%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL016-3 : 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 : 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 12:33:45 PM UTC 2026
% Result : Unsatisfiable 8.24s 2.15s
% Output : Refutation 9.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 29
% Syntax : Number of formulae : 157 ( 157 unt; 16 def)
% Number of atoms : 157 ( 156 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 : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 22 con; 0-2 aty)
% Number of variables : 161 ( 161 !; 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,
meet(composition(sk1,sk2),complement(composition(sk1,sk3))) != meet(composition(sk1,meet(sk2,complement(sk3))),complement(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,
complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3))))) != complement(join(complement(composition(sk1,complement(join(complement(sk2),complement(complement(sk3)))))),complement(complement(composition(sk1,sk3))))),
inference(definition_unfolding,[],[f23,f6,f6,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 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f36,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f38,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF5 = join(sF1,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f40,plain,
join(sF1,sF4) = 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 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f44,plain,
complement(sk2) = sF7,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF8 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f46,plain,
complement(sk3) = sF8,
inference(reorient_equations,[],[f45]) ).
fof(f47,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f48,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f47]) ).
fof(f49,definition,
sF10 = join(sF7,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f50,plain,
join(sF7,sF9) = sF10,
inference(reorient_equations,[],[f49]) ).
fof(f51,definition,
sF11 = complement(sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f52,plain,
complement(sF10) = sF11,
inference(reorient_equations,[],[f51]) ).
fof(f53,definition,
sF12 = composition(sk1,sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f54,plain,
composition(sk1,sF11) = sF12,
inference(reorient_equations,[],[f53]) ).
fof(f55,definition,
sF13 = complement(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f56,plain,
complement(sF12) = sF13,
inference(reorient_equations,[],[f55]) ).
fof(f57,definition,
sF14 = join(sF13,sF4),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f58,plain,
join(sF13,sF4) = sF14,
inference(reorient_equations,[],[f57]) ).
fof(f59,definition,
sF15 = complement(sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f60,plain,
complement(sF14) = sF15,
inference(reorient_equations,[],[f59]) ).
fof(f61,plain,
sF6 != sF15,
inference(definition_folding,[],[f28,f60,f58,f38,f36,f34,f56,f54,f52,f50,f48,f46,f44,f42,f40,f38,f36,f34,f32,f30]) ).
fof(f62,plain,
zero = complement(top),
inference(backward_demodulation,[],[f24,f15]) ).
fof(f63,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f66,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f67,plain,
sF5 = join(sF4,sF1),
inference(forward_demodulation,[],[f40,f1]) ).
fof(f68,plain,
sF14 = join(sF4,sF13),
inference(forward_demodulation,[],[f58,f1]) ).
fof(f149,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f63,f1]) ).
fof(f161,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f63,f15]) ).
fof(f162,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f161,f62]) ).
fof(f200,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f63]) ).
fof(f211,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f244,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)),
inference(superposition,[],[f200,f15]) ).
fof(f260,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f244,f211]) ).
fof(f276,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(join(complement(X0),complement(X0))))),
inference(forward_demodulation,[],[f260,f62]) ).
fof(f392,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f394,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(f402,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f394,f12]) ).
fof(f410,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f402,f11]) ).
fof(f413,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f410,f11]) ).
fof(f415,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f413,f12]) ).
fof(f428,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f415]) ).
fof(f439,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f428,f10]) ).
fof(f461,plain,
! [X0] : composition(sk1,join(X0,sF11)) = join(composition(sk1,X0),sF12),
inference(superposition,[],[f439,f54]) ).
fof(f462,plain,
! [X0] : composition(sk1,join(X0,sk2)) = join(composition(sk1,X0),sF0),
inference(superposition,[],[f439,f30]) ).
fof(f475,plain,
! [X0] : join(sF0,composition(sk1,X0)) = composition(sk1,join(X0,sk2)),
inference(forward_demodulation,[],[f462,f1]) ).
fof(f476,plain,
! [X0] : join(sF12,composition(sk1,X0)) = composition(sk1,join(X0,sF11)),
inference(forward_demodulation,[],[f461,f1]) ).
fof(f528,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f149,f15]) ).
fof(f531,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(superposition,[],[f200,f149]) ).
fof(f543,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(complement(complement(X1)),complement(X0)))),
inference(forward_demodulation,[],[f531,f1]) ).
fof(f544,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f528,f1]) ).
fof(f574,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f544,f1]) ).
