%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL026+1 : 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 : n005.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 7.73s 3.05s
% Output : Refutation 15.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 19
% Syntax : Number of formulae : 149 ( 145 unt; 7 def)
% Number of atoms : 153 ( 152 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 231 ( 229 !; 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(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(f14,conjecture,
! [X0,X1] :
( join(X0,one) = one
=> meet(composition(X0,top),X1) = composition(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( join(X0,one) = one
=> meet(composition(X0,top),X1) = composition(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( composition(X0,X1) != meet(composition(X0,top),X1)
& join(X0,one) = one ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( 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,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f24,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f25,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f29,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
one = join(sK0,one),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
composition(sK0,sK1) != meet(composition(sK0,top),sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
composition(sK0,sK1) != complement(join(complement(composition(sK0,top)),complement(sK1))),
inference(definition_unfolding,[],[f32,f21]) ).
fof(f35,definition,
sF2 = composition(sK0,sK1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f36,plain,
composition(sK0,sK1) = sF2,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF3 = composition(sK0,top),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f38,plain,
composition(sK0,top) = sF3,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f40,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF5 = complement(sK1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f42,plain,
complement(sK1) = sF5,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF6 = join(sF4,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f44,plain,
join(sF4,sF5) = sF6,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF7 = complement(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f46,plain,
complement(sF6) = sF7,
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
sF2 != sF7,
inference(definition_folding,[],[f34,f46,f44,f42,f40,f38,f36]) ).
fof(f48,definition,
sF8 = join(sK0,one),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f49,plain,
join(sK0,one) = sF8,
inference(reorient_equations,[],[f48]) ).
fof(f50,plain,
one = sF8,
inference(definition_folding,[],[f31,f49]) ).
fof(f51,plain,
one = join(sK0,one),
inference(forward_demodulation,[],[f49,f50]) ).
fof(f52,plain,
one = join(one,sK0),
inference(forward_demodulation,[],[f51,f18]) ).
fof(f58,plain,
! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)),
inference(superposition,[],[f28,f25]) ).
fof(f71,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(forward_demodulation,[],[f58,f18]) ).
fof(f80,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f27,f25]) ).
fof(f88,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f24,f27]) ).
fof(f102,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f88,f27]) ).
fof(f103,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f102,f26]) ).
fof(f106,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f103,f26]) ).
fof(f108,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f106,f27]) ).
fof(f119,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f25,f108]) ).
fof(f132,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f119,f25]) ).
fof(f190,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f20,f18]) ).
fof(f198,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f20,f18]) ).
fof(f202,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(superposition,[],[f18,f20]) ).
fof(f203,plain,
! [X0,X1] : join(complement(join(X0,complement(X1))),complement(join(complement(X1),complement(X0)))) = X1,
inference(forward_demodulation,[],[f198,f18]) ).
fof(f211,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(forward_demodulation,[],[f190,f18]) ).
fof(f281,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f19,f20]) ).
fof(f295,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f18,f19]) ).
fof(f297,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f281,f295]) ).
fof(f416,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f80,f23]) ).
fof(f432,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f416,f25]) ).
fof(f449,plain,
! [X0,X1] : composition(join(converse(one),X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f24,f432]) ).
fof(f457,plain,
one = converse(one),
inference(superposition,[],[f23,f432]) ).
fof(f467,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(forward_demodulation,[],[f449,f457]) ).
fof(f561,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f432,f457]) ).
fof(f588,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(converse(one),X0))),
inference(superposition,[],[f71,f561]) ).
fof(f592,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f588,f432]) ).
fof(f615,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,[],[f297,f592]) ).
fof(f617,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),join(complement(X0),X1)),
inference(superposition,[],[f19,f592]) ).
fof(f619,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f615,f202]) ).
fof(f653,plain,
! [X0] : join(X0,complement(top)) = X0,
inference(superposition,[],[f619,f29]) ).
fof(f654,plain,
! [X0] : join(X0,complement(complement(X0))) = X0,
inference(superposition,[],[f619,f619]) ).
fof(f658,plain,
! [X0,X1] : join(X0,X0) = join(complement(join(complement(X0),X1)),X0),
inference(superposition,[],[f297,f619]) ).
