TSTP Solution File: REL044-2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : REL044-2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:48:16 EDT 2024
% Result : Unsatisfiable 34.31s 5.29s
% Output : Refutation 34.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 17
% Syntax : Number of formulae : 322 ( 322 unt; 0 def)
% Number of atoms : 322 ( 321 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 357 ( 357 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f213787,plain,
$false,
inference(trivial_inequality_removal,[],[f213686]) ).
fof(f213686,plain,
sk1 != sk1,
inference(superposition,[],[f22,f213493]) ).
fof(f213493,plain,
sk1 = join(sk1,composition(sk3,converse(sk2))),
inference(forward_demodulation,[],[f213332,f7480]) ).
fof(f7480,plain,
! [X0] : join(X0,zero) = X0,
inference(forward_demodulation,[],[f7324,f7306]) ).
fof(f7306,plain,
! [X0] : join(meet(zero,complement(sk3)),X0) = X0,
inference(backward_demodulation,[],[f2925,f7279]) ).
fof(f7279,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f2203,f326]) ).
fof(f326,plain,
! [X0] : join(zero,meet(X0,X0)) = X0,
inference(forward_demodulation,[],[f304,f4]) ).
fof(f4,axiom,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f304,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[],[f19,f13]) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
fof(f19,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f3,f4]) ).
fof(f3,axiom,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f2203,plain,
! [X0] : join(zero,X0) = join(zero,join(zero,X0)),
inference(superposition,[],[f2,f2037]) ).
fof(f2037,plain,
zero = join(zero,zero),
inference(forward_demodulation,[],[f2036,f33]) ).
fof(f33,plain,
zero = complement(top),
inference(forward_demodulation,[],[f28,f13]) ).
fof(f28,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(superposition,[],[f4,f12]) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
fof(f2036,plain,
zero = join(zero,complement(top)),
inference(backward_demodulation,[],[f1997,f2035]) ).
fof(f2035,plain,
top = join(sk3,complement(zero)),
inference(forward_demodulation,[],[f1890,f33]) ).
fof(f1890,plain,
top = join(sk3,complement(complement(top))),
inference(backward_demodulation,[],[f1688,f1834]) ).
fof(f1834,plain,
top = join(top,complement(sk3)),
inference(forward_demodulation,[],[f1829,f12]) ).
fof(f1829,plain,
join(complement(sk3),complement(complement(sk3))) = join(top,complement(sk3)),
inference(backward_demodulation,[],[f418,f1818]) ).
fof(f1818,plain,
complement(complement(sk3)) = meet(sk3,join(top,complement(sk3))),
inference(backward_demodulation,[],[f485,f1815]) ).
fof(f1815,plain,
join(top,complement(sk3)) = join(top,join(top,top)),
inference(forward_demodulation,[],[f1745,f1680]) ).
fof(f1680,plain,
! [X0] : join(top,X0) = join(sk3,join(top,X0)),
inference(backward_demodulation,[],[f1294,f1665]) ).
fof(f1665,plain,
! [X0] : join(top,X0) = join(complement(complement(sk3)),join(top,X0)),
inference(superposition,[],[f1620,f1293]) ).
fof(f1293,plain,
! [X0] : join(top,X0) = join(sk3,join(complement(complement(complement(sk3))),X0)),
inference(superposition,[],[f2,f1275]) ).
fof(f1275,plain,
top = join(sk3,complement(complement(complement(sk3)))),
inference(backward_demodulation,[],[f874,f1274]) ).
fof(f1274,plain,
top = join(complement(join(top,complement(sk3))),top),
inference(forward_demodulation,[],[f1260,f12]) ).
fof(f1260,plain,
join(sk3,complement(sk3)) = join(complement(join(top,complement(sk3))),top),
inference(superposition,[],[f870,f12]) ).
fof(f870,plain,
! [X0] : join(sk3,X0) = join(complement(join(top,complement(sk3))),join(X0,complement(complement(sk3)))),
inference(superposition,[],[f380,f1]) ).
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f380,plain,
! [X0] : join(sk3,X0) = join(complement(join(top,complement(sk3))),join(complement(complement(sk3)),X0)),
inference(backward_demodulation,[],[f353,f374]) ).
fof(f374,plain,
meet(sk3,composition(complement(sk1),sk2)) = complement(join(top,complement(sk3))),
inference(superposition,[],[f4,f369]) ).
fof(f369,plain,
join(top,complement(sk3)) = join(complement(sk3),complement(composition(complement(sk1),sk2))),
inference(forward_demodulation,[],[f364,f1]) ).
fof(f364,plain,
join(complement(sk3),top) = join(complement(sk3),complement(composition(complement(sk1),sk2))),
inference(superposition,[],[f156,f12]) ).
fof(f156,plain,
! [X0] : join(complement(sk3),X0) = join(complement(sk3),join(composition(complement(sk1),sk2),X0)),
inference(superposition,[],[f2,f20]) ).
fof(f20,plain,
complement(sk3) = join(complement(sk3),composition(complement(sk1),sk2)),
inference(superposition,[],[f1,f17]) ).
fof(f17,axiom,
complement(sk3) = join(composition(complement(sk1),sk2),complement(sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f353,plain,
! [X0] : join(meet(sk3,composition(complement(sk1),sk2)),join(complement(complement(sk3)),X0)) = join(sk3,X0),
inference(superposition,[],[f2,f321]) ).
fof(f321,plain,
sk3 = join(meet(sk3,composition(complement(sk1),sk2)),complement(complement(sk3))),
inference(superposition,[],[f19,f20]) ).
fof(f874,plain,
join(sk3,complement(complement(complement(sk3)))) = join(complement(join(top,complement(sk3))),top),
inference(superposition,[],[f380,f12]) ).
fof(f1620,plain,
! [X0] : join(sk3,X0) = join(complement(complement(sk3)),join(sk3,X0)),
inference(backward_demodulation,[],[f929,f1619]) ).
fof(f1619,plain,
! [X0] : join(sk3,X0) = join(sk3,join(complement(complement(sk3)),X0)),
inference(superposition,[],[f2,f1527]) ).
fof(f1527,plain,
sk3 = join(sk3,complement(complement(sk3))),
inference(forward_demodulation,[],[f1487,f1509]) ).
fof(f1509,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f1455,f1481]) ).
fof(f1481,plain,
one = converse(one),
inference(superposition,[],[f1455,f6]) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f1455,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f1427,f8]) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f1427,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f79,f6]) ).
fof(f79,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f10,f8]) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f1487,plain,
sk3 = join(sk3,complement(composition(one,complement(sk3)))),
inference(superposition,[],[f1290,f1455]) ).
