80]) ).
fof(f1198,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),join(complement(X0),X1)) = join(complement(X0),complement(join(complement(X1),complement(X0)))),
inference(forward_demodulation,[],[f1113,f24]) ).
fof(f1224,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),join(complement(X0),X1)) = join(complement(complement(X1)),complement(X0)),
inference(forward_demodulation,[],[f1198,f980]) ).
fof(f1240,plain,
! [X0,X1] : join(join(complement(X0),X1),complement(join(complement(X1),complement(X0)))) = join(complement(complement(X1)),complement(X0)),
inference(forward_demodulation,[],[f1224,f24]) ).
fof(f1251,plain,
! [X0,X1] : join(complement(X0),join(X1,complement(join(complement(X1),complement(X0))))) = join(complement(complement(X1)),complement(X0)),
inference(forward_demodulation,[],[f1240,f23]) ).
fof(f1255,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(complement(X1)),complement(X0)),
inference(forward_demodulation,[],[f1251,f644]) ).
fof(f1275,plain,
! [X0] : complement(complement(X0)) = join(complement(complement(X0)),X0),
inference(superposition,[],[f617,f1255]) ).
fof(f1302,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),complement(complement(X1))),
inference(superposition,[],[f24,f1255]) ).
fof(f1322,plain,
! [X0] : complement(complement(X0)) = join(X0,complement(complement(X0))),
inference(forward_demodulation,[],[f1275,f24]) ).
fof(f1346,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f1322,f687]) ).
fof(f1364,plain,
complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))) != complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2))),
inference(superposition,[],[f45,f1346]) ).
fof(f1373,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f80,f1346]) ).
fof(f1387,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X1))),
inference(superposition,[],[f862,f1346]) ).
fof(f1389,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f905,f1346]) ).
fof(f1402,plain,
complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))) != complement(join(composition(sK0,sK2),complement(composition(sK0,sK1)))),
inference(forward_demodulation,[],[f1364,f24]) ).
fof(f1405,plain,
complement(join(composition(sK0,sK2),complement(composition(sK0,sK1)))) != complement(join(complement(composition(sK0,sK1)),sK2)),
inference(forward_demodulation,[],[f1402,f1255]) ).
fof(f1406,plain,
complement(join(composition(sK0,sK2),complement(composition(sK0,sK1)))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(forward_demodulation,[],[f1405,f24]) ).
fof(f1483,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f1387,f24]) ).
fof(f2210,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f1389,f24]) ).
fof(f4860,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f38,f350]) ).
fof(f4868,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f4860,f38]) ).
fof(f4899,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(one,X1)),
inference(superposition,[],[f4868,f35]) ).
fof(f4903,plain,
! [X0,X1] : join(composition(X0,X1),X0) = composition(X0,join(X1,one)),
inference(superposition,[],[f4868,f35]) ).
fof(f4936,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(X1,one)),
inference(forward_demodulation,[],[f4903,f24]) ).
fof(f5108,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,sK0)),
inference(superposition,[],[f4936,f21]) ).
fof(f5184,plain,
! [X0] : join(X0,composition(X0,sK0)) = X0,
inference(forward_demodulation,[],[f5108,f35]) ).
fof(f5260,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(composition(converse(X0),sK0))),
inference(superposition,[],[f46,f5184]) ).
fof(f5262,plain,
! [X0] : converse(converse(X0)) = join(X0,composition(converse(sK0),X0)),
inference(forward_demodulation,[],[f5260,f53]) ).
fof(f5288,plain,
! [X0] : join(X0,composition(converse(sK0),X0)) = X0,
inference(forward_demodulation,[],[f5262,f38]) ).
fof(f5343,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,composition(converse(sK0),one))),
inference(superposition,[],[f4899,f5288]) ).
fof(f5347,plain,
! [X0] : composition(X0,one) = join(X0,composition(X0,converse(sK0))),
inference(forward_demodulation,[],[f5343,f35]) ).
fof(f5369,plain,
! [X0] : join(X0,composition(X0,converse(sK0))) = X0,
inference(forward_demodulation,[],[f5347,f35]) ).