fof(f678,plain,
! [X0,X1] : join(X0,X0) = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f658,f18]) ).
fof(f694,plain,
! [X0,X1] : join(join(complement(X0),X1),complement(X0)) = join(join(complement(X0),X1),join(complement(X0),X1)),
inference(superposition,[],[f678,f211]) ).
fof(f697,plain,
! [X2,X0,X1] : join(join(complement(X0),X2),join(complement(X0),X2)) = join(join(complement(X0),X2),complement(join(X0,X1))),
inference(superposition,[],[f678,f297]) ).
fof(f702,plain,
! [X0,X1] : join(X1,X1) = join(X1,complement(join(X0,complement(X1)))),
inference(superposition,[],[f678,f18]) ).
fof(f708,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f619,f678]) ).
fof(f735,plain,
! [X0,X1] : join(X1,complement(join(X0,complement(X1)))) = X1,
inference(forward_demodulation,[],[f702,f708]) ).
fof(f739,plain,
! [X2,X0,X1] : join(join(complement(X0),X2),join(complement(X0),X2)) = join(complement(X0),join(X2,complement(join(X0,X1)))),
inference(forward_demodulation,[],[f697,f19]) ).
fof(f742,plain,
! [X0,X1] : join(join(complement(X0),X1),complement(X0)) = join(X1,join(join(complement(X0),X1),complement(X0))),
inference(forward_demodulation,[],[f694,f295]) ).
fof(f758,plain,
! [X2,X0,X1] : join(complement(X0),join(X2,complement(join(X0,X1)))) = join(X2,join(join(complement(X0),X2),complement(X0))),
inference(forward_demodulation,[],[f739,f295]) ).
fof(f760,plain,
! [X0,X1] : join(complement(X0),join(complement(X0),X1)) = join(X1,join(complement(X0),join(complement(X0),X1))),
inference(forward_demodulation,[],[f742,f18]) ).
fof(f766,plain,
! [X2,X0,X1] : join(complement(X0),join(X2,complement(join(X0,X1)))) = join(X2,join(complement(X0),join(complement(X0),X2))),
inference(forward_demodulation,[],[f758,f18]) ).
fof(f768,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,join(complement(X0),X1)),
inference(forward_demodulation,[],[f760,f617]) ).
fof(f772,plain,
! [X2,X0,X1] : join(complement(X0),join(X2,complement(join(X0,X1)))) = join(X2,join(complement(X0),X2)),
inference(forward_demodulation,[],[f766,f617]) ).
fof(f774,plain,
! [X2,X0,X1] : join(complement(X0),X2) = join(complement(X0),join(X2,complement(join(X0,X1)))),
inference(forward_demodulation,[],[f772,f768]) ).
fof(f792,plain,
! [X0,X1] : join(X1,X0) = join(complement(join(complement(X1),X0)),X0),
inference(superposition,[],[f297,f735]) ).
fof(f803,plain,
! [X2,X0,X1] : join(X0,X1) = join(complement(complement(X0)),join(X1,complement(join(complement(X0),complement(complement(join(X2,complement(complement(X0))))))))),
inference(superposition,[],[f297,f735]) ).
fof(f810,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),X1),
inference(forward_demodulation,[],[f803,f774]) ).
fof(f816,plain,
! [X0,X1] : join(X1,X0) = join(X0,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f792,f18]) ).
fof(f838,plain,
! [X0] : join(X0,complement(complement(X0))) = join(complement(complement(X0)),complement(top)),
inference(superposition,[],[f816,f29]) ).
fof(f882,plain,
! [X0] : complement(complement(X0)) = join(X0,complement(complement(X0))),
inference(forward_demodulation,[],[f838,f653]) ).
fof(f895,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f882,f654]) ).
fof(f908,plain,
sK1 = complement(sF5),
inference(superposition,[],[f895,f42]) ).
fof(f911,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,complement(X1))),complement(join(X0,X1))),
inference(superposition,[],[f20,f895]) ).
fof(f919,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f211,f895]) ).
fof(f925,plain,
! [X0,X1] : join(complement(X0),complement(X0)) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f678,f895]) ).
