%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL018+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 : n007.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 12:33:46 PM UTC 2026
% Result : Theorem 14.36s 2.75s
% Output : Refutation 15.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 16
% Syntax : Number of formulae : 146 ( 142 unt; 3 def)
% Number of atoms : 150 ( 149 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 169 ( 168 !; 1 ?)
% 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(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f14,conjecture,
! [X0] :
( composition(X0,top) = X0
=> composition(complement(X0),top) = complement(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0] :
( composition(X0,top) = X0
=> composition(complement(X0),top) = complement(X0) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0] :
( complement(X0) != composition(complement(X0),top)
& composition(X0,top) = X0 ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( complement(sK0) != composition(complement(sK0),top)
& sK0 = composition(sK0,top) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[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(f30,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
sK0 = composition(sK0,top),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
complement(sK0) != composition(complement(sK0),top),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f30,f21]) ).
fof(f34,definition,
sF1 = complement(sK0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f35,plain,
complement(sK0) = sF1,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF2 = composition(sF1,top),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f37,plain,
composition(sF1,top) = sF2,
inference(reorient_equations,[],[f36]) ).
fof(f38,plain,
sF1 != sF2,
inference(definition_folding,[],[f32,f37,f35,f35]) ).
fof(f39,definition,
sF3 = composition(sK0,top),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f40,plain,
composition(sK0,top) = sF3,
inference(reorient_equations,[],[f39]) ).
fof(f41,plain,
sK0 = sF3,
inference(definition_folding,[],[f31,f40]) ).
fof(f42,plain,
sK0 = composition(sK0,top),
inference(forward_demodulation,[],[f40,f41]) ).
fof(f45,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f27,f25]) ).
fof(f46,plain,
! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)),
inference(superposition,[],[f28,f25]) ).
fof(f48,plain,
complement(top) = join(composition(converse(sK0),complement(sK0)),complement(top)),
inference(superposition,[],[f28,f42]) ).
fof(f53,plain,
complement(top) = join(complement(top),composition(converse(sK0),complement(sK0))),
inference(forward_demodulation,[],[f48,f18]) ).
fof(f55,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(forward_demodulation,[],[f46,f18]) ).
fof(f57,plain,
complement(top) = join(complement(top),composition(converse(sK0),sF1)),
inference(forward_demodulation,[],[f53,f35]) ).
fof(f67,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f45,f23]) ).
fof(f77,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f67,f25]) ).
fof(f92,plain,
one = converse(one),
inference(superposition,[],[f23,f77]) ).
fof(f98,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f77,f92]) ).
fof(f110,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(converse(one),X0))),
inference(superposition,[],[f55,f98]) ).
fof(f111,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f110,f77]) ).
fof(f118,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(f120,plain,
! [X0] : composition(join(sK0,X0),top) = join(sK0,composition(X0,top)),
inference(superposition,[],[f24,f42]) ).
fof(f135,plain,
join(sK0,composition(complement(sK0),top)) = composition(top,top),
inference(superposition,[],[f120,f29]) ).
fof(f141,plain,
composition(top,top) = join(sK0,composition(sF1,top)),
inference(forward_demodulation,[],[f135,f35]) ).
fof(f143,plain,
composition(top,top) = join(sK0,sF2),
inference(forward_demodulation,[],[f141,f37]) ).
fof(f164,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f118,f27]) ).
fof(f169,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f164,f26]) ).
fof(f181,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f169,f26]) ).
fof(f189,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f181,f27]) ).
fof(f209,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f25,f189]) ).
fof(f220,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f209,f25]) ).
fof(f242,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(one,X1)),
inference(superposition,[],[f220,f23]) ).
fof(f332,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f26,f25]) ).
fof(f348,plain,
! [X0,X1] : join(top,X1) = join(X0,join(complement(X0),X1)),
inference(superposition,[],[f19,f29]) ).
fof(f360,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f18,f19]) ).
fof(f367,plain,
! [X0,X1] : join(top,X0) = join(X1,join(X0,complement(X1))),
inference(superposition,[],[f348,f18]) ).