fof(f1290,plain,
! [X0] : sk3 = join(sk3,composition(converse(X0),complement(composition(X0,complement(sk3))))),
inference(forward_demodulation,[],[f1263,f382]) ).
fof(f382,plain,
sk3 = join(complement(join(top,complement(sk3))),complement(complement(sk3))),
inference(backward_demodulation,[],[f321,f374]) ).
fof(f1263,plain,
! [X0] : join(complement(join(top,complement(sk3))),complement(complement(sk3))) = join(sk3,composition(converse(X0),complement(composition(X0,complement(sk3))))),
inference(superposition,[],[f870,f11]) ).
fof(f11,axiom,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f929,plain,
! [X0] : join(sk3,join(complement(complement(sk3)),X0)) = join(complement(complement(sk3)),join(sk3,X0)),
inference(superposition,[],[f378,f380]) ).
fof(f378,plain,
! [X0] : join(sk3,X0) = join(complement(complement(sk3)),join(complement(join(top,complement(sk3))),X0)),
inference(backward_demodulation,[],[f357,f374]) ).
fof(f357,plain,
! [X0] : join(sk3,X0) = join(complement(complement(sk3)),join(meet(sk3,composition(complement(sk1),sk2)),X0)),
inference(superposition,[],[f2,f351]) ).
fof(f351,plain,
sk3 = join(complement(complement(sk3)),meet(sk3,composition(complement(sk1),sk2))),
inference(superposition,[],[f321,f1]) ).
fof(f1294,plain,
! [X0] : join(sk3,join(top,X0)) = join(complement(complement(sk3)),join(top,X0)),
inference(backward_demodulation,[],[f945,f1293]) ).
fof(f945,plain,
! [X0] : join(sk3,join(top,X0)) = join(complement(complement(sk3)),join(sk3,join(complement(complement(complement(sk3))),X0))),
inference(forward_demodulation,[],[f944,f2]) ).
fof(f944,plain,
! [X0] : join(complement(complement(sk3)),join(join(sk3,complement(complement(complement(sk3)))),X0)) = join(sk3,join(top,X0)),
inference(forward_demodulation,[],[f943,f2]) ).
fof(f943,plain,
! [X0] : join(complement(complement(sk3)),join(join(sk3,complement(complement(complement(sk3)))),X0)) = join(join(sk3,top),X0),
inference(superposition,[],[f2,f933]) ).
fof(f933,plain,
join(sk3,top) = join(complement(complement(sk3)),join(sk3,complement(complement(complement(sk3))))),
inference(superposition,[],[f378,f874]) ).
fof(f1745,plain,
join(top,join(top,top)) = join(sk3,join(top,complement(sk3))),
inference(superposition,[],[f154,f821]) ).
fof(f821,plain,
join(top,complement(sk3)) = join(complement(sk3),join(top,top)),
inference(forward_demodulation,[],[f811,f1]) ).
fof(f811,plain,
join(complement(sk3),top) = join(complement(sk3),join(top,top)),
inference(superposition,[],[f643,f12]) ).
fof(f643,plain,
! [X0] : join(complement(sk3),X0) = join(complement(sk3),join(X0,complement(join(top,top)))),
inference(superposition,[],[f423,f1]) ).
fof(f423,plain,
! [X0] : join(complement(sk3),X0) = join(complement(sk3),join(complement(join(top,top)),X0)),
inference(superposition,[],[f2,f411]) ).
fof(f411,plain,
complement(sk3) = join(complement(sk3),complement(join(top,top))),
inference(forward_demodulation,[],[f410,f154]) ).
fof(f410,plain,
complement(sk3) = join(complement(sk3),complement(join(complement(sk3),join(complement(complement(sk3)),top)))),
inference(forward_demodulation,[],[f409,f160]) ).
fof(f160,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f409,plain,
complement(sk3) = join(complement(sk3),complement(join(complement(complement(sk3)),join(top,complement(sk3))))),
inference(superposition,[],[f19,f402]) ).
fof(f402,plain,
complement(sk3) = meet(complement(sk3),join(top,complement(sk3))),
inference(superposition,[],[f29,f382]) ).
fof(f29,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(superposition,[],[f4,f1]) ).
fof(f154,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f12]) ).
fof(f485,plain,
complement(complement(sk3)) = meet(sk3,join(top,join(top,top))),
inference(superposition,[],[f4,f483]) ).
fof(f483,plain,
complement(sk3) = join(complement(sk3),complement(join(top,join(top,top)))),
inference(forward_demodulation,[],[f482,f12]) ).
fof(f482,plain,
complement(sk3) = join(complement(sk3),complement(join(top,join(top,join(complement(sk3),complement(complement(sk3))))))),
inference(forward_demodulation,[],[f481,f2]) ).
fof(f481,plain,
complement(sk3) = join(complement(sk3),complement(join(top,join(join(top,complement(sk3)),complement(complement(sk3)))))),
inference(forward_demodulation,[],[f480,f160]) ).
fof(f480,plain,
complement(sk3) = join(complement(sk3),complement(join(complement(complement(sk3)),join(top,join(top,complement(sk3)))))),
inference(superposition,[],[f19,f470]) ).
fof(f470,plain,
complement(sk3) = meet(complement(sk3),join(top,join(top,complement(sk3)))),
inference(superposition,[],[f4,f432]) ).
fof(f432,plain,
sk3 = join(complement(complement(sk3)),complement(join(top,join(top,complement(sk3))))),
inference(forward_demodulation,[],[f431,f160]) ).
fof(f431,plain,
sk3 = join(complement(complement(sk3)),complement(join(top,join(complement(sk3),top)))),
inference(forward_demodulation,[],[f430,f160]) ).
fof(f430,plain,
sk3 = join(complement(complement(sk3)),complement(join(complement(sk3),join(top,top)))),
inference(superposition,[],[f19,f420]) ).
fof(f420,plain,
complement(complement(sk3)) = meet(sk3,join(top,top)),
inference(superposition,[],[f4,f411]) ).
fof(f418,plain,
join(top,complement(sk3)) = join(complement(sk3),meet(sk3,join(top,complement(sk3)))),
inference(forward_demodulation,[],[f417,f95]) ).
fof(f95,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(superposition,[],[f29,f4]) ).
fof(f417,plain,
join(top,complement(sk3)) = join(complement(sk3),meet(join(top,complement(sk3)),sk3)),
inference(forward_demodulation,[],[f414,f4]) ).
fof(f414,plain,
join(top,complement(sk3)) = join(complement(sk3),complement(join(complement(join(top,complement(sk3))),complement(sk3)))),
inference(superposition,[],[f19,f403]) ).
fof(f403,plain,
complement(sk3) = meet(join(top,complement(sk3)),complement(sk3)),
inference(superposition,[],[f4,f382]) ).