fof(f926,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(superposition,[],[f735,f895]) ).
fof(f927,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X1))),
inference(superposition,[],[f816,f895]) ).
fof(f928,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(forward_demodulation,[],[f925,f708]) ).
fof(f934,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f911,f18]) ).
fof(f1072,plain,
! [X0,X1] : join(X0,X1) = join(join(X0,X1),complement(complement(X0))),
inference(superposition,[],[f735,f928]) ).
fof(f1078,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,complement(complement(X0)))),
inference(forward_demodulation,[],[f1072,f19]) ).
fof(f1099,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,X0)),
inference(forward_demodulation,[],[f1078,f895]) ).
fof(f1126,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f927,f18]) ).
fof(f1499,plain,
! [X0,X1] : join(X0,complement(X0)) = join(complement(complement(join(X1,complement(X0)))),X0),
inference(superposition,[],[f1126,f735]) ).
fof(f1511,plain,
! [X0,X1] : join(complement(join(X0,X1)),complement(complement(X0))) = join(complement(complement(join(X0,complement(X1)))),complement(join(X0,X1))),
inference(superposition,[],[f1126,f934]) ).
fof(f1580,plain,
! [X0,X1] : join(complement(join(X0,X1)),complement(complement(X0))) = join(complement(join(X0,X1)),complement(complement(join(X0,complement(X1))))),
inference(forward_demodulation,[],[f1511,f18]) ).
fof(f1590,plain,
! [X0,X1] : join(X0,complement(X0)) = join(X0,complement(complement(join(X1,complement(X0))))),
inference(forward_demodulation,[],[f1499,f18]) ).
fof(f1614,plain,
! [X0,X1] : join(complement(join(X0,X1)),complement(complement(X0))) = join(complement(join(X0,X1)),join(X0,complement(X1))),
inference(forward_demodulation,[],[f1580,f895]) ).
fof(f1622,plain,
! [X0,X1] : join(X0,complement(X0)) = join(X0,join(X1,complement(X0))),
inference(forward_demodulation,[],[f1590,f895]) ).
fof(f1642,plain,
! [X0,X1] : join(complement(join(X0,X1)),complement(complement(X0))) = join(join(X0,complement(X1)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1614,f18]) ).
fof(f1648,plain,
! [X0,X1] : top = join(X0,join(X1,complement(X0))),
inference(forward_demodulation,[],[f1622,f29]) ).
fof(f1662,plain,
! [X0,X1] : join(complement(join(X0,X1)),complement(complement(X0))) = join(X0,join(complement(X1),complement(join(X0,X1)))),
inference(forward_demodulation,[],[f1642,f19]) ).
fof(f1673,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(join(X0,X1)),complement(complement(X0))),
inference(forward_demodulation,[],[f1662,f926]) ).
fof(f1681,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(complement(X0)),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1673,f18]) ).
fof(f1685,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1681,f810]) ).
fof(f3938,plain,
! [X0,X1] : complement(join(X1,complement(X0))) = join(complement(join(join(X1,complement(X0)),X0)),complement(join(complement(X0),X1))),
inference(superposition,[],[f919,f1099]) ).
fof(f3944,plain,
! [X0,X1] : complement(join(X1,complement(X0))) = join(complement(join(complement(X0),X1)),complement(join(join(X1,complement(X0)),X0))),
inference(forward_demodulation,[],[f3938,f18]) ).
fof(f3990,plain,
! [X0,X1] : complement(join(X1,complement(X0))) = join(complement(join(complement(X0),X1)),complement(join(X0,join(X1,complement(X0))))),
inference(forward_demodulation,[],[f3944,f18]) ).
fof(f4027,plain,
! [X0,X1] : complement(join(X1,complement(X0))) = join(complement(join(complement(X0),X1)),complement(top)),
inference(forward_demodulation,[],[f3990,f1648]) ).
fof(f4047,plain,
! [X0,X1] : complement(join(complement(X0),X1)) = complement(join(X1,complement(X0))),
inference(forward_demodulation,[],[f4027,f653]) ).
fof(f5468,plain,
! [X0] : composition(one,X0) = join(X0,composition(sK0,X0)),
inference(superposition,[],[f467,f52]) ).