fof(f369,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[],[f348,f111]) ).
fof(f379,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f369,f29]) ).
fof(f387,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[],[f20,f29]) ).
fof(f389,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f20,f18]) ).
fof(f394,plain,
! [X0] : join(complement(join(complement(X0),complement(complement(X0)))),complement(complement(X0))) = X0,
inference(superposition,[],[f20,f111]) ).
fof(f395,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(complement(join(complement(X0),complement(X1))),complement(complement(join(complement(X0),X1))))),complement(X0)),
inference(superposition,[],[f20,f20]) ).
fof(f401,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(f404,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f401,f360]) ).
fof(f408,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(complement(join(complement(X0),complement(X1))),complement(complement(join(complement(X0),X1)))))),
inference(forward_demodulation,[],[f395,f18]) ).
fof(f409,plain,
! [X0] : join(complement(complement(X0)),complement(join(complement(X0),complement(complement(X0))))) = X0,
inference(forward_demodulation,[],[f394,f18]) ).
fof(f414,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(forward_demodulation,[],[f389,f18]) ).
fof(f416,plain,
! [X0] : join(complement(top),complement(complement(X0))) = X0,
inference(forward_demodulation,[],[f387,f111]) ).
fof(f421,plain,
! [X0] : join(complement(complement(X0)),zero) = X0,
inference(forward_demodulation,[],[f409,f33]) ).
fof(f426,plain,
! [X0] : join(zero,complement(complement(X0))) = X0,
inference(forward_demodulation,[],[f421,f18]) ).
fof(f503,plain,
! [X0] : join(top,X0) = join(top,complement(complement(X0))),
inference(superposition,[],[f348,f416]) ).
fof(f505,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[],[f503,f379]) ).
fof(f558,plain,
! [X0] : composition(X0,top) = join(X0,composition(X0,complement(one))),
inference(superposition,[],[f242,f29]) ).
fof(f630,plain,
top = composition(top,top),
inference(superposition,[],[f505,f558]) ).
fof(f840,plain,
zero = complement(top),
inference(superposition,[],[f33,f29]) ).
fof(f861,plain,
! [X0,X1] : join(complement(join(complement(X0),join(complement(X1),complement(complement(X1))))),complement(join(zero,complement(X0)))) = X0,
inference(superposition,[],[f414,f33]) ).
fof(f866,plain,
! [X0,X1] : join(complement(join(zero,complement(X0))),complement(join(complement(X0),join(complement(X1),complement(complement(X1)))))) = X0,
inference(forward_demodulation,[],[f861,f18]) ).
fof(f887,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(complement(X0),top))) = X0,
inference(forward_demodulation,[],[f866,f29]) ).
fof(f897,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f887,f18]) ).
fof(f902,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f897,f18]) ).
fof(f907,plain,
! [X0] : join(complement(top),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f902,f379]) ).
fof(f911,plain,
! [X0] : join(zero,complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f907,f840]) ).
fof(f1006,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(superposition,[],[f911,f426]) ).
fof(f1063,plain,
! [X0] : complement(complement(X0)) = X0,
inference(superposition,[],[f426,f1006]) ).
fof(f1064,plain,
top = complement(zero),
inference(superposition,[],[f29,f1006]) ).
fof(f1096,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f1006,f1063]) ).
fof(f1188,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f18,f1096]) ).
fof(f1280,plain,
zero = join(zero,composition(converse(sK0),sF1)),
inference(superposition,[],[f57,f840]) ).
fof(f1293,plain,
zero = composition(converse(sK0),sF1),
inference(forward_demodulation,[],[f1280,f1096]) ).
fof(f1327,plain,
! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
inference(superposition,[],[f332,f29]) ).
fof(f1433,plain,
converse(zero) = composition(converse(sF1),sK0),
inference(superposition,[],[f45,f1293]) ).
fof(f1507,plain,
! [X0,X1] : join(complement(X1),complement(join(X0,complement(complement(X1))))) = join(complement(X1),complement(join(complement(join(complement(X1),complement(join(X0,complement(complement(X1)))))),complement(complement(join(top,X0)))))),
inference(superposition,[],[f408,f367]) ).