fof(f1688,plain,
top = join(sk3,complement(complement(join(top,complement(sk3))))),
inference(backward_demodulation,[],[f1374,f1684]) ).
fof(f1684,plain,
top = join(sk3,top),
inference(backward_demodulation,[],[f1281,f1666]) ).
fof(f1666,plain,
top = join(complement(complement(sk3)),top),
inference(superposition,[],[f1620,f1275]) ).
fof(f1281,plain,
join(complement(complement(sk3)),top) = join(sk3,top),
inference(backward_demodulation,[],[f933,f1275]) ).
fof(f1374,plain,
join(sk3,complement(complement(join(top,complement(sk3))))) = join(sk3,top),
inference(backward_demodulation,[],[f937,f1361]) ).
fof(f1361,plain,
join(sk3,top) = join(top,complement(complement(sk3))),
inference(superposition,[],[f1281,f1]) ).
fof(f937,plain,
join(sk3,complement(complement(join(top,complement(sk3))))) = join(top,complement(complement(sk3))),
inference(forward_demodulation,[],[f931,f1]) ).
fof(f931,plain,
join(complement(complement(sk3)),top) = join(sk3,complement(complement(join(top,complement(sk3))))),
inference(superposition,[],[f378,f12]) ).
fof(f1997,plain,
zero = join(zero,complement(join(sk3,complement(zero)))),
inference(forward_demodulation,[],[f1996,f33]) ).
fof(f1996,plain,
complement(top) = join(complement(top),complement(join(sk3,complement(complement(top))))),
inference(forward_demodulation,[],[f1863,f1912]) ).
fof(f1912,plain,
top = join(top,top),
inference(forward_demodulation,[],[f1911,f12]) ).
fof(f1911,plain,
join(complement(sk3),complement(complement(sk3))) = join(top,top),
inference(forward_demodulation,[],[f1853,f420]) ).
fof(f1853,plain,
join(top,top) = join(complement(sk3),meet(sk3,join(top,top))),
inference(backward_demodulation,[],[f479,f1834]) ).
fof(f479,plain,
join(top,join(top,complement(sk3))) = join(complement(sk3),meet(sk3,join(top,join(top,complement(sk3))))),
inference(forward_demodulation,[],[f478,f95]) ).
fof(f478,plain,
join(top,join(top,complement(sk3))) = join(complement(sk3),meet(join(top,join(top,complement(sk3))),sk3)),
inference(forward_demodulation,[],[f475,f4]) ).
fof(f475,plain,
join(top,join(top,complement(sk3))) = join(complement(sk3),complement(join(complement(join(top,join(top,complement(sk3)))),complement(sk3)))),
inference(superposition,[],[f19,f469]) ).
fof(f469,plain,
complement(sk3) = meet(join(top,join(top,complement(sk3))),complement(sk3)),
inference(superposition,[],[f29,f432]) ).
fof(f1863,plain,
complement(join(top,top)) = join(complement(top),complement(join(sk3,complement(complement(join(top,top)))))),
inference(backward_demodulation,[],[f674,f1834]) ).
fof(f674,plain,
complement(join(top,top)) = join(complement(join(top,complement(sk3))),complement(join(sk3,complement(complement(join(top,top)))))),
inference(forward_demodulation,[],[f671,f1]) ).
fof(f671,plain,
complement(join(top,top)) = join(complement(join(top,complement(sk3))),complement(join(complement(complement(join(top,top))),sk3))),
inference(superposition,[],[f19,f658]) ).
fof(f658,plain,
complement(join(top,complement(sk3))) = meet(complement(join(top,top)),sk3),
inference(superposition,[],[f29,f652]) ).
fof(f652,plain,
join(top,complement(sk3)) = join(complement(sk3),complement(complement(join(top,top)))),
inference(forward_demodulation,[],[f645,f1]) ).
fof(f645,plain,
join(complement(sk3),top) = join(complement(sk3),complement(complement(join(top,top)))),
inference(superposition,[],[f423,f12]) ).
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(f2925,plain,
! [X0] : join(zero,X0) = join(meet(zero,complement(sk3)),join(zero,X0)),
inference(superposition,[],[f2,f2551]) ).
fof(f2551,plain,
zero = join(meet(zero,complement(sk3)),zero),
inference(superposition,[],[f324,f1990]) ).
fof(f1990,plain,
zero = meet(zero,sk3),
inference(forward_demodulation,[],[f1989,f33]) ).
fof(f1989,plain,
complement(top) = meet(complement(top),sk3),
inference(forward_demodulation,[],[f1860,f1912]) ).
fof(f1860,plain,
complement(top) = meet(complement(join(top,top)),sk3),
inference(backward_demodulation,[],[f658,f1834]) ).
fof(f324,plain,
! [X0,X1] : join(meet(X0,complement(X1)),meet(X0,X1)) = X0,
inference(superposition,[],[f19,f4]) ).
fof(f7324,plain,
! [X0] : join(X0,zero) = join(meet(zero,complement(sk3)),X0),
inference(backward_demodulation,[],[f5149,f7279]) ).
fof(f5149,plain,
! [X0] : join(X0,zero) = join(meet(zero,complement(sk3)),join(zero,X0)),
inference(superposition,[],[f160,f2551]) ).
fof(f213332,plain,
join(sk1,composition(sk3,converse(sk2))) = join(sk1,zero),
inference(superposition,[],[f160381,f213044]) ).
fof(f213044,plain,
zero = meet(composition(sk3,converse(sk2)),complement(sk1)),
inference(superposition,[],[f68054,f144269]) ).
fof(f144269,plain,
! [X0,X1] : meet(X1,X0) = join(meet(X0,X1),zero),
inference(backward_demodulation,[],[f4060,f144268]) ).
fof(f144268,plain,
! [X0,X1] : meet(X1,X0) = meet(meet(X0,X1),meet(X1,X0)),
inference(forward_demodulation,[],[f144056,f2560]) ).
fof(f2560,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f2559,f893]) ).
fof(f893,plain,
! [X0] : join(zero,meet(X0,complement(complement(X0)))) = X0,
inference(superposition,[],[f338,f1]) ).
fof(f338,plain,
! [X0] : join(meet(X0,complement(complement(X0))),zero) = X0,
inference(forward_demodulation,[],[f320,f33]) ).
fof(f320,plain,
! [X0] : join(meet(X0,complement(complement(X0))),complement(top)) = X0,
inference(superposition,[],[f19,f12]) ).
fof(f2559,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[],[f2540,f95]) ).
fof(f2540,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(superposition,[],[f324,f104]) ).
fof(f104,plain,
! [X0] : zero = meet(complement(X0),X0),
inference(forward_demodulation,[],[f92,f33]) ).
