%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL010-1 : 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 : n019.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 12:33:41 PM UTC 2026
% Result : Unsatisfiable 9.88s 2.27s
% Output : Refutation 10.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 25
% Syntax : Number of formulae : 168 ( 168 unt; 11 def)
% Number of atoms : 168 ( 167 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 184 ( 184 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
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_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f8,negated_conjecture,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,negated_conjecture,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
fof(f17,negated_conjecture,
meet(composition(sk1,sk2),sk3) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
zero = meet(composition(sk1,sk2),sk3),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
meet(sk2,composition(converse(sk1),sk3)) != zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
zero != meet(sk2,composition(converse(sk1),sk3)),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f22,plain,
zero = complement(join(complement(composition(sk1,sk2)),complement(sk3))),
inference(definition_unfolding,[],[f18,f6]) ).
fof(f23,plain,
zero != complement(join(complement(sk2),complement(composition(converse(sk1),sk3)))),
inference(definition_unfolding,[],[f20,f6]) ).
fof(f24,definition,
sF0 = composition(sk1,sk2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f25,plain,
composition(sk1,sk2) = sF0,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF1 = complement(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f27,plain,
complement(sF0) = sF1,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF2 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f29,plain,
complement(sk3) = sF2,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF3 = join(sF1,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f31,plain,
join(sF1,sF2) = sF3,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f33,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
zero = sF4,
inference(definition_folding,[],[f22,f33,f31,f29,f27,f25]) ).
fof(f35,definition,
sF5 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f36,plain,
complement(sk2) = sF5,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF6 = converse(sk1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f38,plain,
converse(sk1) = sF6,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF7 = composition(sF6,sk3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f40,plain,
composition(sF6,sk3) = sF7,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF8 = complement(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f42,plain,
complement(sF7) = sF8,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF9 = join(sF5,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f44,plain,
join(sF5,sF8) = sF9,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF10 = complement(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f46,plain,
complement(sF9) = sF10,
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
zero != sF10,
inference(definition_folding,[],[f23,f46,f44,f42,f40,f38,f36]) ).
fof(f48,plain,
zero = complement(top),
inference(backward_demodulation,[],[f21,f15]) ).
fof(f49,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f50,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f51,plain,
zero = complement(sF3),
inference(forward_demodulation,[],[f33,f34]) ).
fof(f53,plain,
! [X0] : top = join(complement(join(zero,X0)),complement(join(zero,complement(X0)))),
inference(superposition,[],[f50,f48]) ).
fof(f101,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f50,f15]) ).
fof(f102,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f101,f48]) ).
fof(f119,plain,
! [X0] : sF3 = join(complement(join(zero,X0)),complement(join(zero,complement(X0)))),
inference(superposition,[],[f50,f51]) ).
fof(f120,plain,
top = sF3,
inference(backward_demodulation,[],[f53,f119]) ).
fof(f122,plain,
! [X0] : join(X0,complement(X0)) = sF3,
inference(backward_demodulation,[],[f15,f120]) ).
fof(f138,plain,
complement(sk2) = join(complement(sk2),composition(converse(sk1),complement(sF0))),
inference(superposition,[],[f49,f25]) ).
fof(f139,plain,
complement(sk2) = join(complement(sk2),composition(converse(sk1),sF1)),
inference(forward_demodulation,[],[f138,f27]) ).
fof(f140,plain,
complement(sk2) = join(complement(sk2),composition(sF6,sF1)),
inference(forward_demodulation,[],[f139,f38]) ).
fof(f141,plain,
sF5 = join(sF5,composition(sF6,sF1)),
inference(forward_demodulation,[],[f140,f36]) ).
fof(f154,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f50,f1]) ).
fof(f182,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f49,f10]) ).
fof(f185,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(X0,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f188,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(sF3,X1),
inference(superposition,[],[f2,f122]) ).
fof(f198,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f211,plain,
! [X0,X1] : join(sF3,X0) = join(X1,join(X0,complement(X1))),
inference(superposition,[],[f188,f1]) ).