fof(f5423,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(composition(converse(X0),converse(sK0)))),
inference(superposition,[],[f46,f5369]) ).
fof(f5425,plain,
! [X0] : converse(converse(X0)) = join(X0,composition(converse(converse(sK0)),X0)),
inference(forward_demodulation,[],[f5423,f53]) ).
fof(f5453,plain,
! [X0] : converse(converse(X0)) = join(X0,composition(sK0,X0)),
inference(forward_demodulation,[],[f5425,f38]) ).
fof(f5470,plain,
! [X0] : join(X0,composition(sK0,X0)) = X0,
inference(forward_demodulation,[],[f5453,f38]) ).
fof(f5481,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(composition(sK0,X0),X1)),
inference(superposition,[],[f23,f5470]) ).
fof(f5504,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(complement(join(composition(sK0,complement(X0)),X0)),complement(complement(X0))),
inference(superposition,[],[f1373,f5470]) ).
fof(f5512,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(complement(join(composition(sK0,complement(X0)),X0)),X0),
inference(forward_demodulation,[],[f5504,f1302]) ).
fof(f5531,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(X0,complement(join(composition(sK0,complement(X0)),X0))),
inference(forward_demodulation,[],[f5512,f24]) ).
fof(f5539,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(X0,complement(composition(sK0,complement(X0)))),
inference(forward_demodulation,[],[f5531,f1389]) ).
fof(f5830,plain,
! [X0,X1] : join(X0,composition(sK0,X1)) = join(X0,composition(sK0,join(X0,X1))),
inference(superposition,[],[f5481,f4868]) ).
fof(f6033,plain,
! [X0] : join(X0,composition(sK0,complement(X0))) = join(X0,composition(sK0,top)),
inference(superposition,[],[f5830,f26]) ).
fof(f6230,plain,
! [X0] : join(X0,complement(composition(sK0,complement(X0)))) = join(X0,complement(join(X0,composition(sK0,top)))),
inference(superposition,[],[f2210,f6033]) ).
fof(f6271,plain,
! [X0] : join(X0,complement(composition(sK0,complement(X0)))) = join(complement(composition(sK0,top)),X0),
inference(forward_demodulation,[],[f6230,f1483]) ).
fof(f6297,plain,
! [X0] : complement(composition(sK0,complement(X0))) = join(complement(composition(sK0,top)),X0),
inference(forward_demodulation,[],[f6271,f5539]) ).
fof(f7268,plain,
! [X0,X1] : complement(composition(sK0,complement(join(X0,X1)))) = join(X1,join(complement(composition(sK0,top)),X0)),
inference(superposition,[],[f122,f6297]) ).
fof(f7335,plain,
! [X0,X1] : complement(composition(sK0,complement(join(X0,X1)))) = join(X1,complement(composition(sK0,complement(X0)))),
inference(forward_demodulation,[],[f7268,f6297]) ).
fof(f7589,plain,
! [X0,X1] : join(X1,complement(composition(sK0,X0))) = complement(composition(sK0,complement(join(complement(X0),X1)))),
inference(superposition,[],[f7335,f1346]) ).
fof(f7858,plain,
! [X0,X1] : join(X0,complement(composition(sK0,X1))) = complement(composition(sK0,complement(join(X0,complement(X1))))),
inference(superposition,[],[f7589,f24]) ).
fof(f7879,plain,
! [X0,X1] : complement(composition(sK0,complement(join(complement(X0),complement(X1))))) = join(complement(join(complement(X1),X0)),complement(composition(sK0,X1))),
inference(superposition,[],[f7589,f1483]) ).
fof(f7992,plain,
! [X0,X1] : complement(composition(sK0,complement(join(complement(X0),complement(X1))))) = join(complement(composition(sK0,X1)),complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f7879,f24]) ).
fof(f8069,plain,
! [X0,X1] : join(complement(composition(sK0,X1)),complement(join(complement(X1),X0))) = join(complement(X0),complement(composition(sK0,X1))),
inference(forward_demodulation,[],[f7992,f7858]) ).