fof(f5576,plain,
! [X0] : join(X0,composition(sK0,X0)) = X0,
inference(forward_demodulation,[],[f5468,f561]) ).
fof(f5632,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(composition(sK0,X0),X1)),
inference(superposition,[],[f19,f5576]) ).
fof(f5641,plain,
! [X0] : join(X0,complement(X0)) = join(X0,complement(composition(sK0,X0))),
inference(superposition,[],[f1685,f5576]) ).
fof(f5674,plain,
! [X0] : top = join(X0,complement(composition(sK0,X0))),
inference(forward_demodulation,[],[f5641,f29]) ).
fof(f5850,plain,
! [X0,X1] : join(X0,composition(sK0,X1)) = join(X0,composition(sK0,join(X0,X1))),
inference(superposition,[],[f5632,f132]) ).
fof(f6008,plain,
! [X0] : join(X0,composition(sK0,complement(X0))) = join(X0,composition(sK0,top)),
inference(superposition,[],[f5850,f29]) ).
fof(f6149,plain,
! [X0] : join(X0,sF3) = join(X0,composition(sK0,complement(X0))),
inference(forward_demodulation,[],[f6008,f38]) ).
fof(f6209,plain,
! [X0] : join(X0,complement(composition(sK0,complement(X0)))) = join(X0,complement(join(X0,sF3))),
inference(superposition,[],[f1685,f6149]) ).
fof(f6250,plain,
! [X0] : join(complement(sF3),X0) = join(X0,complement(composition(sK0,complement(X0)))),
inference(forward_demodulation,[],[f6209,f1126]) ).
fof(f6285,plain,
! [X0] : join(sF4,X0) = join(X0,complement(composition(sK0,complement(X0)))),
inference(forward_demodulation,[],[f6250,f40]) ).
fof(f6354,plain,
! [X0] : composition(sK0,complement(X0)) = join(complement(join(sF4,X0)),complement(join(complement(composition(sK0,complement(X0))),complement(X0)))),
inference(superposition,[],[f203,f6285]) ).
fof(f6427,plain,
! [X0] : composition(sK0,complement(X0)) = join(complement(join(sF4,X0)),complement(join(complement(X0),complement(composition(sK0,complement(X0)))))),
inference(forward_demodulation,[],[f6354,f4047]) ).
fof(f6475,plain,
! [X0] : composition(sK0,complement(X0)) = join(complement(join(sF4,X0)),complement(top)),
inference(forward_demodulation,[],[f6427,f5674]) ).
fof(f6515,plain,
! [X0] : complement(join(sF4,X0)) = composition(sK0,complement(X0)),
inference(forward_demodulation,[],[f6475,f653]) ).
fof(f6575,plain,
composition(sK0,sK1) = complement(join(sF4,sF5)),
inference(superposition,[],[f6515,f908]) ).
fof(f6600,plain,
composition(sK0,sK1) = complement(sF6),
inference(forward_demodulation,[],[f6575,f44]) ).
fof(f6611,plain,
composition(sK0,sK1) = sF7,
inference(forward_demodulation,[],[f6600,f46]) ).
fof(f6618,plain,
sF2 = sF7,
inference(forward_demodulation,[],[f6611,f36]) ).
fof(f6623,plain,
$false,
inference(forward_subsumption_resolution,[],[f6618,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL026+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n005.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 27 22:52:46 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 Running first-order theorem proving
% 0.23/0.48 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
% 7.73/3.05 % (266867)Detected formulas, will run a generic FOF schedule.
% 7.73/3.05 % (266878)dis-21_1_sil=8000:lcm=predicate:random_seed=909081494: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)
% 7.73/3.05 % (266878)Refutation not found, incomplete strategy
% 7.73/3.05 % (266878)------------------------------
% 7.73/3.05 % (266878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266878)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266878)Termination reason: Refutation not found, incomplete strategy
% 7.73/3.05 % (266878)Time elapsed: 0.002 s
% 7.73/3.05 % (266878)Peak memory usage: 88 MB
% 7.73/3.05 % (266878)Instructions burned: 1 (million)
% 7.73/3.05 % (266875)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=324538050:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.73/3.05 % (266876)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=906016941:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.73/3.05 % (266874)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=4023455896:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.73/3.05 % (266872)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=1947835709:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.73/3.05 % (266873)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=992821146:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.73/3.05 % (266877)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3222998091:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.73/3.05 % (266875)Instruction limit reached!
