TSTP Solution File: REL027-3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : REL027-3 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 May 21 02:35:30 EDT 2024
% Result : Timeout 290.54s 41.89s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 90
% Number of leaves : 18
% Syntax : Number of formulae : 489 ( 489 unt; 0 def)
% Number of atoms : 489 ( 488 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 646 ( 646 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1053907,plain,
$false,
inference(trivial_inequality_removal,[],[f1053906]) ).
fof(f1053906,plain,
meet(one,complement(sk1)) != meet(one,complement(sk1)),
inference(superposition,[],[f1053584,f93]) ).
fof(f93,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(superposition,[],[f27,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(f27,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(superposition,[],[f4,f1]) ).
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f1053584,plain,
meet(complement(sk1),one) != meet(one,complement(sk1)),
inference(backward_demodulation,[],[f18,f1053583]) ).
fof(f1053583,plain,
meet(complement(composition(sk1,top)),one) = meet(one,complement(sk1)),
inference(forward_demodulation,[],[f1053582,f93]) ).
fof(f1053582,plain,
meet(complement(composition(sk1,top)),one) = meet(complement(sk1),one),
inference(forward_demodulation,[],[f1052516,f925782]) ).
fof(f925782,plain,
! [X0,X1] : complement(X0) = join(complement(X0),meet(X1,complement(composition(X0,top)))),
inference(forward_demodulation,[],[f925194,f6930]) ).
fof(f6930,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f5496,f295]) ).
fof(f295,plain,
! [X0] : join(zero,meet(X0,X0)) = X0,
inference(forward_demodulation,[],[f274,f4]) ).
fof(f274,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(f5496,plain,
! [X0] : join(zero,X0) = join(zero,join(zero,X0)),
inference(forward_demodulation,[],[f5495,f31]) ).
fof(f31,plain,
zero = complement(top),
inference(forward_demodulation,[],[f26,f13]) ).
fof(f26,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(f5495,plain,
! [X0] : join(zero,X0) = join(zero,join(complement(top),X0)),
inference(forward_demodulation,[],[f5354,f5358]) ).
fof(f5358,plain,
top = join(one,top),
inference(forward_demodulation,[],[f5351,f35]) ).
fof(f35,plain,
top = join(top,zero),
inference(superposition,[],[f12,f31]) ).
fof(f5351,plain,
top = join(one,join(top,zero)),
inference(superposition,[],[f3080,f5263]) ).
fof(f5263,plain,
zero = join(zero,complement(join(one,top))),
inference(backward_demodulation,[],[f306,f5262]) ).
fof(f5262,plain,
join(one,top) = join(top,complement(zero)),
inference(forward_demodulation,[],[f5261,f4841]) ).
fof(f4841,plain,
join(one,top) = join(top,top),
inference(forward_demodulation,[],[f4834,f296]) ).
fof(f296,plain,
top = join(zero,top),
inference(backward_demodulation,[],[f162,f295]) ).
fof(f162,plain,
top = join(zero,join(zero,meet(top,top))),
inference(superposition,[],[f2,f56]) ).
fof(f56,plain,
top = join(join(zero,zero),meet(top,top)),
inference(superposition,[],[f12,f45]) ).
fof(f45,plain,
meet(top,top) = complement(join(zero,zero)),
inference(superposition,[],[f33,f31]) ).
fof(f33,plain,
! [X0] : meet(top,X0) = complement(join(zero,complement(X0))),
inference(superposition,[],[f4,f31]) ).
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(f4834,plain,
join(top,top) = join(one,join(zero,top)),
inference(superposition,[],[f2997,f4748]) ).
fof(f4748,plain,
top = join(top,complement(one)),
inference(superposition,[],[f2778,f4724]) ).
fof(f4724,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f4698,f8]) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f4698,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f77,f6]) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f77,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(f2778,plain,
! [X0] : top = join(top,composition(converse(X0),complement(X0))),
inference(forward_demodulation,[],[f2777,f12]) ).
fof(f2777,plain,
! [X0] : join(one,complement(one)) = join(top,composition(converse(X0),complement(X0))),
inference(forward_demodulation,[],[f2745,f6]) ).
fof(f2745,plain,
! [X0] : join(one,complement(one)) = join(top,composition(converse(X0),complement(composition(X0,one)))),
inference(superposition,[],[f2665,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(f2665,plain,
! [X0] : join(top,X0) = join(one,join(X0,complement(one))),
inference(superposition,[],[f1913,f427]) ).