fof(f92,plain,
! [X0] : complement(top) = meet(complement(X0),X0),
inference(superposition,[],[f29,f12]) ).
fof(f144056,plain,
! [X0,X1] : meet(X1,X0) = meet(complement(complement(meet(X0,X1))),meet(X1,X0)),
inference(backward_demodulation,[],[f142276,f143872]) ).
fof(f143872,plain,
! [X0] : complement(X0) = converse(complement(converse(X0))),
inference(forward_demodulation,[],[f143862,f7279]) ).
fof(f143862,plain,
! [X0] : join(zero,complement(X0)) = converse(complement(converse(X0))),
inference(backward_demodulation,[],[f139382,f143705]) ).
fof(f143705,plain,
! [X0] : zero = meet(X0,converse(complement(converse(X0)))),
inference(superposition,[],[f143288,f8]) ).
fof(f143288,plain,
! [X0] : zero = meet(converse(X0),converse(complement(X0))),
inference(forward_demodulation,[],[f143287,f9792]) ).
fof(f9792,plain,
! [X0] : zero = meet(X0,zero),
inference(forward_demodulation,[],[f9773,f33]) ).
fof(f9773,plain,
! [X0] : complement(top) = meet(X0,zero),
inference(superposition,[],[f3056,f9674]) ).
fof(f9674,plain,
! [X0] : top = complement(meet(zero,X0)),
inference(superposition,[],[f9636,f2560]) ).
fof(f9636,plain,
! [X0] : top = complement(meet(zero,complement(X0))),
inference(forward_demodulation,[],[f9633,f12]) ).
fof(f9633,plain,
! [X0] : join(X0,complement(X0)) = complement(meet(zero,complement(X0))),
inference(backward_demodulation,[],[f9524,f9592]) ).
fof(f9592,plain,
! [X0] : join(X0,meet(zero,complement(X0))) = X0,
inference(superposition,[],[f9552,f1]) ).
fof(f9552,plain,
! [X0] : join(meet(zero,complement(X0)),X0) = X0,
inference(superposition,[],[f9349,f2560]) ).
fof(f9349,plain,
! [X0] : complement(X0) = join(meet(zero,X0),complement(X0)),
inference(forward_demodulation,[],[f9288,f7279]) ).
fof(f9288,plain,
! [X0] : join(zero,complement(X0)) = join(meet(zero,X0),complement(X0)),
inference(superposition,[],[f3134,f8268]) ).
fof(f8268,plain,
! [X0] : join(meet(zero,X0),X0) = X0,
inference(superposition,[],[f7522,f95]) ).
fof(f7522,plain,
! [X0] : join(meet(X0,zero),X0) = X0,
inference(backward_demodulation,[],[f4057,f7520]) ).
fof(f7520,plain,
! [X0] : meet(top,X0) = X0,
inference(forward_demodulation,[],[f7363,f2560]) ).
fof(f7363,plain,
! [X0] : complement(complement(X0)) = meet(top,X0),
inference(backward_demodulation,[],[f41,f7279]) ).
fof(f41,plain,
! [X0] : meet(top,X0) = complement(join(zero,complement(X0))),
inference(superposition,[],[f4,f33]) ).
fof(f4057,plain,
! [X0] : join(meet(X0,zero),meet(top,X0)) = X0,
inference(superposition,[],[f3131,f3038]) ).
fof(f3038,plain,
top = complement(zero),
inference(superposition,[],[f2560,f33]) ).
fof(f3131,plain,
! [X0,X1] : join(meet(X0,X1),meet(complement(X1),X0)) = X0,
inference(backward_demodulation,[],[f318,f3039]) ).
fof(f3039,plain,
! [X0,X1] : complement(join(X0,complement(X1))) = meet(complement(X0),X1),
inference(superposition,[],[f4,f2560]) ).
fof(f318,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(X1,complement(X0)))) = X0,
inference(superposition,[],[f19,f1]) ).
fof(f3134,plain,
! [X2,X0,X1] : join(X0,X2) = join(meet(X0,X1),join(meet(X0,complement(X1)),X2)),
inference(backward_demodulation,[],[f325,f3040]) ).
fof(f3040,plain,
! [X0,X1] : complement(join(complement(X1),X0)) = meet(X1,complement(X0)),
inference(superposition,[],[f4,f2560]) ).
fof(f325,plain,
! [X2,X0,X1] : join(X0,X2) = join(meet(X0,X1),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f2,f19]) ).
fof(f9524,plain,
! [X0] : complement(meet(zero,complement(X0))) = join(X0,complement(join(X0,meet(zero,complement(X0))))),
inference(forward_demodulation,[],[f9523,f95]) ).
fof(f9523,plain,
! [X0] : complement(meet(zero,complement(X0))) = join(X0,complement(join(X0,meet(complement(X0),zero)))),
inference(forward_demodulation,[],[f9488,f8712]) ).
fof(f8712,plain,
! [X2,X0,X1] : meet(complement(X0),complement(meet(X2,X1))) = complement(join(X0,meet(X1,X2))),
inference(superposition,[],[f3058,f2560]) ).
fof(f3058,plain,
! [X2,X0,X1] : complement(join(complement(X2),meet(X0,X1))) = meet(X2,complement(meet(X1,X0))),
inference(backward_demodulation,[],[f27,f3034]) ).
fof(f3034,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X1,X0)),
inference(superposition,[],[f2560,f29]) ).
fof(f27,plain,
! [X2,X0,X1] : meet(X2,join(complement(X0),complement(X1))) = complement(join(complement(X2),meet(X0,X1))),
inference(superposition,[],[f4,f4]) ).
fof(f9488,plain,
! [X0] : complement(meet(zero,complement(X0))) = join(X0,meet(complement(X0),complement(meet(zero,complement(X0))))),
inference(superposition,[],[f3131,f8533]) ).
fof(f8533,plain,
! [X0] : meet(complement(meet(zero,complement(X0))),X0) = X0,
inference(forward_demodulation,[],[f8484,f2560]) ).
fof(f8484,plain,
! [X0] : complement(complement(X0)) = meet(complement(meet(zero,complement(X0))),X0),
inference(superposition,[],[f3057,f7522]) ).
fof(f3057,plain,
! [X2,X0,X1] : complement(join(meet(X0,X1),complement(X2))) = meet(complement(meet(X1,X0)),X2),
inference(backward_demodulation,[],[f26,f3034]) ).
fof(f26,plain,
! [X2,X0,X1] : meet(join(complement(X0),complement(X1)),X2) = complement(join(meet(X0,X1),complement(X2))),
inference(superposition,[],[f4,f4]) ).
fof(f3056,plain,
! [X0,X1] : meet(X0,X1) = complement(complement(meet(X1,X0))),
inference(backward_demodulation,[],[f4,f3034]) ).