fof(f590,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f574,f62]) ).
fof(f601,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f162,f590]) ).
fof(f611,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,complement(join(X1,complement(X0)))),
inference(backward_demodulation,[],[f543,f601]) ).
fof(f612,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f590,f601]) ).
fof(f631,plain,
! [X0,X1] : join(complement(X0),X1) = join(zero,join(complement(join(X0,X0)),X1)),
inference(superposition,[],[f2,f612]) ).
fof(f635,plain,
sk2 = complement(sF7),
inference(superposition,[],[f601,f44]) ).
fof(f636,plain,
sk3 = complement(sF8),
inference(superposition,[],[f601,f46]) ).
fof(f638,plain,
sF2 = complement(sF3),
inference(superposition,[],[f601,f36]) ).
fof(f646,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f63,f601]) ).
fof(f650,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f149,f601]) ).
fof(f682,plain,
sF2 = sF4,
inference(forward_demodulation,[],[f638,f38]) ).
fof(f683,plain,
sk3 = sF9,
inference(forward_demodulation,[],[f636,f48]) ).
fof(f690,plain,
composition(sk1,sk3) = sF4,
inference(backward_demodulation,[],[f34,f682]) ).
fof(f713,plain,
sF4 = composition(sk1,sF9),
inference(forward_demodulation,[],[f690,f683]) ).
fof(f715,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f646,f1]) ).
fof(f823,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,[],[f646,f650]) ).
fof(f824,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,[],[f823,f601]) ).
fof(f847,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,[],[f824,f211]) ).
fof(f862,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,[],[f847,f1]) ).
fof(f875,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f862,f601]) ).
fof(f885,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f875,f601]) ).
fof(f918,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(join(X0,X0)),complement(zero)))),
inference(superposition,[],[f715,f612]) ).
fof(f939,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,[],[f650,f715]) ).
fof(f951,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,[],[f939,f1]) ).
fof(f961,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(zero),complement(join(X0,X0))))),
inference(forward_demodulation,[],[f918,f1]) ).
fof(f973,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,[],[f951,f1]) ).
fof(f982,plain,
! [X0] : complement(complement(join(X0,X0))) = join(X0,complement(join(complement(zero),complement(join(X0,X0))))),
inference(forward_demodulation,[],[f961,f601]) ).
fof(f990,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,[],[f973,f2]) ).
fof(f998,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(complement(zero),complement(join(X0,X0))))),
inference(forward_demodulation,[],[f982,f601]) ).
fof(f1005,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f990,f601]) ).
fof(f1016,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f1005,f601]) ).
fof(f1043,plain,
top = complement(zero),
inference(superposition,[],[f601,f62]) ).
fof(f1047,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(backward_demodulation,[],[f998,f1043]) ).
fof(f1231,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f392,f8]) ).
fof(f1247,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f1231,f10]) ).
fof(f1262,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f66,f1247]) ).
fof(f1273,plain,
one = converse(one),
inference(superposition,[],[f8,f1247]) ).
fof(f1278,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f1247,f1273]) ).
fof(f1289,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f1262,f1278]) ).
fof(f1297,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,complement(complement(X0)))),
inference(backward_demodulation,[],[f276,f1289]) ).
fof(f1299,plain,
! [X0,X1] : join(X0,X1) = join(zero,join(X1,X0)),
inference(forward_demodulation,[],[f1297,f601]) ).
fof(f1302,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X0))),
inference(backward_demodulation,[],[f631,f1299]) ).
fof(f1303,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(complement(X0),top))),
inference(backward_demodulation,[],[f1047,f1302]) ).
fof(f1304,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[],[f612,f1302]) ).
fof(f1306,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f1304,f1]) ).
fof(f1307,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(X0)))),
inference(forward_demodulation,[],[f1303,f611]) ).
fof(f1355,plain,
! [X0] : complement(complement(X0)) = join(complement(complement(X0)),complement(join(complement(X0),complement(zero)))),
inference(superposition,[],[f715,f1306]) ).
fof(f1356,plain,
! [X0] : complement(complement(X0)) = join(complement(complement(X0)),complement(join(complement(X0),top))),
inference(forward_demodulation,[],[f1355,f1043]) ).
fof(f1374,plain,
! [X0] : complement(complement(X0)) = join(complement(complement(X0)),complement(join(top,complement(X0)))),
inference(forward_demodulation,[],[f1356,f1]) ).