% 7.73/3.05 % (266875)------------------------------
% 7.73/3.05 % (266875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266875)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266875)Termination reason: Instruction limit
% 7.73/3.05 % (266875)Termination phase: Saturation
% 7.73/3.05 % (266875)Time elapsed: 0.101 s
% 7.73/3.05 % (266875)Peak memory usage: 89 MB
% 7.73/3.05 % (266875)Instructions burned: 109 (million)
% 7.73/3.05 % (266876)Instruction limit reached!
% 7.73/3.05 % (266876)------------------------------
% 7.73/3.05 % (266876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266876)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266876)Termination reason: Instruction limit
% 7.73/3.05 % (266876)Termination phase: Saturation
% 7.73/3.05 % (266876)Time elapsed: 0.107 s
% 7.73/3.05 % (266876)Peak memory usage: 88 MB
% 7.73/3.05 % (266876)Instructions burned: 120 (million)
% 7.73/3.05 % (266877)Instruction limit reached!
% 7.73/3.05 % (266877)------------------------------
% 7.73/3.05 % (266877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266877)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266877)Termination reason: Instruction limit
% 7.73/3.05 % (266877)Termination phase: Saturation
% 7.73/3.05 % (266877)Time elapsed: 0.139 s
% 7.73/3.05 % (266877)Peak memory usage: 89 MB
% 7.73/3.05 % (266877)Instructions burned: 139 (million)
% 7.73/3.05 % (266878)------------------------------
% 7.73/3.05 % (266878)------------------------------
% 7.73/3.05 % (266886)lrs+10_1_sil=8000:sp=occurrence:random_seed=2130994677:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 7.73/3.05 % (266887)lrs+10_1_sil=32000:urr=on:br=off:random_seed=640986459:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 7.73/3.05 % (266887)Instruction limit reached!
% 7.73/3.05 % (266887)------------------------------
% 7.73/3.05 % (266887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266887)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266887)Termination reason: Instruction limit
% 7.73/3.05 % (266887)Termination phase: Saturation
% 7.73/3.05 % (266887)Time elapsed: 0.141 s
% 7.73/3.05 % (266887)Peak memory usage: 89 MB
% 7.73/3.05 % (266887)Instructions burned: 158 (million)
% 7.73/3.05 % (266888)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2949765995:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 7.73/3.05 % (266886)Instruction limit reached!
% 7.73/3.05 % (266886)------------------------------
% 7.73/3.05 % (266886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266886)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266886)Termination reason: Instruction limit
% 7.73/3.05 % (266886)Termination phase: Saturation
% 7.73/3.05 % (266886)Time elapsed: 0.154 s
% 7.73/3.05 % (266886)Peak memory usage: 91 MB
% 7.73/3.05 % (266886)Instructions burned: 285 (million)
% 7.73/3.05 % (266889)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=1796450951:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 7.73/3.05 % (266894)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1988159140:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 7.73/3.05 % (266893)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2990345001:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 7.73/3.05 % (266888)Instruction limit reached!
% 7.73/3.05 % (266888)------------------------------
% 7.73/3.05 % (266888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266888)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266888)Termination reason: Instruction limit
% 7.73/3.05 % (266888)Termination phase: Saturation
% 7.73/3.05 % (266888)Time elapsed: 0.321 s
% 7.73/3.05 % (266888)Peak memory usage: 92 MB
% 7.73/3.05 % (266888)Instructions burned: 325 (million)
% 7.73/3.05 % (266889)Instruction limit reached!
% 7.73/3.05 % (266889)------------------------------
% 7.73/3.05 % (266889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266889)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266889)Termination reason: Instruction limit
% 7.73/3.05 % (266889)Termination phase: Saturation
% 7.73/3.05 % (266889)Time elapsed: 0.254 s
% 7.73/3.05 % (266889)Peak memory usage: 91 MB
% 7.73/3.05 % (266889)Instructions burned: 248 (million)
% 7.73/3.05 % (266893)Instruction limit reached!