fof(f143287,plain,
! [X0] : meet(converse(X0),converse(complement(X0))) = meet(meet(converse(X0),converse(complement(X0))),zero),
inference(forward_demodulation,[],[f143286,f8083]) ).
fof(f8083,plain,
zero = converse(zero),
inference(forward_demodulation,[],[f8075,f33]) ).
fof(f8075,plain,
complement(top) = converse(zero),
inference(superposition,[],[f2560,f7922]) ).
fof(f7922,plain,
top = complement(converse(zero)),
inference(forward_demodulation,[],[f7892,f4313]) ).
fof(f4313,plain,
top = converse(top),
inference(backward_demodulation,[],[f4218,f4293]) ).
fof(f4293,plain,
top = join(top,converse(top)),
inference(superposition,[],[f4287,f1]) ).
fof(f4287,plain,
top = join(converse(top),top),
inference(forward_demodulation,[],[f4282,f8]) ).
fof(f4282,plain,
converse(converse(top)) = join(converse(top),top),
inference(superposition,[],[f35,f4218]) ).
fof(f35,plain,
! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[],[f9,f8]) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f4218,plain,
converse(top) = join(top,converse(top)),
inference(superposition,[],[f2199,f127]) ).
fof(f127,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f34,f12]) ).
fof(f34,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f9,f8]) ).
fof(f2199,plain,
! [X0] : join(top,X0) = join(top,join(top,X0)),
inference(superposition,[],[f2,f1912]) ).
fof(f7892,plain,
converse(top) = complement(converse(zero)),
inference(superposition,[],[f8,f7664]) ).
fof(f7664,plain,
top = converse(complement(converse(zero))),
inference(superposition,[],[f7480,f4823]) ).
fof(f4823,plain,
! [X0] : top = join(converse(complement(converse(X0))),X0),
inference(superposition,[],[f4784,f8]) ).
fof(f4784,plain,
! [X0] : top = join(converse(complement(X0)),converse(X0)),
inference(superposition,[],[f4315,f2560]) ).
fof(f4315,plain,
! [X0] : top = join(converse(X0),converse(complement(X0))),
inference(backward_demodulation,[],[f140,f4313]) ).
fof(f140,plain,
! [X0] : converse(top) = join(converse(X0),converse(complement(X0))),
inference(superposition,[],[f127,f8]) ).
fof(f143286,plain,
! [X0] : meet(converse(X0),converse(complement(X0))) = meet(meet(converse(X0),converse(complement(X0))),converse(zero)),
inference(forward_demodulation,[],[f143093,f33]) ).
fof(f143093,plain,
! [X0] : meet(converse(X0),converse(complement(X0))) = meet(meet(converse(X0),converse(complement(X0))),converse(complement(top))),
inference(superposition,[],[f138941,f142186]) ).
fof(f142186,plain,
! [X0] : top = converse(complement(meet(converse(X0),converse(complement(X0))))),
inference(forward_demodulation,[],[f142185,f4313]) ).
fof(f142185,plain,
! [X0] : converse(top) = converse(complement(meet(converse(X0),converse(complement(X0))))),
inference(forward_demodulation,[],[f142184,f3265]) ).
fof(f3265,plain,
! [X0,X1] : complement(meet(X1,X0)) = complement(meet(X0,X1)),
inference(superposition,[],[f2560,f3056]) ).
fof(f142184,plain,
! [X0] : converse(top) = converse(complement(meet(converse(complement(X0)),converse(X0)))),
inference(forward_demodulation,[],[f142046,f3034]) ).
fof(f142046,plain,
! [X0] : converse(top) = converse(join(complement(converse(X0)),complement(converse(complement(X0))))),
inference(superposition,[],[f1142,f139174]) ).
fof(f139174,plain,
! [X0] : top = join(complement(converse(complement(X0))),complement(converse(X0))),
inference(superposition,[],[f13420,f138941]) ).
fof(f13420,plain,
! [X0,X1] : top = join(X1,complement(converse(meet(X0,converse(X1))))),
inference(superposition,[],[f10976,f12002]) ).
fof(f12002,plain,
! [X0,X1] : join(converse(meet(X0,converse(X1))),X1) = X1,
inference(forward_demodulation,[],[f11991,f8]) ).
fof(f11991,plain,
! [X0,X1] : converse(converse(X1)) = join(converse(meet(X0,converse(X1))),X1),
inference(superposition,[],[f35,f11903]) ).
fof(f11903,plain,
! [X0,X1] : join(meet(X1,X0),X0) = X0,
inference(superposition,[],[f11883,f95]) ).
fof(f11883,plain,
! [X0,X1] : join(meet(X0,X1),X0) = X0,
inference(backward_demodulation,[],[f9357,f11847]) ).
fof(f11847,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(superposition,[],[f11802,f95]) ).
fof(f11802,plain,
! [X0,X1] : join(X1,meet(X1,X0)) = X1,
inference(superposition,[],[f11193,f2560]) ).
fof(f11193,plain,
! [X0,X1] : join(X0,meet(X0,complement(X1))) = X0,
inference(forward_demodulation,[],[f11173,f2553]) ).
fof(f2553,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,complement(X1))) = X0,
inference(superposition,[],[f324,f1]) ).
fof(f11173,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,complement(X1))) = join(X0,meet(X0,complement(X1))),
inference(superposition,[],[f3134,f11134]) ).
fof(f11134,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[],[f11112,f7663]) ).
fof(f7663,plain,
! [X0] : meet(X0,X0) = X0,
inference(superposition,[],[f7480,f2562]) ).
fof(f2562,plain,
! [X0] : join(meet(X0,X0),zero) = X0,
inference(backward_demodulation,[],[f338,f2560]) ).
fof(f11112,plain,
! [X0] : meet(X0,X0) = join(X0,meet(X0,X0)),
inference(superposition,[],[f1521,f7663]) ).
fof(f1521,plain,
! [X0,X1] : meet(X1,meet(X0,X1)) = join(meet(X0,X1),meet(X1,meet(X0,X1))),
inference(forward_demodulation,[],[f1511,f6]) ).
fof(f1511,plain,
! [X0,X1] : meet(X1,meet(X0,composition(X1,one))) = join(meet(X0,X1),meet(X1,meet(X0,composition(X1,one)))),
inference(backward_demodulation,[],[f609,f1481]) ).
fof(f609,plain,
! [X0,X1] : meet(X1,meet(X0,composition(X1,converse(one)))) = join(meet(X0,X1),meet(X1,meet(X0,composition(X1,converse(one))))),
inference(forward_demodulation,[],[f608,f6]) ).