fof(f8219,plain,
! [X0,X1] : join(complement(X1),complement(composition(sK0,X0))) = join(complement(X0),complement(composition(sK0,X1))),
inference(superposition,[],[f7589,f7858]) ).
fof(f9097,plain,
! [X0,X1] : join(X1,complement(composition(sK0,X0))) = join(complement(composition(sK0,X0)),complement(join(complement(X0),complement(composition(sK0,X1))))),
inference(superposition,[],[f862,f8219]) ).
fof(f9142,plain,
! [X0,X1] : join(X1,complement(composition(sK0,X0))) = join(complement(complement(composition(sK0,X1))),complement(composition(sK0,X0))),
inference(forward_demodulation,[],[f9097,f8069]) ).
fof(f9227,plain,
! [X0,X1] : join(X1,complement(composition(sK0,X0))) = join(complement(composition(sK0,X0)),composition(sK0,X1)),
inference(forward_demodulation,[],[f9142,f1255]) ).
fof(f9374,plain,
! [X0,X1] : join(X0,complement(composition(sK0,X1))) = join(composition(sK0,X0),complement(composition(sK0,X1))),
inference(superposition,[],[f24,f9227]) ).
fof(f9487,plain,
complement(join(sK2,complement(composition(sK0,sK1)))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(superposition,[],[f1406,f9374]) ).
fof(f9514,plain,
$false,
inference(trivial_inequality_removal,[],[f9487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL030+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n016.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 22:58:47 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.08/3.27 % (3084305)Detected formulas, will run a generic FOF schedule.
% 16.08/3.27 % (3084310)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=1387624463:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 16.08/3.27 % (3084316)dis-21_1_sil=8000:lcm=predicate:random_seed=3237520283: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)
% 16.08/3.27 % (3084316)Refutation not found, incomplete strategy
% 16.08/3.27 % (3084316)------------------------------
% 16.08/3.27 % (3084316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084316)CaDiCaL version: 2.1.3
% 16.08/3.27 % (3084316)Termination reason: Refutation not found, incomplete strategy
% 16.08/3.27 % (3084316)Time elapsed: 0.003 s
% 16.08/3.27 % (3084316)Peak memory usage: 88 MB
% 16.08/3.27 % (3084316)Instructions burned: 1 (million)
% 16.08/3.27 % (3084311)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=3607033639:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 16.08/3.27 % (3084312)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=385317807:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 16.08/3.27 % (3084314)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=539800883:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 16.08/3.27 % (3084313)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3135522610:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 16.08/3.27 % (3084315)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1385571128:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 16.08/3.27 % (3084313)Instruction limit reached!
% 16.08/3.27 % (3084313)------------------------------
% 16.08/3.27 % (3084313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084313)CaDiCaL version: 2.1.3
% 16.08/3.27 % (3084313)Termination reason: Instruction limit
% 16.08/3.27 % (3084313)Termination phase: Saturation
% 16.08/3.27 % (3084313)Time elapsed: 0.103 s
% 16.08/3.27 % (3084313)Peak memory usage: 89 MB
% 16.08/3.27 % (3084313)Instructions burned: 109 (million)
% 16.08/3.27 % (3084314)Instruction limit reached!
% 16.08/3.27 % (3084314)------------------------------
% 16.08/3.27 % (3084314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084314)CaDiCaL version: 2.1.3
% 16.08/3.27 % (3084314)Termination reason: Instruction limit
% 16.08/3.27 % (3084314)Termination phase: Saturation
% 16.08/3.27 % (3084314)Time elapsed: 0.110 s
% 16.08/3.27 % (3084314)Peak memory usage: 88 MB
% 16.08/3.27 % (3084314)Instructions burned: 120 (million)
% 16.08/3.27 % (3084315)Instruction limit reached!