fof(f427,plain,
! [X0,X1] : join(one,join(X0,X1)) = join(one,join(sk1,join(X1,X0))),
inference(forward_demodulation,[],[f416,f2]) ).
fof(f416,plain,
! [X0,X1] : join(one,join(X0,X1)) = join(one,join(join(sk1,X1),X0)),
inference(superposition,[],[f213,f1]) ).
fof(f213,plain,
! [X0,X1] : join(one,join(X0,X1)) = join(one,join(X0,join(sk1,X1))),
inference(forward_demodulation,[],[f212,f2]) ).
fof(f212,plain,
! [X0,X1] : join(join(one,X0),X1) = join(one,join(X0,join(sk1,X1))),
inference(forward_demodulation,[],[f211,f2]) ).
fof(f211,plain,
! [X0,X1] : join(join(one,X0),X1) = join(one,join(join(X0,sk1),X1)),
inference(superposition,[],[f2,f184]) ).
fof(f184,plain,
! [X0] : join(one,X0) = join(one,join(X0,sk1)),
inference(superposition,[],[f158,f1]) ).
fof(f158,plain,
! [X0] : join(one,join(sk1,X0)) = join(one,X0),
inference(superposition,[],[f2,f20]) ).
fof(f20,plain,
one = join(one,sk1),
inference(superposition,[],[f1,f17]) ).
fof(f17,axiom,
one = join(sk1,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f1913,plain,
! [X0] : join(top,X0) = join(one,join(sk1,join(complement(one),X0))),
inference(superposition,[],[f436,f1874]) ).
fof(f1874,plain,
top = join(one,join(sk1,complement(one))),
inference(forward_demodulation,[],[f1855,f1]) ).
fof(f1855,plain,
top = join(one,join(complement(one),sk1)),
inference(superposition,[],[f1692,f427]) ).
fof(f1692,plain,
top = join(one,join(sk1,join(sk1,complement(one)))),
inference(superposition,[],[f1476,f20]) ).
fof(f1476,plain,
! [X0] : top = join(one,join(X0,join(sk1,complement(join(one,X0))))),
inference(superposition,[],[f1194,f184]) ).
fof(f1194,plain,
! [X0,X1] : top = join(one,join(X0,join(X1,complement(join(one,join(X0,X1)))))),
inference(superposition,[],[f436,f12]) ).
fof(f436,plain,
! [X2,X0,X1] : join(join(one,join(X0,X1)),X2) = join(one,join(X0,join(X1,X2))),
inference(forward_demodulation,[],[f435,f213]) ).
fof(f435,plain,
! [X2,X0,X1] : join(join(one,join(X0,X1)),X2) = join(one,join(X0,join(sk1,join(X1,X2)))),
inference(forward_demodulation,[],[f434,f2]) ).
fof(f434,plain,
! [X2,X0,X1] : join(join(one,join(X0,X1)),X2) = join(one,join(X0,join(join(sk1,X1),X2))),
inference(forward_demodulation,[],[f426,f2]) ).
fof(f426,plain,
! [X2,X0,X1] : join(join(one,join(X0,X1)),X2) = join(one,join(join(X0,join(sk1,X1)),X2)),
inference(superposition,[],[f2,f213]) ).
fof(f2997,plain,
! [X0] : join(top,X0) = join(one,join(zero,join(X0,complement(one)))),
inference(superposition,[],[f1989,f1]) ).
fof(f1989,plain,
! [X0] : join(top,X0) = join(one,join(zero,join(complement(one),X0))),
inference(superposition,[],[f436,f1956]) ).
fof(f1956,plain,
top = join(one,join(zero,complement(one))),
inference(forward_demodulation,[],[f1941,f1]) ).
fof(f1941,plain,
top = join(one,join(complement(one),zero)),
inference(superposition,[],[f1801,f427]) ).
fof(f1801,plain,
top = join(one,join(sk1,join(zero,complement(one)))),
inference(forward_demodulation,[],[f1800,f1]) ).
fof(f1800,plain,
top = join(one,join(sk1,join(complement(one),zero))),
inference(forward_demodulation,[],[f1799,f31]) ).
fof(f1799,plain,
top = join(one,join(sk1,join(complement(one),complement(top)))),
inference(forward_demodulation,[],[f1798,f1]) ).
fof(f1798,plain,
top = join(one,join(sk1,join(complement(top),complement(one)))),
inference(forward_demodulation,[],[f1693,f164]) ).
fof(f164,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f1693,plain,
top = join(one,join(complement(one),join(sk1,complement(top)))),
inference(superposition,[],[f1476,f12]) ).