fof(f1520,plain,
! [X0,X1] : join(complement(X1),complement(join(X0,complement(complement(X1))))) = join(complement(X1),complement(join(complement(complement(join(top,X0))),complement(join(complement(X1),complement(join(X0,complement(complement(X1))))))))),
inference(forward_demodulation,[],[f1507,f18]) ).
fof(f1552,plain,
! [X0,X1] : join(complement(X1),complement(join(X0,X1))) = join(complement(X1),complement(join(complement(complement(join(top,X0))),complement(join(complement(X1),complement(join(X0,X1))))))),
inference(forward_demodulation,[],[f1520,f1063]) ).
fof(f1566,plain,
! [X0,X1] : join(complement(X1),complement(join(X0,X1))) = join(complement(X1),complement(join(join(top,X0),complement(join(complement(X1),complement(join(X0,X1))))))),
inference(forward_demodulation,[],[f1552,f1063]) ).
fof(f1575,plain,
! [X0,X1] : join(complement(X1),complement(join(X0,X1))) = join(complement(X1),complement(join(top,join(X0,complement(join(complement(X1),complement(join(X0,X1)))))))),
inference(forward_demodulation,[],[f1566,f19]) ).
fof(f1579,plain,
! [X0,X1] : join(complement(X1),complement(join(X0,X1))) = join(complement(X1),complement(top)),
inference(forward_demodulation,[],[f1575,f505]) ).
fof(f1581,plain,
! [X0,X1] : join(complement(X1),zero) = join(complement(X1),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1579,f840]) ).
fof(f1582,plain,
! [X0,X1] : join(zero,complement(X1)) = join(complement(X1),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1581,f18]) ).
fof(f1583,plain,
! [X0,X1] : complement(X1) = join(complement(X1),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1582,f1006]) ).
fof(f1594,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f1583,f18]) ).
fof(f1719,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(superposition,[],[f1594,f1063]) ).
fof(f2383,plain,
top = join(sK0,sF2),
inference(superposition,[],[f143,f630]) ).
fof(f2524,plain,
! [X0,X1] : join(X1,complement(complement(X0))) = join(complement(join(complement(X1),X0)),complement(complement(X0))),
inference(superposition,[],[f404,f1583]) ).
fof(f2567,plain,
! [X0,X1] : join(X1,complement(complement(X0))) = join(complement(complement(X0)),complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f2524,f18]) ).
fof(f2628,plain,
! [X0,X1] : join(X1,X0) = join(X0,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f2567,f1063]) ).
fof(f2769,plain,
top = converse(top),
inference(superposition,[],[f505,f1327]) ).
fof(f2783,plain,
! [X0] : join(X0,complement(converse(top))) = X0,
inference(superposition,[],[f1719,f1327]) ).
fof(f2933,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X1))),
inference(superposition,[],[f2628,f1063]) ).
fof(f3161,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f2933,f18]) ).
fof(f3203,plain,
join(sF2,complement(top)) = join(complement(sK0),sF2),
inference(superposition,[],[f2933,f2383]) ).
fof(f3277,plain,
join(sF2,complement(top)) = join(sF2,complement(sK0)),
inference(forward_demodulation,[],[f3203,f18]) ).
fof(f3320,plain,
join(sF2,complement(top)) = join(sF2,sF1),
inference(forward_demodulation,[],[f3277,f35]) ).
fof(f3354,plain,
join(sF2,complement(top)) = join(sF1,sF2),
inference(forward_demodulation,[],[f3320,f18]) ).
fof(f3377,plain,
join(sF2,zero) = join(sF1,sF2),
inference(forward_demodulation,[],[f3354,f840]) ).
fof(f3391,plain,
sF2 = join(sF1,sF2),
inference(forward_demodulation,[],[f3377,f1188]) ).