fof(f213,plain,
! [X0,X1] : join(sF3,complement(join(complement(X0),complement(X1)))) = join(join(complement(X0),X1),X0),
inference(superposition,[],[f188,f50]) ).
fof(f222,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(sF3,complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[],[f213,f1]) ).
fof(f226,plain,
! [X0,X1] : join(sF3,X1) = join(sF3,complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[],[f222,f188]) ).
fof(f230,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f232,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f9,f12]) ).
fof(f261,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(sF3)),
inference(superposition,[],[f154,f122]) ).
fof(f270,plain,
! [X0] : complement(X0) = join(complement(sF3),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f261,f1]) ).
fof(f292,plain,
! [X0] : complement(X0) = join(complement(sF3),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f270,f1]) ).
fof(f303,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f292,f51]) ).
fof(f310,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f102,f303]) ).
fof(f313,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f303,f310]) ).
fof(f324,plain,
sk3 = complement(sF2),
inference(superposition,[],[f310,f29]) ).
fof(f325,plain,
sF0 = complement(sF1),
inference(superposition,[],[f310,f27]) ).
fof(f334,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f154,f310]) ).
fof(f359,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(complement(join(complement(X1),X0))),complement(join(X0,X1))))),
inference(superposition,[],[f334,f334]) ).
fof(f365,plain,
! [X0,X1] : complement(X1) = join(complement(join(X1,complement(X0))),complement(join(X0,X1))),
inference(superposition,[],[f334,f310]) ).
fof(f369,plain,
! [X0] : complement(X0) = join(complement(join(X0,sF3)),complement(join(zero,X0))),
inference(superposition,[],[f334,f51]) ).
fof(f378,plain,
! [X0,X1] : join(sF3,complement(join(complement(X1),X0))) = join(join(X0,X1),complement(X0)),
inference(superposition,[],[f188,f334]) ).
fof(f381,plain,
! [X0,X1] : join(complement(X0),join(X0,X1)) = join(sF3,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f378,f1]) ).
fof(f386,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(forward_demodulation,[],[f365,f1]) ).
fof(f390,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),complement(complement(join(complement(X1),X0)))))),
inference(forward_demodulation,[],[f359,f1]) ).
fof(f395,plain,
! [X0,X1] : join(X0,join(X1,complement(X0))) = join(sF3,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f381,f198]) ).
fof(f404,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(complement(X1),X0)))),
inference(forward_demodulation,[],[f390,f310]) ).
fof(f407,plain,
! [X0,X1] : join(sF3,X1) = join(sF3,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f395,f211]) ).
fof(f414,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(X0,join(complement(join(X0,X1)),complement(X1))))),
inference(forward_demodulation,[],[f404,f198]) ).
fof(f417,plain,
! [X0,X1] : join(sF3,X1) = join(sF3,X0),
inference(backward_demodulation,[],[f226,f407]) ).
fof(f422,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f414,f1]) ).
fof(f425,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f422,f310]) ).
fof(f426,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f425,f310]) ).
fof(f450,plain,
! [X0,X1] : join(sF3,X0) = join(X1,sF3),
inference(superposition,[],[f1,f417]) ).
fof(f452,plain,
! [X0] : sF3 = join(sF3,X0),
inference(superposition,[],[f122,f417]) ).
fof(f472,plain,
! [X1] : sF3 = join(X1,sF3),
inference(forward_demodulation,[],[f450,f452]) ).
fof(f498,plain,
! [X0] : complement(X0) = join(complement(sF3),complement(join(zero,X0))),
inference(backward_demodulation,[],[f369,f472]) ).
fof(f505,plain,
! [X0] : complement(X0) = join(zero,complement(join(zero,X0))),
inference(forward_demodulation,[],[f498,f51]) ).
fof(f632,plain,
! [X0] : complement(complement(join(X0,X0))) = join(zero,complement(complement(X0))),
inference(superposition,[],[f505,f313]) ).
fof(f648,plain,
! [X0] : join(zero,X0) = complement(complement(join(X0,X0))),
inference(forward_demodulation,[],[f632,f310]) ).
