%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL017-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Unsatisfiable 9.26s 2.36s
% Output : Refutation 10.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 25
% Syntax : Number of formulae : 148 ( 148 unt; 12 def)
% Number of atoms : 148 ( 147 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 23 ( 23 usr; 18 con; 0-2 aty)
% Number of variables : 165 ( 165 !; 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(f23,negated_conjecture,
join(complement(composition(sk1,sk2)),composition(sk1,sk3)) != join(complement(composition(sk1,meet(sk2,complement(sk3)))),composition(sk1,sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f28,plain,
join(complement(composition(sk1,sk2)),composition(sk1,sk3)) != join(complement(composition(sk1,complement(join(complement(sk2),complement(complement(sk3)))))),composition(sk1,sk3)),
inference(definition_unfolding,[],[f23,f6]) ).
fof(f29,definition,
sF0 = composition(sk1,sk2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f30,plain,
composition(sk1,sk2) = sF0,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF1 = complement(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f32,plain,
complement(sF0) = sF1,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF2 = composition(sk1,sk3),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f34,plain,
composition(sk1,sk3) = sF2,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF3 = join(sF1,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f36,plain,
join(sF1,sF2) = sF3,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF4 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f38,plain,
complement(sk2) = sF4,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF5 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f40,plain,
complement(sk3) = sF5,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF6 = complement(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f42,plain,
complement(sF5) = sF6,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF7 = join(sF4,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f44,plain,
join(sF4,sF6) = sF7,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF8 = complement(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f46,plain,
complement(sF7) = sF8,
inference(reorient_equations,[],[f45]) ).
fof(f47,definition,
sF9 = composition(sk1,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f48,plain,
composition(sk1,sF8) = sF9,
inference(reorient_equations,[],[f47]) ).
fof(f49,definition,
sF10 = complement(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f50,plain,
complement(sF9) = sF10,
inference(reorient_equations,[],[f49]) ).
fof(f51,definition,
sF11 = join(sF10,sF2),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f52,plain,
join(sF10,sF2) = sF11,
inference(reorient_equations,[],[f51]) ).
fof(f53,plain,
sF3 != sF11,
inference(definition_folding,[],[f28,f52,f34,f50,f48,f46,f44,f42,f40,f38,f36,f34,f32,f30]) ).
fof(f54,plain,
zero = complement(top),
inference(backward_demodulation,[],[f24,f15]) ).
fof(f55,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f58,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f59,plain,
sF3 = join(sF2,sF1),
inference(forward_demodulation,[],[f36,f1]) ).
fof(f60,plain,
sF11 = join(sF2,sF10),
inference(forward_demodulation,[],[f52,f1]) ).
fof(f114,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f55,f1]) ).
fof(f140,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f55,f15]) ).
fof(f141,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f140,f54]) ).
fof(f157,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f55]) ).
fof(f168,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f193,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f157,f15]) ).
fof(f209,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f193,f168]) ).
fof(f221,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f209,f54]) ).
fof(f246,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f248,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(f256,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f248,f12]) ).
fof(f262,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f256,f11]) ).
fof(f265,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f262,f11]) ).
fof(f267,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f265,f12]) ).
fof(f280,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f267]) ).
fof(f291,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f280,f10]) ).
fof(f314,plain,
! [X0] : composition(sk1,join(X0,sk2)) = join(composition(sk1,X0),sF0),
inference(superposition,[],[f291,f30]) ).
fof(f315,plain,
! [X0] : composition(sk1,join(X0,sF8)) = join(composition(sk1,X0),sF9),
inference(superposition,[],[f291,f48]) ).
fof(f324,plain,
! [X0] : join(sF9,composition(sk1,X0)) = composition(sk1,join(X0,sF8)),
inference(forward_demodulation,[],[f315,f1]) ).
fof(f325,plain,
! [X0] : join(sF0,composition(sk1,X0)) = composition(sk1,join(X0,sk2)),
inference(forward_demodulation,[],[f314,f1]) ).
fof(f451,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[],[f55,f54]) ).
fof(f453,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f451,f1]) ).
fof(f455,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(complement(X0),top))) = X0,
inference(forward_demodulation,[],[f453,f1]) ).
fof(f457,plain,
! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f455,f1]) ).
fof(f459,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f457,f1]) ).
fof(f486,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f114,f15]) ).
fof(f489,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(superposition,[],[f157,f114]) ).
fof(f501,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(forward_demodulation,[],[f489,f1]) ).
fof(f502,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f486,f1]) ).
fof(f526,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f502,f1]) ).
fof(f539,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f526,f54]) ).
fof(f548,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f141,f539]) ).
fof(f558,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(X1,complement(X0)))),
inference(backward_demodulation,[],[f501,f548]) ).
fof(f559,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f539,f548]) ).
fof(f578,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f559]) ).
fof(f582,plain,
top = complement(zero),
inference(superposition,[],[f548,f54]) ).