fof(f3470,plain,
! [X0] : join(X0,complement(converse(top))) = join(complement(converse(complement(converse(X0)))),X0),
inference(superposition,[],[f3161,f1327]) ).
fof(f3565,plain,
! [X0] : join(X0,complement(converse(top))) = join(X0,complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f3470,f18]) ).
fof(f3619,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(forward_demodulation,[],[f3565,f2783]) ).
fof(f6402,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(complement(converse(complement(converse(converse(X0))))))),
inference(superposition,[],[f332,f3619]) ).
fof(f6404,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = X0,
inference(forward_demodulation,[],[f6402,f25]) ).
fof(f6495,plain,
zero = converse(complement(converse(complement(zero)))),
inference(superposition,[],[f1096,f6404]) ).
fof(f6535,plain,
zero = converse(complement(converse(top))),
inference(forward_demodulation,[],[f6495,f1064]) ).
fof(f6553,plain,
zero = converse(complement(top)),
inference(forward_demodulation,[],[f6535,f2769]) ).
fof(f6560,plain,
zero = converse(zero),
inference(forward_demodulation,[],[f6553,f840]) ).
fof(f7412,plain,
complement(sK0) = join(complement(sK0),composition(sF1,complement(converse(zero)))),
inference(superposition,[],[f55,f1433]) ).
fof(f7438,plain,
complement(sK0) = join(complement(sK0),composition(sF1,complement(zero))),
inference(forward_demodulation,[],[f7412,f6560]) ).
fof(f7450,plain,
complement(sK0) = join(complement(sK0),composition(sF1,top)),
inference(forward_demodulation,[],[f7438,f1064]) ).
fof(f7459,plain,
complement(sK0) = join(complement(sK0),sF2),
inference(forward_demodulation,[],[f7450,f37]) ).
fof(f7465,plain,
complement(sK0) = join(sF2,complement(sK0)),
inference(forward_demodulation,[],[f7459,f18]) ).
fof(f7470,plain,
sF1 = join(sF2,sF1),
inference(forward_demodulation,[],[f7465,f35]) ).
fof(f7474,plain,
sF1 = join(sF1,sF2),
inference(forward_demodulation,[],[f7470,f18]) ).
fof(f7481,plain,
sF1 = sF2,
inference(superposition,[],[f3391,f7474]) ).
fof(f7501,plain,
$false,
inference(forward_subsumption_resolution,[],[f7481,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:49:55 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.36/2.75 % (1860523)Detected formulas, will run a generic FOF schedule.
% 14.36/2.75 % (1860540)dis-21_1_sil=8000:lcm=predicate:random_seed=829471237: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)
% 14.36/2.75 % (1860540)Refutation not found, incomplete strategy
% 14.36/2.75 % (1860540)------------------------------
% 14.36/2.75 % (1860540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860540)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860540)Termination reason: Refutation not found, incomplete strategy
% 14.36/2.75 % (1860540)Time elapsed: 0.002 s
% 14.36/2.75 % (1860540)Peak memory usage: 88 MB
% 14.36/2.75 % (1860540)Instructions burned: 1 (million)
% 14.36/2.75 % (1860538)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=884420256:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 14.36/2.75 % (1860536)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=3902644991:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 14.36/2.75 % (1860539)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=750503674:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 14.36/2.75 % (1860534)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=4268914567:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 14.36/2.75 % (1860537)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2855381426:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 14.36/2.75 % (1860535)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=4574703:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 14.36/2.75 % (1860538)Instruction limit reached!
% 14.36/2.75 % (1860538)------------------------------
% 14.36/2.75 % (1860538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860538)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860538)Termination reason: Instruction limit
% 14.36/2.75 % (1860538)Termination phase: Saturation
% 14.36/2.75 % (1860538)Time elapsed: 0.092 s
% 14.36/2.75 % (1860538)Peak memory usage: 88 MB
% 14.36/2.75 % (1860538)Instructions burned: 120 (million)
% 14.36/2.75 % (1860537)Instruction limit reached!