fof(f5261,plain,
join(top,top) = join(top,complement(zero)),
inference(forward_demodulation,[],[f5118,f5025]) ).
fof(f5025,plain,
! [X0,X1] : join(top,X1) = join(X0,join(X1,complement(X0))),
inference(superposition,[],[f152,f1]) ).
fof(f152,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f12]) ).
fof(f5118,plain,
join(top,complement(zero)) = join(one,join(top,complement(one))),
inference(superposition,[],[f2997,f152]) ).
fof(f306,plain,
zero = join(zero,complement(join(top,complement(zero)))),
inference(forward_demodulation,[],[f281,f1]) ).
fof(f281,plain,
zero = join(zero,complement(join(complement(zero),top))),
inference(superposition,[],[f19,f73]) ).
fof(f73,plain,
zero = meet(zero,top),
inference(forward_demodulation,[],[f62,f31]) ).
fof(f62,plain,
complement(top) = meet(zero,top),
inference(superposition,[],[f36,f12]) ).
fof(f36,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[],[f32,f1]) ).
fof(f32,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(superposition,[],[f4,f31]) ).
fof(f3080,plain,
! [X0] : top = join(one,join(X0,join(zero,complement(join(one,X0))))),
inference(superposition,[],[f2412,f1]) ).
fof(f2412,plain,
! [X0] : top = join(one,join(X0,join(zero,complement(join(X0,one))))),
inference(forward_demodulation,[],[f2411,f31]) ).
fof(f2411,plain,
! [X0] : top = join(one,join(X0,join(complement(top),complement(join(X0,one))))),
inference(forward_demodulation,[],[f2379,f1]) ).
fof(f2379,plain,
! [X0] : top = join(one,join(X0,join(complement(join(X0,one)),complement(top)))),
inference(superposition,[],[f1194,f2303]) ).
fof(f2303,plain,
! [X0] : top = join(one,join(X0,complement(join(X0,one)))),
inference(forward_demodulation,[],[f2266,f1]) ).
fof(f2266,plain,
! [X0] : top = join(one,join(complement(join(X0,one)),X0)),
inference(superposition,[],[f1694,f398]) ).
fof(f398,plain,
! [X0,X1] : join(one,join(X0,X1)) = join(one,join(X1,join(sk1,X0))),
inference(forward_demodulation,[],[f383,f2]) ).
fof(f383,plain,
! [X0,X1] : join(one,join(X0,X1)) = join(one,join(join(X1,sk1),X0)),
inference(superposition,[],[f209,f1]) ).
fof(f209,plain,
! [X0,X1] : join(one,join(X0,X1)) = join(one,join(X0,join(X1,sk1))),
inference(superposition,[],[f184,f2]) ).
fof(f1694,plain,
! [X0] : top = join(one,join(X0,join(sk1,complement(join(X0,one))))),
inference(superposition,[],[f1476,f1]) ).
fof(f5354,plain,
! [X0] : join(zero,X0) = join(zero,join(complement(join(one,top)),X0)),
inference(superposition,[],[f2,f5263]) ).
fof(f925194,plain,
! [X0,X1] : join(zero,complement(X0)) = join(complement(X0),meet(X1,complement(composition(X0,top)))),
inference(superposition,[],[f177475,f343429]) ).
fof(f343429,plain,
! [X0,X1] : zero = meet(X0,meet(X1,complement(composition(X0,top)))),
inference(superposition,[],[f300811,f79723]) ).
fof(f79723,plain,
! [X0] : composition(X0,top) = join(X0,composition(X0,top)),
inference(superposition,[],[f19299,f78689]) ).
fof(f78689,plain,
! [X0] : meet(X0,composition(X0,top)) = X0,
inference(forward_demodulation,[],[f78688,f19142]) ).
fof(f19142,plain,
! [X0,X1] : join(X1,meet(X1,X0)) = X1,
inference(superposition,[],[f18169,f6216]) ).
fof(f6216,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f6215,f3670]) ).
fof(f3670,plain,
! [X0] : join(zero,meet(X0,complement(complement(X0)))) = X0,
inference(superposition,[],[f307,f1]) ).
fof(f307,plain,
! [X0] : join(meet(X0,complement(complement(X0))),zero) = X0,
inference(forward_demodulation,[],[f288,f31]) ).
fof(f288,plain,
! [X0] : join(meet(X0,complement(complement(X0))),complement(top)) = X0,
inference(superposition,[],[f19,f12]) ).