fof(f1381,plain,
! [X0] : join(X0,complement(join(top,complement(X0)))) = X0,
inference(forward_demodulation,[],[f1374,f601]) ).
fof(f1385,plain,
! [X0] : join(X0,X0) = X0,
inference(backward_demodulation,[],[f1307,f1381]) ).
fof(f1400,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f1385]) ).
fof(f1402,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f211,f1385]) ).
fof(f1523,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f1400,f715]) ).
fof(f1565,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1523,f1]) ).
fof(f1580,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f885,f1565]) ).
fof(f1587,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f1016,f1580]) ).
fof(f1590,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1587,f1402]) ).
fof(f1607,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1590,f1]) ).
fof(f1748,plain,
join(sF9,complement(sF7)) = join(sF9,complement(sF10)),
inference(superposition,[],[f1607,f50]) ).
fof(f1783,plain,
join(sF9,complement(sF7)) = join(sF9,sF11),
inference(forward_demodulation,[],[f1748,f52]) ).
fof(f1807,plain,
join(sF9,sk2) = join(sF9,sF11),
inference(forward_demodulation,[],[f1783,f635]) ).
fof(f2789,plain,
join(sF0,composition(sk1,sF9)) = composition(sk1,join(sF9,sF11)),
inference(superposition,[],[f475,f1807]) ).
fof(f2809,plain,
join(sF0,composition(sk1,sF9)) = join(sF12,composition(sk1,sF9)),
inference(forward_demodulation,[],[f2789,f476]) ).
fof(f2816,plain,
join(sF0,sF4) = join(sF12,sF4),
inference(forward_demodulation,[],[f2809,f713]) ).
fof(f2822,plain,
join(sF4,sF12) = join(sF0,sF4),
inference(forward_demodulation,[],[f2816,f1]) ).
fof(f2828,plain,
join(sF4,sF12) = join(sF4,sF0),
inference(forward_demodulation,[],[f2822,f1]) ).
fof(f2853,plain,
join(sF4,complement(join(sF4,sF0))) = join(sF4,complement(sF12)),
inference(superposition,[],[f1590,f2828]) ).
fof(f2856,plain,
join(sF4,sF13) = join(sF4,complement(join(sF4,sF0))),
inference(forward_demodulation,[],[f2853,f56]) ).
fof(f2864,plain,
join(sF4,sF13) = join(sF4,complement(sF0)),
inference(forward_demodulation,[],[f2856,f1590]) ).
fof(f2869,plain,
join(sF4,sF1) = join(sF4,sF13),
inference(forward_demodulation,[],[f2864,f32]) ).
fof(f2873,plain,
sF14 = join(sF4,sF1),
inference(forward_demodulation,[],[f2869,f68]) ).
fof(f2876,plain,
sF5 = sF14,
inference(forward_demodulation,[],[f2873,f67]) ).
fof(f2879,plain,
complement(sF5) = sF15,
inference(backward_demodulation,[],[f60,f2876]) ).
fof(f2907,plain,
sF6 = sF15,
inference(forward_demodulation,[],[f2879,f42]) ).
fof(f2908,plain,
$false,
inference(forward_subsumption_resolution,[],[f2907,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL016-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n019.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 22:51:34 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 8.24/2.15 % (3492497)Detected a unit-equality problem, will run specialized UEQ schedule.
% 8.24/2.15 % (3492502)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=2593833170:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 8.24/2.15 % (3492508)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=894769577:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 8.24/2.15 % (3492505)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3052335239:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 8.24/2.15 % (3492504)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1558830064:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 8.24/2.15 % (3492503)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=1398757606:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 8.24/2.15 % (3492506)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2118295636:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 8.24/2.15 % (3492507)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1443650646:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 8.24/2.15 % (3492505)Instruction limit reached!
% 8.24/2.15 % (3492505)------------------------------
% 8.24/2.15 % (3492505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.15 % (3492505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.15 % (3492505)CaDiCaL version: 2.1.3
% 8.24/2.15 % (3492505)Termination reason: Instruction limit
% 8.24/2.15 % (3492505)Termination phase: Saturation
% 8.24/2.15 % (3492505)Time elapsed: 0.082 s
% 8.24/2.15 % (3492505)Peak memory usage: 89 MB
% 8.24/2.15 % (3492505)Instructions burned: 137 (million)
% 8.24/2.15 % (3492506)Instruction limit reached!