% 14.36/2.75 % (1860537)------------------------------
% 14.36/2.75 % (1860537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860537)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860537)Termination reason: Instruction limit
% 14.36/2.75 % (1860537)Termination phase: Saturation
% 14.36/2.75 % (1860537)Time elapsed: 0.104 s
% 14.36/2.75 % (1860537)Peak memory usage: 90 MB
% 14.36/2.75 % (1860537)Instructions burned: 109 (million)
% 14.36/2.75 % (1860539)Instruction limit reached!
% 14.36/2.75 % (1860539)------------------------------
% 14.36/2.75 % (1860539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860539)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860539)Termination reason: Instruction limit
% 14.36/2.75 % (1860539)Termination phase: Saturation
% 14.36/2.75 % (1860539)Time elapsed: 0.124 s
% 14.36/2.75 % (1860539)Peak memory usage: 89 MB
% 14.36/2.75 % (1860539)Instructions burned: 139 (million)
% 14.36/2.75 % (1860540)------------------------------
% 14.36/2.75 % (1860540)------------------------------
% 14.36/2.75 % (1860581)lrs+10_1_sil=8000:sp=occurrence:random_seed=1680548216:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 14.36/2.75 % (1860585)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2527177662:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 14.36/2.75 % (1860586)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=3297915568:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 14.36/2.75 % (1860583)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1987841102:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 14.36/2.75 % (1860586)Instruction limit reached!
% 14.36/2.75 % (1860586)------------------------------
% 14.36/2.75 % (1860586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860586)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860586)Termination reason: Instruction limit
% 14.36/2.75 % (1860586)Termination phase: Saturation
% 14.36/2.75 % (1860586)Time elapsed: 0.118 s
% 14.36/2.75 % (1860586)Peak memory usage: 92 MB
% 14.36/2.75 % (1860586)Instructions burned: 248 (million)
% 14.36/2.75 % (1860583)Instruction limit reached!
% 14.36/2.75 % (1860583)------------------------------
% 14.36/2.75 % (1860583)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860583)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860583)Termination reason: Instruction limit
% 14.36/2.75 % (1860583)Termination phase: Saturation
% 14.36/2.75 % (1860583)Time elapsed: 0.159 s
% 14.36/2.75 % (1860583)Peak memory usage: 91 MB
% 14.36/2.75 % (1860583)Instructions burned: 157 (million)
% 14.36/2.75 % (1860581)Instruction limit reached!
% 14.36/2.75 % (1860581)------------------------------
% 14.36/2.75 % (1860581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860581)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860581)Termination reason: Instruction limit
% 14.36/2.75 % (1860581)Termination phase: Saturation
% 14.36/2.75 % (1860581)Time elapsed: 0.294 s
% 14.36/2.75 % (1860581)Peak memory usage: 91 MB
% 14.36/2.75 % (1860581)Instructions burned: 285 (million)
% 14.36/2.75 % (1860585)Instruction limit reached!
% 14.36/2.75 % (1860585)------------------------------
% 14.36/2.75 % (1860585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860585)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860585)Termination reason: Instruction limit
% 14.36/2.75 % (1860585)Termination phase: Saturation
% 14.36/2.75 % (1860585)Time elapsed: 0.320 s
% 14.36/2.75 % (1860585)Peak memory usage: 91 MB
% 14.36/2.75 % (1860585)Instructions burned: 326 (million)
% 14.36/2.75 % (1860597)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2934058585:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 14.36/2.75 % (1860598)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=901252688:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 14.36/2.75 % (1860600)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3481630140:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 14.36/2.75 % (1860600)Refutation not found, incomplete strategy
% 14.36/2.75 % (1860600)------------------------------
% 14.36/2.75 % (1860600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860600)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860600)Termination reason: Refutation not found, incomplete strategy
% 14.36/2.75 % (1860600)Time elapsed: 0.001 s
% 14.36/2.75 % (1860600)Peak memory usage: 87 MB
% 14.36/2.75 % (1860599)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2019133233:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 14.36/2.75 % (1860597)Instruction limit reached!