fof(f583,plain,
sk2 = complement(sF4),
inference(superposition,[],[f548,f38]) ).
fof(f584,plain,
sk3 = complement(sF5),
inference(superposition,[],[f548,f40]) ).
fof(f590,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f55,f548]) ).
fof(f594,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f114,f548]) ).
fof(f620,plain,
sk3 = sF6,
inference(forward_demodulation,[],[f584,f42]) ).
fof(f625,plain,
sF2 = composition(sk1,sF6),
inference(backward_demodulation,[],[f34,f620]) ).
fof(f646,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f590,f1]) ).
fof(f757,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(superposition,[],[f590,f594]) ).
fof(f758,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,[],[f757,f548]) ).
fof(f781,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,[],[f758,f168]) ).
fof(f796,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,[],[f781,f1]) ).
fof(f807,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f796,f548]) ).
fof(f816,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f807,f548]) ).
fof(f838,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(join(X0,X0)),complement(zero)))),
inference(superposition,[],[f646,f559]) ).
fof(f857,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,[],[f594,f646]) ).
fof(f869,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,[],[f857,f1]) ).
fof(f879,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(zero),complement(join(X0,X0))))),
inference(forward_demodulation,[],[f838,f1]) ).
fof(f891,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,[],[f869,f1]) ).
fof(f898,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f879,f582]) ).
fof(f906,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,[],[f891,f2]) ).
fof(f912,plain,
! [X0] : complement(complement(join(X0,X0))) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f898,f548]) ).
fof(f919,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f906,f548]) ).
fof(f924,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f912,f548]) ).
fof(f931,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f919,f548]) ).
fof(f1137,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f246,f8]) ).
fof(f1155,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f1137,f10]) ).
fof(f1172,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f58,f1155]) ).
fof(f1186,plain,
one = converse(one),
inference(superposition,[],[f8,f1155]) ).
fof(f1191,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f1155,f1186]) ).
fof(f1204,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f1172,f1191]) ).
fof(f1216,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f221,f1204]) ).
fof(f1221,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f1216,f548]) ).
fof(f1226,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f578,f1221]) ).
fof(f1229,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(complement(X0),top))),
inference(backward_demodulation,[],[f924,f1226]) ).
fof(f1230,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f559,f1226]) ).
fof(f1232,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f1230,f1]) ).
fof(f1233,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(X0)))),
inference(forward_demodulation,[],[f1229,f558]) ).
fof(f1236,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(complement(X0))) = X0,
inference(backward_demodulation,[],[f459,f1232]) ).
fof(f1246,plain,
! [X0] : join(complement(complement(X0)),complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f1236,f1]) ).
fof(f1249,plain,
! [X0] : join(X0,complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f1246,f548]) ).
fof(f1252,plain,
! [X0] : join(X0,X0) = X0,
inference(backward_demodulation,[],[f1233,f1249]) ).
fof(f1388,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f1252]) ).
fof(f1390,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f168,f1252]) ).
fof(f1462,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f1388,f646]) ).
fof(f1501,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1462,f1]) ).
fof(f1516,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f816,f1501]) ).
fof(f1523,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f931,f1516]) ).
fof(f1528,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1523,f1390]) ).
fof(f1546,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1528,f1]) ).
fof(f1687,plain,
join(sF6,complement(sF4)) = join(sF6,complement(sF7)),
inference(superposition,[],[f1546,f44]) ).
fof(f1719,plain,
join(sF6,complement(sF4)) = join(sF6,sF8),
inference(forward_demodulation,[],[f1687,f46]) ).
fof(f1742,plain,
join(sF6,sk2) = join(sF6,sF8),
inference(forward_demodulation,[],[f1719,f583]) ).
fof(f2924,plain,
join(sF0,composition(sk1,sF6)) = composition(sk1,join(sF6,sF8)),
inference(superposition,[],[f325,f1742]) ).
fof(f2944,plain,
join(sF0,composition(sk1,sF6)) = join(sF9,composition(sk1,sF6)),
inference(forward_demodulation,[],[f2924,f324]) ).
fof(f2951,plain,
join(sF0,sF2) = join(sF9,sF2),
inference(forward_demodulation,[],[f2944,f625]) ).
fof(f2956,plain,
join(sF2,sF9) = join(sF0,sF2),
inference(forward_demodulation,[],[f2951,f1]) ).
fof(f2961,plain,
join(sF2,sF9) = join(sF2,sF0),
inference(forward_demodulation,[],[f2956,f1]) ).
fof(f2983,plain,
join(sF2,complement(sF9)) = join(sF2,complement(join(sF2,sF0))),
inference(superposition,[],[f1528,f2961]) ).
fof(f2985,plain,
join(sF2,complement(sF9)) = join(sF2,complement(sF0)),
inference(forward_demodulation,[],[f2983,f1528]) ).