fof(f653,plain,
! [X0] : join(zero,X0) = join(X0,X0),
inference(forward_demodulation,[],[f648,f310]) ).
fof(f672,plain,
! [X0] : join(X0,X0) = join(X0,zero),
inference(superposition,[],[f1,f653]) ).
fof(f726,plain,
! [X0,X1] : join(join(X0,X0),X1) = join(X0,join(zero,X1)),
inference(superposition,[],[f2,f672]) ).
fof(f729,plain,
! [X0,X1] : join(X0,join(X0,X1)) = join(X0,join(zero,X1)),
inference(forward_demodulation,[],[f726,f2]) ).
fof(f802,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(join(complement(join(X0,complement(X1))),join(X1,X0))),complement(complement(X0))),
inference(superposition,[],[f334,f386]) ).
fof(f810,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(complement(join(X0,complement(X1))),join(X1,X0)))),
inference(forward_demodulation,[],[f802,f1]) ).
fof(f839,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(join(X1,X0),complement(join(X0,complement(X1)))))),
inference(forward_demodulation,[],[f810,f1]) ).
fof(f865,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f839,f2]) ).
fof(f886,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f865,f310]) ).
fof(f902,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f886,f310]) ).
fof(f1023,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,join(zero,X0)),
inference(superposition,[],[f198,f653]) ).
fof(f1076,plain,
! [X0,X1] : join(X0,join(zero,X1)) = join(X1,join(X0,X0)),
inference(superposition,[],[f198,f672]) ).
fof(f1329,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f232,f12]) ).
fof(f1342,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f1329,f11]) ).
fof(f1351,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f1342,f11]) ).
fof(f1354,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f1351,f12]) ).
fof(f1576,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f230,f8]) ).
fof(f1593,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f1576,f10]) ).
fof(f1608,plain,
! [X0] : complement(X0) = join(complement(X0),composition(one,complement(X0))),
inference(superposition,[],[f182,f1593]) ).
fof(f1615,plain,
one = converse(one),
inference(superposition,[],[f8,f1593]) ).
fof(f1618,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f1593,f1615]) ).
fof(f1628,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f1608,f1618]) ).
fof(f1634,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f1628,f653]) ).
fof(f1640,plain,
! [X0] : complement(X0) = complement(join(X0,X0)),
inference(backward_demodulation,[],[f313,f1634]) ).
fof(f1699,plain,
! [X0] : complement(complement(X0)) = join(X0,X0),
inference(superposition,[],[f310,f1640]) ).
fof(f1706,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[],[f1699,f310]) ).
fof(f1722,plain,
! [X0] : join(X0,zero) = X0,
inference(backward_demodulation,[],[f672,f1706]) ).
fof(f1728,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(zero,X1)),
inference(backward_demodulation,[],[f1076,f1706]) ).
fof(f1752,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,X0)),
inference(backward_demodulation,[],[f1023,f1728]) ).
fof(f1754,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X0,X1)),
inference(backward_demodulation,[],[f729,f1728]) ).
fof(f2066,plain,
! [X0,X1] : join(complement(join(X0,complement(X1))),complement(join(X1,X0))) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f1754,f386]) ).
fof(f2125,plain,
! [X0,X1] : join(complement(X0),complement(join(X1,X0))) = join(complement(join(X0,complement(X1))),complement(join(X1,X0))),
inference(forward_demodulation,[],[f2066,f1]) ).
fof(f2155,plain,
! [X0,X1] : join(complement(X0),complement(join(X1,X0))) = join(complement(join(X1,X0)),complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f2125,f1]) ).
fof(f2169,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f2155,f386]) ).
fof(f2175,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f426,f2169]) ).
fof(f2180,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f902,f2175]) ).
fof(f2183,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,X0))),
inference(forward_demodulation,[],[f2180,f1752]) ).
fof(f2192,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f2183,f1]) ).
fof(f2208,plain,
join(sF2,complement(sF1)) = join(sF2,complement(sF3)),
inference(superposition,[],[f2183,f31]) ).