% 14.36/2.75 % (1860597)------------------------------
% 14.36/2.75 % (1860597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860597)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860597)Termination reason: Instruction limit
% 14.36/2.75 % (1860597)Termination phase: Saturation
% 14.36/2.75 % (1860597)Time elapsed: 0.293 s
% 14.36/2.75 % (1860597)Peak memory usage: 92 MB
% 14.36/2.75 % (1860597)Instructions burned: 294 (million)
% 14.36/2.75 % (1860599)Instruction limit reached!
% 14.36/2.75 % (1860599)------------------------------
% 14.36/2.75 % (1860599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860599)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860599)Termination reason: Instruction limit
% 14.36/2.75 % (1860599)Termination phase: Saturation
% 14.36/2.75 % (1860599)Time elapsed: 0.106 s
% 14.36/2.75 % (1860599)Peak memory usage: 89 MB
% 14.36/2.75 % (1860599)Instructions burned: 114 (million)
% 14.36/2.75 % (1860600)------------------------------
% 14.36/2.75 % (1860600)------------------------------
% 14.36/2.75 % (1860613)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1324536032:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2988 on theBenchmark for (2988ds/114Mi)
% 14.36/2.75 % (1860614)lrs+10_1_sil=8000:sp=occurrence:random_seed=4141618485:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2987 on theBenchmark for (2987ds/907Mi)
% 14.36/2.75 % (1860613)Instruction limit reached!
% 14.36/2.75 % (1860613)------------------------------
% 14.36/2.75 % (1860613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860613)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860613)Termination reason: Instruction limit
% 14.36/2.75 % (1860613)Termination phase: Saturation
% 14.36/2.75 % (1860613)Time elapsed: 0.105 s
% 14.36/2.75 % (1860613)Peak memory usage: 89 MB
% 14.36/2.75 % (1860613)Instructions burned: 114 (million)
% 14.36/2.75 % (1860616)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=195651309:i=437:sd=1:aac=none:ss=included_2985 on theBenchmark for (2985ds/437Mi)
% 14.36/2.75 % (1860598)First to succeed.
% 14.36/2.75 % (1860598)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1860523"
% 14.36/2.75 % (1860620)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4187242105:i=5202:ss=axioms:sgt=16_2984 on theBenchmark for (2984ds/5202Mi)
% 14.36/2.75 % (1860534)Also succeeded, but the first one will report.
% 14.36/2.75 % (1860535)Also succeeded, but the first one will report.
% 14.36/2.75 % (1860616)Instruction limit reached!
% 14.36/2.75 % (1860616)------------------------------
% 14.36/2.75 % (1860616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.36/2.75 % (1860616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.36/2.75 % (1860616)CaDiCaL version: 2.1.3
% 14.36/2.75 % (1860616)Termination reason: Instruction limit
% 14.36/2.75 % (1860616)Termination phase: Saturation
% 14.36/2.75 % (1860616)Time elapsed: 0.254 s
% 14.36/2.75 % (1860616)Peak memory usage: 92 MB
% 14.36/2.75 % (1860616)Instructions burned: 438 (million)
% 14.36/2.75 % (1860598)Refutation found. Thanks to Tanya!
% 14.36/2.75 % SZS status Theorem for theBenchmark
% 14.36/2.75 % SZS output start Proof for theBenchmark
% See solution above
% 15.39/2.98 % (1860598)------------------------------
% 15.39/2.98 % (1860598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.39/2.98 % (1860598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.39/2.98 % (1860598)CaDiCaL version: 2.1.3
% 15.39/2.98 % (1860598)Termination reason: Refutation
% 15.39/2.98 % (1860598)Time elapsed: 0.908 s
% 15.39/2.98 % (1860598)Peak memory usage: 135 MB
% 15.39/2.98 % (1860598)Instructions burned: 1561 (million)
% 15.39/2.98 % (1860598)------------------------------
% 15.39/2.98 % (1860598)------------------------------
% 15.39/2.98 % (1860523)Success in time 2.134 s
% 15.39/2.98 % Vampire exiting
%------------------------------------------------------------------------------