fof(f608,plain,
! [X0,X1] : meet(X1,composition(meet(X0,composition(X1,converse(one))),one)) = join(meet(X0,X1),meet(X1,composition(meet(X0,composition(X1,converse(one))),one))),
inference(forward_demodulation,[],[f590,f95]) ).
fof(f590,plain,
! [X0,X1] : meet(composition(meet(X0,composition(X1,converse(one))),one),X1) = join(meet(X0,X1),meet(composition(meet(X0,composition(X1,converse(one))),one),X1)),
inference(superposition,[],[f16,f6]) ).
fof(f16,axiom,
! [X2,X0,X1] : meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2) = join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_2_16) ).
fof(f9357,plain,
! [X0,X1] : join(meet(X0,X1),X0) = join(X0,meet(X1,X0)),
inference(forward_demodulation,[],[f9300,f2560]) ).
fof(f9300,plain,
! [X0,X1] : join(meet(X0,X1),X0) = join(X0,meet(complement(complement(X1)),X0)),
inference(superposition,[],[f3134,f3131]) ).
fof(f10976,plain,
! [X0,X1] : top = join(join(X0,X1),complement(X0)),
inference(superposition,[],[f10307,f2560]) ).
fof(f10307,plain,
! [X0,X1] : top = join(join(complement(X0),X1),X0),
inference(backward_demodulation,[],[f8911,f10182]) ).
fof(f10182,plain,
! [X0] : top = join(X0,top),
inference(backward_demodulation,[],[f8898,f10181]) ).
fof(f10181,plain,
! [X0] : top = join(join(top,X0),composition(complement(sk1),sk2)),
inference(forward_demodulation,[],[f10180,f7279]) ).
fof(f10180,plain,
! [X0] : top = join(join(top,X0),join(zero,composition(complement(sk1),sk2))),
inference(forward_demodulation,[],[f10162,f1]) ).
fof(f10162,plain,
! [X0] : top = join(join(top,X0),join(composition(complement(sk1),sk2),zero)),
inference(backward_demodulation,[],[f2265,f10133]) ).
fof(f10133,plain,
! [X0] : zero = complement(join(top,X0)),
inference(superposition,[],[f9736,f7663]) ).
fof(f9736,plain,
! [X0,X1] : zero = complement(join(top,meet(X0,X1))),
inference(backward_demodulation,[],[f8715,f9719]) ).
fof(f9719,plain,
! [X0] : zero = meet(zero,complement(X0)),
inference(forward_demodulation,[],[f9693,f33]) ).
fof(f9693,plain,
! [X0] : complement(top) = meet(zero,complement(X0)),
inference(superposition,[],[f2560,f9636]) ).
fof(f8715,plain,
! [X0,X1] : meet(zero,complement(meet(X1,X0))) = complement(join(top,meet(X0,X1))),
inference(superposition,[],[f3058,f3038]) ).
fof(f2265,plain,
! [X0] : top = join(join(top,X0),join(composition(complement(sk1),sk2),complement(join(top,X0)))),
inference(superposition,[],[f162,f201]) ).
fof(f201,plain,
! [X0] : join(top,X0) = join(join(top,X0),composition(complement(sk1),sk2)),
inference(superposition,[],[f181,f1]) ).
fof(f181,plain,
! [X0] : join(top,X0) = join(composition(complement(sk1),sk2),join(top,X0)),
inference(superposition,[],[f2,f174]) ).
fof(f174,plain,
top = join(composition(complement(sk1),sk2),top),
inference(superposition,[],[f153,f12]) ).
fof(f153,plain,
! [X0] : join(complement(sk3),X0) = join(composition(complement(sk1),sk2),join(complement(sk3),X0)),
inference(superposition,[],[f2,f17]) ).
fof(f162,plain,
! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))),
inference(superposition,[],[f2,f12]) ).
fof(f8898,plain,
! [X0] : join(X0,top) = join(join(top,X0),composition(complement(sk1),sk2)),
inference(forward_demodulation,[],[f8781,f7464]) ).
fof(f7464,plain,
! [X0,X1] : join(X1,X0) = join(zero,join(X0,X1)),
inference(backward_demodulation,[],[f5100,f7305]) ).
fof(f7305,plain,
! [X0,X1] : join(X0,X1) = join(meet(X0,X0),X1),
inference(backward_demodulation,[],[f2564,f7279]) ).
fof(f2564,plain,
! [X0,X1] : join(X0,X1) = join(meet(X0,X0),join(zero,X1)),
inference(backward_demodulation,[],[f895,f2560]) ).
fof(f895,plain,
! [X0,X1] : join(X0,X1) = join(meet(X0,complement(complement(X0))),join(zero,X1)),
inference(superposition,[],[f2,f338]) ).
fof(f5100,plain,
! [X0,X1] : join(X1,X0) = join(zero,join(meet(X0,X0),X1)),
inference(superposition,[],[f160,f326]) ).
fof(f8781,plain,
! [X0] : join(join(top,X0),composition(complement(sk1),sk2)) = join(zero,join(top,X0)),
inference(superposition,[],[f7464,f181]) ).
fof(f8911,plain,
! [X0,X1] : join(X1,top) = join(join(complement(X0),X1),X0),
inference(forward_demodulation,[],[f8792,f7464]) ).
fof(f8792,plain,
! [X0,X1] : join(join(complement(X0),X1),X0) = join(zero,join(top,X1)),
inference(superposition,[],[f7464,f154]) ).
fof(f1142,plain,
! [X0,X1] : converse(join(X0,X1)) = converse(join(X1,X0)),
inference(superposition,[],[f36,f9]) ).
fof(f36,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(superposition,[],[f9,f1]) ).
fof(f138941,plain,
! [X0] : meet(X0,converse(complement(converse(complement(X0))))) = X0,
inference(superposition,[],[f4390,f7480]) ).
fof(f4390,plain,
! [X0] : join(meet(X0,converse(complement(converse(complement(X0))))),zero) = X0,
inference(forward_demodulation,[],[f4323,f33]) ).
fof(f4323,plain,
! [X0] : join(meet(X0,converse(complement(converse(complement(X0))))),complement(top)) = X0,
inference(backward_demodulation,[],[f322,f4313]) ).
fof(f322,plain,
! [X0] : join(meet(X0,converse(complement(converse(complement(X0))))),complement(converse(top))) = X0,
inference(superposition,[],[f19,f127]) ).
fof(f139382,plain,
! [X0] : converse(complement(converse(X0))) = join(meet(X0,converse(complement(converse(X0)))),complement(X0)),
inference(forward_demodulation,[],[f139381,f2560]) ).
fof(f139381,plain,
! [X0] : converse(complement(converse(complement(complement(X0))))) = join(meet(X0,converse(complement(converse(complement(complement(X0)))))),complement(X0)),
inference(forward_demodulation,[],[f139285,f95]) ).