fof(f2992,plain,
join(sF2,sF1) = join(sF2,complement(sF9)),
inference(forward_demodulation,[],[f2985,f32]) ).
fof(f2996,plain,
join(sF2,sF1) = join(sF2,sF10),
inference(forward_demodulation,[],[f2992,f50]) ).
fof(f2999,plain,
sF11 = join(sF2,sF1),
inference(forward_demodulation,[],[f2996,f60]) ).
fof(f3001,plain,
sF3 = sF11,
inference(forward_demodulation,[],[f2999,f59]) ).
fof(f3002,plain,
$false,
inference(forward_subsumption_resolution,[],[f3001,f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL017-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n004.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 22:51:22 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 9.26/2.36 % (3974355)Detected a unit-equality problem, will run specialized UEQ schedule.
% 9.26/2.36 % (3974365)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2722132280:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 9.26/2.36 % (3974363)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=3718121893:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 9.26/2.36 % (3974367)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1405996332:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 9.26/2.36 % (3974368)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=508827157:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 9.26/2.36 % (3974364)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=1076896404:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 9.26/2.36 % (3974366)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=881021491:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 9.26/2.36 % (3974369)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2934544750:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 9.26/2.36 % (3974366)Instruction limit reached!
% 9.26/2.36 % (3974366)------------------------------
% 9.26/2.36 % (3974366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.36 % (3974366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.36 % (3974366)CaDiCaL version: 2.1.3
% 9.26/2.36 % (3974366)Termination reason: Instruction limit
% 9.26/2.36 % (3974366)Termination phase: Saturation
% 9.26/2.36 % (3974366)Time elapsed: 0.138 s
% 9.26/2.36 % (3974366)Peak memory usage: 89 MB
% 9.26/2.36 % (3974366)Instructions burned: 136 (million)
% 9.26/2.36 % (3974367)Instruction limit reached!
% 9.26/2.36 % (3974367)------------------------------
% 9.26/2.36 % (3974367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.36 % (3974367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.36 % (3974367)CaDiCaL version: 2.1.3
% 9.26/2.36 % (3974367)Termination reason: Instruction limit
% 9.26/2.36 % (3974367)Termination phase: Saturation
% 9.26/2.36 % (3974367)Time elapsed: 0.175 s
% 9.26/2.36 % (3974367)Peak memory usage: 89 MB
% 9.26/2.36 % (3974367)Instructions burned: 181 (million)
% 9.26/2.36 % (3974368)Instruction limit reached!
% 9.26/2.36 % (3974368)------------------------------
% 9.26/2.36 % (3974368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.36 % (3974368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.36 % (3974368)CaDiCaL version: 2.1.3
% 9.26/2.36 % (3974368)Termination reason: Instruction limit
% 9.26/2.36 % (3974368)Termination phase: Saturation
% 9.26/2.36 % (3974368)Time elapsed: 0.275 s
% 9.26/2.36 % (3974368)Peak memory usage: 90 MB
% 9.26/2.36 % (3974368)Instructions burned: 257 (million)
% 9.26/2.36 % (3974377)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=646890815:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 9.26/2.36 % (3974378)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=777361127:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 9.26/2.36 % (3974379)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1148751038:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 9.26/2.36 % (3974379)Instruction limit reached!
% 9.26/2.36 % (3974379)------------------------------
% 9.26/2.36 % (3974379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.36 % (3974379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.36 % (3974379)CaDiCaL version: 2.1.3
% 9.26/2.36 % (3974379)Termination reason: Instruction limit
% 9.26/2.36 % (3974379)Termination phase: Saturation
% 9.26/2.36 % (3974379)Time elapsed: 0.195 s
% 9.26/2.36 % (3974379)Peak memory usage: 89 MB
% 9.26/2.36 % (3974379)Instructions burned: 216 (million)
% 9.26/2.36 % (3974365)First to succeed.
% 9.26/2.36 % (3974365)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3974355"
% 9.26/2.36 % (3974365)Refutation found. Thanks to Tanya!
% 9.26/2.36 % SZS status Unsatisfiable for theBenchmark
% 9.26/2.36 % SZS output start Proof for theBenchmark
% See solution above
% 10.15/2.66 % (3974365)------------------------------
% 10.15/2.66 % (3974365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.15/2.66 % (3974365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.15/2.66 % (3974365)CaDiCaL version: 2.1.3
% 10.15/2.66 % (3974365)Termination reason: Refutation
% 10.15/2.66 % (3974365)Time elapsed: 0.867 s
% 10.15/2.66 % (3974365)Peak memory usage: 134 MB
% 10.15/2.66 % (3974365)Instructions burned: 1521 (million)
% 10.15/2.66 % (3974365)------------------------------
% 10.15/2.66 % (3974365)------------------------------
% 10.15/2.66 % (3974355)Success in time 1.303 s
% 10.15/2.66 % Vampire exiting
%------------------------------------------------------------------------------