fof(f6215,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[],[f6195,f93]) ).
fof(f6195,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(superposition,[],[f293,f102]) ).
fof(f102,plain,
! [X0] : zero = meet(complement(X0),X0),
inference(forward_demodulation,[],[f90,f31]) ).
fof(f90,plain,
! [X0] : complement(top) = meet(complement(X0),X0),
inference(superposition,[],[f27,f12]) ).
fof(f293,plain,
! [X0,X1] : join(meet(X0,complement(X1)),meet(X0,X1)) = X0,
inference(superposition,[],[f19,f4]) ).
fof(f18169,plain,
! [X0,X1] : join(X0,meet(X0,complement(X1))) = X0,
inference(forward_demodulation,[],[f18108,f6203]) ).
fof(f6203,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,complement(X1))) = X0,
inference(superposition,[],[f293,f1]) ).
fof(f18108,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,complement(X1))) = join(X0,meet(X0,complement(X1))),
inference(superposition,[],[f6585,f18045]) ).
fof(f18045,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[],[f18020,f7219]) ).
fof(f7219,plain,
! [X0] : meet(X0,X0) = X0,
inference(superposition,[],[f6930,f295]) ).
fof(f18020,plain,
! [X0] : meet(X0,X0) = join(X0,meet(X0,X0)),
inference(superposition,[],[f4778,f7219]) ).
fof(f4778,plain,
! [X0,X1] : meet(X1,meet(X0,X1)) = join(meet(X0,X1),meet(X1,meet(X0,X1))),
inference(forward_demodulation,[],[f4767,f6]) ).
fof(f4767,plain,
! [X0,X1] : meet(X1,meet(X0,composition(X1,one))) = join(meet(X0,X1),meet(X1,meet(X0,composition(X1,one)))),
inference(backward_demodulation,[],[f2234,f4744]) ).
fof(f4744,plain,
one = converse(one),
inference(superposition,[],[f4724,f6]) ).
fof(f2234,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,[],[f2233,f6]) ).
fof(f2233,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,[],[f2213,f93]) ).
fof(f2213,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(f6585,plain,
! [X2,X0,X1] : join(X0,X2) = join(meet(X0,X1),join(meet(X0,complement(X1)),X2)),
inference(backward_demodulation,[],[f294,f6491]) ).
fof(f6491,plain,
! [X0,X1] : complement(join(complement(X1),X0)) = meet(X1,complement(X0)),
inference(superposition,[],[f4,f6216]) ).
fof(f294,plain,
! [X2,X0,X1] : join(X0,X2) = join(meet(X0,X1),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f2,f19]) ).
fof(f78688,plain,
! [X0] : meet(X0,composition(X0,top)) = join(X0,meet(X0,composition(X0,top))),
inference(forward_demodulation,[],[f78687,f7084]) ).
fof(f7084,plain,
! [X0] : meet(top,X0) = X0,
inference(forward_demodulation,[],[f6992,f6216]) ).
fof(f6992,plain,
! [X0] : complement(complement(X0)) = meet(top,X0),
inference(backward_demodulation,[],[f33,f6930]) ).
fof(f78687,plain,
! [X0] : meet(X0,composition(X0,top)) = join(meet(top,X0),meet(X0,composition(X0,top))),
inference(forward_demodulation,[],[f78686,f78104]) ).
fof(f78104,plain,
top = composition(top,top),
inference(backward_demodulation,[],[f40512,f78102]) ).
fof(f78102,plain,
! [X0] : top = join(converse(X0),composition(top,top)),
inference(backward_demodulation,[],[f40465,f78098]) ).
fof(f78098,plain,
! [X0] : top = converse(join(X0,composition(top,top))),
inference(backward_demodulation,[],[f40476,f78097]) ).
fof(f78097,plain,
! [X0] : top = join(composition(top,top),converse(X0)),
inference(forward_demodulation,[],[f78082,f6930]) ).
fof(f78082,plain,
! [X0] : top = join(composition(top,top),converse(join(zero,X0))),
inference(backward_demodulation,[],[f42973,f77997]) ).
fof(f77997,plain,
zero = complement(composition(top,top)),
inference(superposition,[],[f75369,f4776]) ).
fof(f4776,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f4724,f4744]) ).
fof(f75369,plain,
! [X0] : zero = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f75368,f74864]) ).
fof(f74864,plain,
zero = composition(top,complement(composition(top,top))),
inference(superposition,[],[f74434,f11776]) ).