fof(f2251,plain,
join(sF2,complement(sF1)) = join(sF2,zero),
inference(forward_demodulation,[],[f2208,f51]) ).
fof(f2285,plain,
sF2 = join(sF2,complement(sF1)),
inference(forward_demodulation,[],[f2251,f1722]) ).
fof(f2307,plain,
sF2 = join(sF2,sF0),
inference(forward_demodulation,[],[f2285,f325]) ).
fof(f2319,plain,
sF2 = join(sF0,sF2),
inference(forward_demodulation,[],[f2307,f1]) ).
fof(f2344,plain,
complement(sF0) = join(complement(sF2),complement(join(complement(sF2),sF0))),
inference(superposition,[],[f334,f2319]) ).
fof(f2350,plain,
complement(sF0) = join(complement(sF2),complement(sF0)),
inference(forward_demodulation,[],[f2344,f2192]) ).
fof(f2354,plain,
complement(sF0) = join(complement(sF0),complement(sF2)),
inference(forward_demodulation,[],[f2350,f1]) ).
fof(f2357,plain,
complement(sF0) = join(complement(sF0),sk3),
inference(forward_demodulation,[],[f2354,f324]) ).
fof(f2359,plain,
complement(sF0) = join(sk3,complement(sF0)),
inference(forward_demodulation,[],[f2357,f1]) ).
fof(f2361,plain,
sF1 = join(sk3,sF1),
inference(forward_demodulation,[],[f2359,f27]) ).
fof(f2363,plain,
sF1 = join(sF1,sk3),
inference(forward_demodulation,[],[f2361,f1]) ).
fof(f4172,plain,
! [X0] : join(sF5,X0) = join(composition(sF6,sF1),join(sF5,X0)),
inference(superposition,[],[f185,f141]) ).
fof(f4296,plain,
! [X0] : join(sF5,X0) = join(sF5,join(X0,composition(sF6,sF1))),
inference(forward_demodulation,[],[f4172,f198]) ).
fof(f6814,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f1354]) ).
fof(f6833,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f6814,f10]) ).
fof(f6944,plain,
! [X0] : composition(sF6,join(X0,sk3)) = join(composition(sF6,X0),sF7),
inference(superposition,[],[f6833,f40]) ).
fof(f6994,plain,
! [X0] : join(sF7,composition(sF6,X0)) = composition(sF6,join(X0,sk3)),
inference(forward_demodulation,[],[f6944,f1]) ).
fof(f7481,plain,
composition(sF6,sF1) = join(sF7,composition(sF6,sF1)),
inference(superposition,[],[f6994,f2363]) ).
fof(f7520,plain,
join(sF5,composition(sF6,sF1)) = join(sF5,sF7),
inference(superposition,[],[f4296,f7481]) ).
fof(f7546,plain,
sF5 = join(sF5,sF7),
inference(forward_demodulation,[],[f7520,f141]) ).
fof(f7575,plain,
join(sF5,complement(sF5)) = join(sF5,complement(sF7)),
inference(superposition,[],[f2192,f7546]) ).
fof(f7579,plain,
join(sF5,sF8) = join(sF5,complement(sF5)),
inference(forward_demodulation,[],[f7575,f42]) ).
fof(f7588,plain,
sF3 = join(sF5,sF8),
inference(forward_demodulation,[],[f7579,f122]) ).
fof(f7594,plain,
sF3 = sF9,
inference(backward_demodulation,[],[f44,f7588]) ).
fof(f7598,plain,
complement(sF3) = sF10,
inference(backward_demodulation,[],[f46,f7594]) ).
fof(f7713,plain,
zero = sF10,
inference(forward_demodulation,[],[f7598,f51]) ).
fof(f7744,plain,
$false,
inference(forward_subsumption_resolution,[],[f7713,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL010-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:50:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 9.88/2.27 % (3490935)Detected a unit-equality problem, will run specialized UEQ schedule.