% 7.73/3.05 % (266893)------------------------------
% 7.73/3.05 % (266893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266893)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266893)Termination reason: Instruction limit
% 7.73/3.05 % (266893)Termination phase: Saturation
% 7.73/3.05 % (266893)Time elapsed: 0.280 s
% 7.73/3.05 % (266893)Peak memory usage: 91 MB
% 7.73/3.05 % (266893)Instructions burned: 294 (million)
% 7.73/3.05 % (266900)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1239907085:cts=off:i=113:fsr=off:ss=included:sgt=4_2989 on theBenchmark for (2989ds/113Mi)
% 7.73/3.05 % (266901)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2016431746:i=127:av=off:fsr=off:sup=off_2989 on theBenchmark for (2989ds/127Mi)
% 7.73/3.05 % (266901)Refutation not found, incomplete strategy
% 7.73/3.05 % (266901)------------------------------
% 7.73/3.05 % (266901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266901)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266901)Termination reason: Refutation not found, incomplete strategy
% 7.73/3.05 % (266901)Time elapsed: 0.002 s
% 7.73/3.05 % (266901)Peak memory usage: 88 MB
% 7.73/3.05 % (266900)Instruction limit reached!
% 7.73/3.05 % (266900)------------------------------
% 7.73/3.05 % (266900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266900)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266900)Termination reason: Instruction limit
% 7.73/3.05 % (266900)Termination phase: Saturation
% 7.73/3.05 % (266900)Time elapsed: 0.112 s
% 7.73/3.05 % (266900)Peak memory usage: 90 MB
% 7.73/3.05 % (266900)Instructions burned: 114 (million)
% 7.73/3.05 % (266902)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4246851378:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2986 on theBenchmark for (2986ds/114Mi)
% 7.73/3.05 % (266902)Instruction limit reached!
% 7.73/3.05 % (266902)------------------------------
% 7.73/3.05 % (266902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.73/3.05 % (266902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.73/3.05 % (266902)CaDiCaL version: 2.1.3
% 7.73/3.05 % (266902)Termination reason: Instruction limit
% 7.73/3.05 % (266902)Termination phase: Saturation
% 7.73/3.05 % (266902)Time elapsed: 0.098 s
% 7.73/3.05 % (266902)Peak memory usage: 88 MB
% 7.73/3.05 % (266902)Instructions burned: 115 (million)
% 7.73/3.05 % (266901)------------------------------
% 7.73/3.05 % (266901)------------------------------
% 7.73/3.05 % (266905)lrs+10_1_sil=8000:sp=occurrence:random_seed=107678819:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2985 on theBenchmark for (2985ds/907Mi)
% 7.73/3.05 % (266894)First to succeed.
% 7.73/3.05 % (266894)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-266867"
% 7.73/3.05 % (266907)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1959993891:i=437:sd=1:aac=none:ss=included_2982 on theBenchmark for (2982ds/437Mi)
% 7.73/3.05 % (266873)Also succeeded, but the first one will report.
% 7.73/3.05 % (266894)Refutation found. Thanks to Tanya!
% 7.73/3.05 % SZS status Theorem for theBenchmark
% 7.73/3.05 % SZS output start Proof for theBenchmark
% See solution above
% 15.28/3.27 % (266894)------------------------------
% 15.28/3.27 % (266894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.28/3.27 % (266894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.28/3.27 % (266894)CaDiCaL version: 2.1.3
% 15.28/3.27 % (266894)Termination reason: Refutation
% 15.28/3.27 % (266894)Time elapsed: 0.823 s
% 15.28/3.27 % (266894)Peak memory usage: 133 MB
% 15.28/3.27 % (266894)Instructions burned: 1471 (million)
% 15.28/3.27 % (266894)------------------------------
% 15.28/3.27 % (266894)------------------------------
% 15.28/3.27 % (266867)Success in time 2.055 s
% 15.28/3.27 % Vampire exiting
%------------------------------------------------------------------------------