fof(f139285,plain,
! [X0] : converse(complement(converse(complement(complement(X0))))) = join(meet(converse(complement(converse(complement(complement(X0))))),X0),complement(X0)),
inference(superposition,[],[f3131,f138941]) ).
fof(f142276,plain,
! [X0,X1] : meet(X1,X0) = meet(converse(complement(converse(complement(meet(X0,X1))))),meet(X1,X0)),
inference(superposition,[],[f139412,f3056]) ).
fof(f139412,plain,
! [X0] : complement(X0) = meet(converse(complement(converse(X0))),complement(X0)),
inference(superposition,[],[f139341,f2560]) ).
fof(f139341,plain,
! [X0] : meet(converse(complement(converse(complement(X0)))),X0) = X0,
inference(forward_demodulation,[],[f139178,f2560]) ).
fof(f139178,plain,
! [X0] : complement(complement(X0)) = meet(converse(complement(converse(complement(X0)))),X0),
inference(superposition,[],[f3056,f138941]) ).
fof(f4060,plain,
! [X0,X1] : meet(X1,X0) = join(meet(meet(X1,X0),meet(X0,X1)),zero),
inference(superposition,[],[f3131,f3060]) ).
fof(f3060,plain,
! [X0,X1] : zero = meet(complement(meet(X1,X0)),meet(X0,X1)),
inference(backward_demodulation,[],[f31,f3034]) ).
fof(f31,plain,
! [X0,X1] : zero = meet(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(superposition,[],[f13,f4]) ).
fof(f68054,plain,
zero = join(meet(complement(sk1),composition(sk3,converse(sk2))),zero),
inference(backward_demodulation,[],[f50028,f67902]) ).
fof(f67902,plain,
! [X2] : zero = composition(zero,X2),
inference(forward_demodulation,[],[f67867,f67861]) ).
fof(f67861,plain,
! [X0,X1] : zero = composition(converse(X1),composition(zero,X0)),
inference(backward_demodulation,[],[f17516,f67858]) ).
fof(f67858,plain,
! [X0,X1] : zero = converse(composition(X0,composition(zero,X1))),
inference(forward_demodulation,[],[f67761,f67191]) ).
fof(f67191,plain,
! [X0] : zero = composition(X0,zero),
inference(forward_demodulation,[],[f67190,f67169]) ).
fof(f67169,plain,
! [X0] : zero = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f67168,f66842]) ).
fof(f66842,plain,
zero = composition(top,complement(composition(top,top))),
inference(superposition,[],[f66413,f4313]) ).
fof(f66413,plain,
! [X0] : zero = composition(converse(X0),complement(composition(X0,top))),
inference(superposition,[],[f16051,f7480]) ).
fof(f16051,plain,
! [X0,X1] : join(composition(converse(X1),complement(composition(X1,top))),X0) = X0,
inference(forward_demodulation,[],[f15971,f7279]) ).
fof(f15971,plain,
! [X0,X1] : join(zero,X0) = join(composition(converse(X1),complement(composition(X1,top))),join(zero,X0)),
inference(superposition,[],[f456,f33]) ).
fof(f456,plain,
! [X2,X0,X1] : join(complement(X1),X2) = join(composition(converse(X0),complement(composition(X0,X1))),join(complement(X1),X2)),
inference(superposition,[],[f2,f11]) ).
fof(f67168,plain,
! [X0] : composition(top,complement(composition(top,top))) = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f67167,f10182]) ).
fof(f67167,plain,
! [X0] : composition(join(X0,top),complement(composition(top,top))) = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f67112,f7480]) ).
fof(f67112,plain,
! [X0] : composition(join(X0,top),complement(composition(top,top))) = join(composition(X0,complement(composition(top,top))),zero),
inference(superposition,[],[f7,f66842]) ).
fof(f7,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(f67190,plain,
! [X0,X1] : composition(X0,zero) = composition(join(composition(X0,X1),top),complement(composition(top,top))),
inference(forward_demodulation,[],[f67189,f67169]) ).
fof(f67189,plain,
! [X0,X1] : composition(join(composition(X0,X1),top),complement(composition(top,top))) = composition(X0,composition(X1,complement(composition(top,top)))),
inference(forward_demodulation,[],[f67120,f7480]) ).
fof(f67120,plain,
! [X0,X1] : composition(join(composition(X0,X1),top),complement(composition(top,top))) = join(composition(X0,composition(X1,complement(composition(top,top)))),zero),
inference(superposition,[],[f386,f66842]) ).
fof(f386,plain,
! [X2,X3,X0,X1] : composition(join(composition(X0,X1),X3),X2) = join(composition(X0,composition(X1,X2)),composition(X3,X2)),
inference(superposition,[],[f7,f5]) ).
fof(f5,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
fof(f67761,plain,
! [X0,X1] : composition(converse(X1),zero) = converse(composition(X0,composition(zero,X1))),
inference(backward_demodulation,[],[f17601,f67759]) ).
fof(f67759,plain,
! [X0] : zero = composition(zero,converse(X0)),
inference(forward_demodulation,[],[f67193,f8083]) ).
fof(f67193,plain,
! [X0] : converse(zero) = composition(zero,converse(X0)),
inference(backward_demodulation,[],[f8103,f67191]) ).
fof(f8103,plain,
! [X0] : converse(composition(X0,zero)) = composition(zero,converse(X0)),
inference(superposition,[],[f10,f8083]) ).
fof(f17601,plain,
! [X0,X1] : converse(composition(X0,composition(zero,X1))) = composition(converse(X1),composition(zero,converse(X0))),
inference(forward_demodulation,[],[f17555,f5]) ).
fof(f17555,plain,
! [X0,X1] : converse(composition(composition(X0,zero),X1)) = composition(converse(X1),composition(zero,converse(X0))),
inference(superposition,[],[f10,f8103]) ).
fof(f17516,plain,
! [X0,X1] : composition(converse(X1),composition(zero,X0)) = converse(composition(converse(X0),composition(zero,X1))),
inference(forward_demodulation,[],[f17473,f5]) ).
fof(f17473,plain,
! [X0,X1] : composition(converse(X1),composition(zero,X0)) = converse(composition(composition(converse(X0),zero),X1)),
inference(superposition,[],[f79,f8102]) ).
fof(f8102,plain,
! [X0] : composition(converse(X0),zero) = converse(composition(zero,X0)),
inference(superposition,[],[f10,f8083]) ).
fof(f67867,plain,
! [X2,X0,X1] : composition(zero,X2) = composition(converse(X1),composition(zero,composition(X0,X2))),
inference(backward_demodulation,[],[f18723,f67861]) ).