% 9.88/2.27 % (3491016)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=602680281:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 9.88/2.27 % (3491018)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=810898729:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 9.88/2.27 % (3491015)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1583852535:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 9.88/2.27 % (3491014)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3427393699:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 9.88/2.27 % (3491027)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3967108512:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 9.88/2.27 % (3491022)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=655636639:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 9.88/2.27 % (3491028)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1903922197:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 9.88/2.27 % (3491018)Instruction limit reached!
% 9.88/2.27 % (3491018)------------------------------
% 9.88/2.27 % (3491018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.27 % (3491018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.27 % (3491018)CaDiCaL version: 2.1.3
% 9.88/2.27 % (3491018)Termination reason: Instruction limit
% 9.88/2.27 % (3491018)Termination phase: Saturation
% 9.88/2.27 % (3491018)Time elapsed: 0.112 s
% 9.88/2.27 % (3491018)Peak memory usage: 88 MB
% 9.88/2.27 % (3491018)Instructions burned: 137 (million)
% 9.88/2.27 % (3491022)Instruction limit reached!
% 9.88/2.27 % (3491022)------------------------------
% 9.88/2.27 % (3491022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.27 % (3491022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.27 % (3491022)CaDiCaL version: 2.1.3
% 9.88/2.27 % (3491022)Termination reason: Instruction limit
% 9.88/2.27 % (3491022)Termination phase: Saturation
% 9.88/2.27 % (3491022)Time elapsed: 0.181 s
% 9.88/2.27 % (3491022)Peak memory usage: 89 MB
% 9.88/2.27 % (3491022)Instructions burned: 181 (million)
% 9.88/2.27 % (3491027)Instruction limit reached!
% 9.88/2.27 % (3491027)------------------------------
% 9.88/2.27 % (3491027)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.27 % (3491027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.27 % (3491027)CaDiCaL version: 2.1.3
% 9.88/2.27 % (3491027)Termination reason: Instruction limit
% 9.88/2.27 % (3491027)Termination phase: Saturation
% 9.88/2.27 % (3491027)Time elapsed: 0.271 s
% 9.88/2.27 % (3491027)Peak memory usage: 90 MB
% 9.88/2.27 % (3491027)Instructions burned: 258 (million)
% 9.88/2.27 % (3491053)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3170780367:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 9.88/2.27 % (3491056)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=93533426:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 9.88/2.27 % (3491057)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2917726591:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 9.88/2.27 % (3491057)Instruction limit reached!
% 9.88/2.27 % (3491057)------------------------------
% 9.88/2.27 % (3491057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.27 % (3491057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.27 % (3491057)CaDiCaL version: 2.1.3
% 9.88/2.27 % (3491057)Termination reason: Instruction limit
% 9.88/2.27 % (3491057)Termination phase: Saturation
% 9.88/2.27 % (3491057)Time elapsed: 0.204 s
% 9.88/2.27 % (3491057)Peak memory usage: 92 MB
% 9.88/2.27 % (3491057)Instructions burned: 216 (million)
% 9.88/2.27 % (3491016)First to succeed.
% 9.88/2.27 % (3491016)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3490935"
% 9.88/2.27 % (3491067)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=187601060:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2989 on theBenchmark for (2989ds/317Mi)
% 9.88/2.27 % (3491016)Refutation found. Thanks to Tanya!
% 9.88/2.27 % SZS status Unsatisfiable for theBenchmark
% 9.88/2.27 % SZS output start Proof for theBenchmark
% See solution above
% 10.57/2.47 % (3491016)------------------------------
% 10.57/2.47 % (3491016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.57/2.47 % (3491016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.57/2.47 % (3491016)CaDiCaL version: 2.1.3
% 10.57/2.47 % (3491016)Termination reason: Refutation
% 10.57/2.47 % (3491016)Time elapsed: 1.004 s
% 10.57/2.47 % (3491016)Peak memory usage: 135 MB
% 10.57/2.47 % (3491016)Instructions burned: 1709 (million)
% 10.57/2.47 % (3491016)------------------------------
% 10.57/2.47 % (3491016)------------------------------
% 10.57/2.47 % (3490935)Success in time 1.422 s
% 10.57/2.47 % Vampire exiting
%------------------------------------------------------------------------------