% 16.08/3.27 % (3084315)------------------------------
% 16.08/3.27 % (3084315)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084315)CaDiCaL version: 2.1.3
% 16.08/3.27 % (3084315)Termination reason: Instruction limit
% 16.08/3.27 % (3084315)Termination phase: Saturation
% 16.08/3.27 % (3084315)Time elapsed: 0.141 s
% 16.08/3.27 % (3084315)Peak memory usage: 90 MB
% 16.08/3.27 % (3084315)Instructions burned: 140 (million)
% 16.08/3.27 % (3084316)------------------------------
% 16.08/3.27 % (3084316)------------------------------
% 16.08/3.27 % (3084325)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4040699645:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 16.08/3.27 % (3084324)lrs+10_1_sil=8000:sp=occurrence:random_seed=1151639308:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 16.08/3.27 % (3084326)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4038573087:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 16.08/3.27 % (3084325)Instruction limit reached!
% 16.08/3.27 % (3084325)------------------------------
% 16.08/3.27 % (3084325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084325)CaDiCaL version: 2.1.3
% 16.08/3.27 % (3084325)Termination reason: Instruction limit
% 16.08/3.27 % (3084325)Termination phase: Saturation
% 16.08/3.27 % (3084325)Time elapsed: 0.154 s
% 16.08/3.27 % (3084325)Peak memory usage: 90 MB
% 16.08/3.27 % (3084325)Instructions burned: 157 (million)
% 16.08/3.27 % (3084327)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=1940656381:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 16.08/3.27 % (3084324)Instruction limit reached!
% 16.08/3.27 % (3084324)------------------------------
% 16.08/3.27 % (3084324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084324)CaDiCaL version: 2.1.3
% 16.08/3.27 % (3084324)Termination reason: Instruction limit
% 16.08/3.27 % (3084324)Termination phase: Saturation
% 16.08/3.27 % (3084324)Time elapsed: 0.275 s
% 16.08/3.27 % (3084324)Peak memory usage: 91 MB
% 16.08/3.27 % (3084324)Instructions burned: 285 (million)
% 16.08/3.27 % (3084326)Instruction limit reached!
% 16.08/3.27 % (3084326)------------------------------
% 16.08/3.27 % (3084326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084326)CaDiCaL version: 2.1.3
% 16.08/3.27 % (3084326)Termination reason: Instruction limit
% 16.08/3.27 % (3084326)Termination phase: Saturation
% 16.08/3.27 % (3084326)Time elapsed: 0.323 s
% 16.08/3.27 % (3084326)Peak memory usage: 92 MB
% 16.08/3.27 % (3084326)Instructions burned: 325 (million)
% 16.08/3.27 % (3084331)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=102040221:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 16.08/3.27 % (3084327)Instruction limit reached!
% 16.08/3.27 % (3084327)------------------------------
% 16.08/3.27 % (3084327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084327)CaDiCaL version: 2.1.3
% 16.08/3.27 % (3084327)Termination reason: Instruction limit
% 16.08/3.27 % (3084327)Termination phase: Saturation
% 16.08/3.27 % (3084327)Time elapsed: 0.227 s
% 16.08/3.27 % (3084327)Peak memory usage: 92 MB
% 16.08/3.27 % (3084327)Instructions burned: 248 (million)
% 16.08/3.27 % (3084333)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1569018468:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 16.08/3.27 % (3084334)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1712475131:cts=off:i=113:fsr=off:ss=included:sgt=4_2989 on theBenchmark for (2989ds/113Mi)
% 16.08/3.27 % (3084331)Instruction limit reached!
% 16.08/3.27 % (3084331)------------------------------
% 16.08/3.27 % (3084331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084331)CaDiCaL version: 2.1.3
% 16.08/3.27 % (3084331)Termination reason: Instruction limit
% 16.08/3.27 % (3084331)Termination phase: Saturation
% 16.08/3.27 % (3084331)Time elapsed: 0.286 s
% 16.08/3.27 % (3084331)Peak memory usage: 90 MB
% 16.08/3.27 % (3084331)Instructions burned: 294 (million)
% 16.08/3.27 % (3084336)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3431979740:i=127:av=off:fsr=off:sup=off_2989 on theBenchmark for (2989ds/127Mi)
% 16.08/3.27 % (3084336)Refutation not found, incomplete strategy
% 16.08/3.27 % (3084336)------------------------------
% 16.08/3.27 % (3084336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084336)CaDiCaL version: 2.1.3
% 16.08/3.27 % (3084336)Termination reason: Refutation not found, incomplete strategy
% 16.08/3.27 % (3084336)Time elapsed: 0.002 s
% 16.08/3.27 % (3084336)Peak memory usage: 88 MB
% 16.08/3.27 % (3084336)Instructions burned: 1 (million)
% 16.08/3.27 % (3084334)Instruction limit reached!