fof(f18723,plain,
! [X2,X0,X1] : composition(converse(X1),composition(zero,composition(X0,X2))) = composition(composition(converse(X1),composition(zero,X0)),X2),
inference(forward_demodulation,[],[f18722,f5]) ).
fof(f18722,plain,
! [X2,X0,X1] : composition(converse(X1),composition(zero,composition(X0,X2))) = composition(composition(composition(converse(X1),zero),X0),X2),
inference(forward_demodulation,[],[f18721,f8102]) ).
fof(f18721,plain,
! [X2,X0,X1] : composition(converse(X1),composition(zero,composition(X0,X2))) = composition(composition(converse(composition(zero,X1)),X0),X2),
inference(forward_demodulation,[],[f18720,f79]) ).
fof(f18720,plain,
! [X2,X0,X1] : composition(converse(X1),composition(zero,composition(X0,X2))) = composition(converse(composition(converse(X0),composition(zero,X1))),X2),
inference(forward_demodulation,[],[f18719,f5]) ).
fof(f18719,plain,
! [X2,X0,X1] : composition(converse(composition(composition(converse(X0),zero),X1)),X2) = composition(converse(X1),composition(zero,composition(X0,X2))),
inference(forward_demodulation,[],[f18658,f5]) ).
fof(f18658,plain,
! [X2,X0,X1] : composition(converse(composition(composition(converse(X0),zero),X1)),X2) = composition(converse(X1),composition(composition(zero,X0),X2)),
inference(superposition,[],[f216,f17458]) ).
fof(f17458,plain,
! [X0] : composition(zero,X0) = converse(composition(converse(X0),zero)),
inference(superposition,[],[f8,f8102]) ).
fof(f216,plain,
! [X2,X0,X1] : composition(converse(X0),composition(converse(X1),X2)) = composition(converse(composition(X1,X0)),X2),
inference(superposition,[],[f5,f10]) ).
fof(f50028,plain,
composition(zero,meet(converse(sk2),composition(converse(sk3),complement(sk1)))) = join(meet(complement(sk1),composition(sk3,converse(sk2))),composition(zero,meet(converse(sk2),composition(converse(sk3),complement(sk1))))),
inference(forward_demodulation,[],[f49886,f95]) ).
fof(f49886,plain,
composition(zero,meet(converse(sk2),composition(converse(sk3),complement(sk1)))) = join(meet(composition(sk3,converse(sk2)),complement(sk1)),composition(zero,meet(converse(sk2),composition(converse(sk3),complement(sk1))))),
inference(superposition,[],[f692,f1899]) ).
fof(f1899,plain,
zero = meet(sk3,composition(complement(sk1),sk2)),
inference(forward_demodulation,[],[f1837,f33]) ).
fof(f1837,plain,
complement(top) = meet(sk3,composition(complement(sk1),sk2)),
inference(backward_demodulation,[],[f374,f1834]) ).
fof(f692,plain,
! [X2,X0,X1] : composition(meet(X1,composition(X2,X0)),meet(converse(X0),composition(converse(X1),X2))) = join(meet(composition(X1,converse(X0)),X2),composition(meet(X1,composition(X2,X0)),meet(converse(X0),composition(converse(X1),X2)))),
inference(superposition,[],[f14,f8]) ).
fof(f14,axiom,
! [X2,X0,X1] : composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) = join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dedekind_law_14) ).
fof(f160381,plain,
! [X0,X1] : join(X1,X0) = join(X1,meet(X0,complement(X1))),
inference(superposition,[],[f65930,f324]) ).
fof(f65930,plain,
! [X2,X0,X1] : join(X0,X2) = join(X0,join(X2,meet(X1,X0))),
inference(superposition,[],[f11895,f95]) ).
fof(f11895,plain,
! [X2,X0,X1] : join(X0,X2) = join(X0,join(X2,meet(X0,X1))),
inference(backward_demodulation,[],[f9352,f11861]) ).
fof(f11861,plain,
! [X2,X0,X1] : join(X0,X2) = join(X0,join(meet(X0,X1),X2)),
inference(superposition,[],[f2,f11802]) ).
fof(f9352,plain,
! [X2,X0,X1] : join(X0,join(X2,meet(X0,X1))) = join(X0,join(meet(X0,X1),X2)),
inference(forward_demodulation,[],[f9351,f2560]) ).
fof(f9351,plain,
! [X2,X0,X1] : join(X0,join(meet(X0,complement(complement(X1))),X2)) = join(X0,join(X2,meet(X0,X1))),
inference(forward_demodulation,[],[f9292,f160]) ).
fof(f9292,plain,
! [X2,X0,X1] : join(X0,join(meet(X0,complement(complement(X1))),X2)) = join(meet(X0,X1),join(X0,X2)),
inference(superposition,[],[f3134,f3134]) ).
fof(f22,plain,
sk1 != join(sk1,composition(sk3,converse(sk2))),
inference(superposition,[],[f18,f1]) ).
fof(f18,axiom,
sk1 != join(composition(sk3,converse(sk2)),sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL044-2 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 00:31:25 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.21/0.35 % (31987)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (31990)WARNING: value z3 for option sas not known
% 0.21/0.37 % (31988)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (31989)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (31991)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (31990)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.37 % (31992)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.37 % (31993)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.37 % (31994)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.42 TRYING [3]
% 0.21/0.47 TRYING [4]
% 0.21/0.52 TRYING [4]
% 2.00/0.65 TRYING [5]
% 6.32/1.31 TRYING [6]
% 7.89/1.47 TRYING [1]
% 7.89/1.47 TRYING [2]
% 7.89/1.48 TRYING [3]
% 8.05/1.51 TRYING [4]
% 9.47/1.70 TRYING [5]
% 11.06/1.92 TRYING [5]
% 14.28/2.42 TRYING [6]
% 24.61/3.85 TRYING [7]
% 34.31/5.26 % (31993)First to succeed.
% 34.31/5.29 % (31993)Refutation found. Thanks to Tanya!
% 34.31/5.29 % SZS status Unsatisfiable for theBenchmark
% 34.31/5.29 % SZS output start Proof for theBenchmark
% See solution above
% 34.31/5.29 % (31993)------------------------------
% 34.31/5.29 % (31993)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 34.31/5.29 % (31993)Termination reason: Refutation
% 34.31/5.29
% 34.31/5.29 % (31993)Memory used [KB]: 90714
% 34.31/5.29 % (31993)Time elapsed: 4.908 s
% 34.31/5.29 % (31993)Instructions burned: 14801 (million)
% 34.31/5.29 % (31993)------------------------------
% 34.31/5.29 % (31993)------------------------------
% 34.31/5.29 % (31987)Success in time 4.901 s
%------------------------------------------------------------------------------