% 8.24/2.15 % (3492506)------------------------------
% 8.24/2.15 % (3492506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.15 % (3492506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.15 % (3492506)CaDiCaL version: 2.1.3
% 8.24/2.15 % (3492506)Termination reason: Instruction limit
% 8.24/2.15 % (3492506)Termination phase: Saturation
% 8.24/2.15 % (3492506)Time elapsed: 0.101 s
% 8.24/2.15 % (3492506)Peak memory usage: 89 MB
% 8.24/2.15 % (3492506)Instructions burned: 181 (million)
% 8.24/2.15 % (3492507)Instruction limit reached!
% 8.24/2.15 % (3492507)------------------------------
% 8.24/2.15 % (3492507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.15 % (3492507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.15 % (3492507)CaDiCaL version: 2.1.3
% 8.24/2.15 % (3492507)Termination reason: Instruction limit
% 8.24/2.15 % (3492507)Termination phase: Saturation
% 8.24/2.15 % (3492507)Time elapsed: 0.167 s
% 8.24/2.15 % (3492507)Peak memory usage: 91 MB
% 8.24/2.15 % (3492507)Instructions burned: 257 (million)
% 8.24/2.15 % (3492516)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=467179088:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 8.24/2.15 % (3492517)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4031501198:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 8.24/2.15 % (3492518)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2621340906:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 8.24/2.15 % (3492518)Instruction limit reached!
% 8.24/2.15 % (3492518)------------------------------
% 8.24/2.15 % (3492518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.15 % (3492518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.15 % (3492518)CaDiCaL version: 2.1.3
% 8.24/2.15 % (3492518)Termination reason: Instruction limit
% 8.24/2.15 % (3492518)Termination phase: Saturation
% 8.24/2.15 % (3492518)Time elapsed: 0.112 s
% 8.24/2.15 % (3492518)Peak memory usage: 89 MB
% 8.24/2.15 % (3492518)Instructions burned: 216 (million)
% 8.24/2.15 % (3492522)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=1084965939:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 8.24/2.15 % (3492508)Instruction limit reached!
% 8.24/2.15 % (3492508)------------------------------
% 8.24/2.15 % (3492508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.15 % (3492508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.15 % (3492508)CaDiCaL version: 2.1.3
% 8.24/2.15 % (3492508)Termination reason: Instruction limit
% 8.24/2.15 % (3492508)Termination phase: Saturation
% 8.24/2.15 % (3492508)Time elapsed: 0.658 s
% 8.24/2.15 % (3492508)Peak memory usage: 101 MB
% 8.24/2.15 % (3492508)Instructions burned: 1188 (million)
% 8.24/2.15 % (3492522)Instruction limit reached!
% 8.24/2.15 % (3492522)------------------------------
% 8.24/2.15 % (3492522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.15 % (3492522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.15 % (3492522)CaDiCaL version: 2.1.3
% 8.24/2.15 % (3492522)Termination reason: Instruction limit
% 8.24/2.15 % (3492522)Termination phase: Saturation
% 8.24/2.15 % (3492522)Time elapsed: 0.200 s
% 8.24/2.15 % (3492522)Peak memory usage: 94 MB
% 8.24/2.15 % (3492522)Instructions burned: 317 (million)
% 8.24/2.15 % (3492524)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=1071295046:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 8.24/2.15 % (3492525)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=489911186:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 8.24/2.15 % (3492504)First to succeed.
% 8.24/2.15 % (3492504)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3492497"
% 8.24/2.15 % (3492504)Refutation found. Thanks to Tanya!
% 8.24/2.15 % SZS status Unsatisfiable for theBenchmark
% 8.24/2.15 % SZS output start Proof for theBenchmark
% See solution above
% 9.75/2.25 % (3492504)------------------------------
% 9.75/2.25 % (3492504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.75/2.25 % (3492504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.75/2.25 % (3492504)CaDiCaL version: 2.1.3
% 9.75/2.25 % (3492504)Termination reason: Refutation
% 9.75/2.25 % (3492504)Time elapsed: 0.914 s
% 9.75/2.25 % (3492504)Peak memory usage: 133 MB
% 9.75/2.25 % (3492504)Instructions burned: 1424 (million)
% 9.75/2.25 % (3492504)------------------------------
% 9.75/2.25 % (3492504)------------------------------
% 9.75/2.25 % (3492497)Success in time 1.313 s
% 9.75/2.25 % Vampire exiting
%------------------------------------------------------------------------------