% 16.08/3.27 % (3084334)------------------------------
% 16.08/3.27 % (3084334)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.27 % (3084334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.27 % (3084334)CaDiCaL version: 2.1.3
% 16.08/3.28 % (3084334)Termination reason: Instruction limit
% 16.08/3.28 % (3084334)Termination phase: Saturation
% 16.08/3.28 % (3084334)Time elapsed: 0.107 s
% 16.08/3.28 % (3084334)Peak memory usage: 90 MB
% 16.08/3.28 % (3084334)Instructions burned: 114 (million)
% 16.08/3.28 % (3084339)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3270210657:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2986 on theBenchmark for (2986ds/114Mi)
% 16.08/3.28 % (3084339)Instruction limit reached!
% 16.08/3.28 % (3084339)------------------------------
% 16.08/3.28 % (3084339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.28 % (3084339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.28 % (3084339)CaDiCaL version: 2.1.3
% 16.08/3.28 % (3084339)Termination reason: Instruction limit
% 16.08/3.28 % (3084339)Termination phase: Saturation
% 16.08/3.28 % (3084339)Time elapsed: 0.097 s
% 16.08/3.28 % (3084339)Peak memory usage: 89 MB
% 16.08/3.28 % (3084339)Instructions burned: 115 (million)
% 16.08/3.28 % (3084341)lrs+10_1_sil=8000:sp=occurrence:random_seed=1230113627:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2985 on theBenchmark for (2985ds/907Mi)
% 16.08/3.28 % (3084336)------------------------------
% 16.08/3.28 % (3084336)------------------------------
% 16.08/3.28 % (3084311)First to succeed.
% 16.08/3.28 % (3084343)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2719561014:i=437:sd=1:aac=none:ss=included_2983 on theBenchmark for (2983ds/437Mi)
% 16.08/3.28 % (3084311)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3084305"
% 16.08/3.28 % (3084345)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=734762659:i=5202:ss=axioms:sgt=16_2982 on theBenchmark for (2982ds/5202Mi)
% 16.08/3.28 % (3084310)Also succeeded, but the first one will report.
% 16.08/3.28 % (3084343)Instruction limit reached!
% 16.08/3.28 % (3084343)------------------------------
% 16.08/3.28 % (3084343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.08/3.28 % (3084343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.08/3.28 % (3084343)CaDiCaL version: 2.1.3
% 16.08/3.28 % (3084343)Termination reason: Instruction limit
% 16.08/3.28 % (3084343)Termination phase: Saturation
% 16.08/3.28 % (3084343)Time elapsed: 0.365 s
% 16.08/3.28 % (3084343)Peak memory usage: 90 MB
% 16.08/3.28 % (3084343)Instructions burned: 437 (million)
% 16.08/3.28 % (3084311)Refutation found. Thanks to Tanya!
% 16.08/3.28 % SZS status Theorem for theBenchmark
% 16.08/3.28 % SZS output start Proof for theBenchmark
% See solution above
% 17.46/3.55 % (3084311)------------------------------
% 17.46/3.55 % (3084311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.46/3.55 % (3084311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.46/3.55 % (3084311)CaDiCaL version: 2.1.3
% 17.46/3.55 % (3084311)Termination reason: Refutation
% 17.46/3.55 % (3084311)Time elapsed: 1.677 s
% 17.46/3.55 % (3084311)Peak memory usage: 135 MB
% 17.46/3.55 % (3084311)Instructions burned: 1643 (million)
% 17.46/3.55 % (3084311)------------------------------
% 17.46/3.55 % (3084311)------------------------------
% 17.46/3.55 % (3084305)Success in time 2.372 s
% 17.46/3.55 % Vampire exiting
%------------------------------------------------------------------------------