fof(f11776,plain,
top = converse(top),
inference(forward_demodulation,[],[f11713,f11709]) ).
fof(f11709,plain,
top = join(top,converse(top)),
inference(superposition,[],[f11706,f1]) ).
fof(f11706,plain,
top = join(converse(top),top),
inference(forward_demodulation,[],[f11698,f12]) ).
fof(f11698,plain,
top = join(converse(top),join(converse(top),complement(converse(top)))),
inference(superposition,[],[f163,f11634]) ).
fof(f11634,plain,
converse(top) = join(converse(top),converse(top)),
inference(forward_demodulation,[],[f11583,f6812]) ).
fof(f6812,plain,
converse(top) = join(converse(top),converse(complement(converse(sk1)))),
inference(backward_demodulation,[],[f4894,f6768]) ).
fof(f6768,plain,
converse(top) = join(one,converse(top)),
inference(superposition,[],[f5422,f128]) ).
fof(f128,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f37,f12]) ).
fof(f37,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
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(f5422,plain,
! [X0] : join(top,X0) = join(one,join(top,X0)),
inference(backward_demodulation,[],[f258,f5411]) ).
fof(f5411,plain,
! [X0] : join(top,X0) = join(one,join(X0,complement(sk1))),
inference(backward_demodulation,[],[f412,f5381]) ).
fof(f5381,plain,
! [X0] : join(top,X0) = join(one,join(X0,top)),
inference(backward_demodulation,[],[f4999,f5358]) ).
fof(f4999,plain,
! [X0] : join(join(one,top),X0) = join(one,join(X0,top)),
inference(forward_demodulation,[],[f4991,f4784]) ).
fof(f4784,plain,
! [X0] : join(one,join(X0,top)) = join(one,join(complement(converse(sk1)),X0)),
inference(forward_demodulation,[],[f4774,f164]) ).
fof(f4774,plain,
! [X0] : join(top,join(one,X0)) = join(one,join(complement(converse(sk1)),X0)),
inference(backward_demodulation,[],[f4311,f4744]) ).
fof(f4311,plain,
! [X0] : join(converse(one),join(complement(converse(sk1)),X0)) = join(top,join(converse(one),X0)),
inference(forward_demodulation,[],[f4305,f2]) ).
fof(f4305,plain,
! [X0] : join(converse(one),join(complement(converse(sk1)),X0)) = join(join(top,converse(one)),X0),
inference(superposition,[],[f2,f3955]) ).
fof(f3955,plain,
join(converse(one),complement(converse(sk1))) = join(top,converse(one)),
inference(forward_demodulation,[],[f3954,f1]) ).
fof(f3954,plain,
join(converse(one),top) = join(converse(one),complement(converse(sk1))),
inference(forward_demodulation,[],[f3923,f38]) ).
fof(f38,plain,
! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[],[f9,f8]) ).
fof(f3923,plain,
converse(join(one,converse(top))) = join(converse(one),complement(converse(sk1))),
inference(superposition,[],[f38,f186]) ).
fof(f186,plain,
join(one,converse(top)) = join(one,converse(complement(converse(sk1)))),
inference(superposition,[],[f158,f128]) ).
fof(f4991,plain,
! [X0] : join(join(one,top),X0) = join(one,join(complement(converse(sk1)),X0)),
inference(superposition,[],[f2,f4781]) ).
fof(f4781,plain,
join(one,top) = join(one,complement(converse(sk1))),
inference(forward_demodulation,[],[f4771,f1]) ).
fof(f4771,plain,
join(top,one) = join(one,complement(converse(sk1))),
inference(backward_demodulation,[],[f3955,f4744]) ).
fof(f412,plain,
! [X0] : join(one,join(X0,top)) = join(one,join(X0,complement(sk1))),
inference(superposition,[],[f213,f12]) ).
fof(f258,plain,
! [X0] : join(one,join(top,X0)) = join(one,join(X0,complement(sk1))),
inference(superposition,[],[f193,f1]) ).
fof(f193,plain,
! [X0] : join(one,join(complement(sk1),X0)) = join(one,join(top,X0)),
inference(forward_demodulation,[],[f192,f2]) ).
fof(f192,plain,
! [X0] : join(one,join(complement(sk1),X0)) = join(join(one,top),X0),
inference(superposition,[],[f2,f183]) ).
fof(f183,plain,
join(one,top) = join(one,complement(sk1)),
inference(superposition,[],[f158,f12]) ).
fof(f4894,plain,
join(one,converse(top)) = join(converse(top),converse(complement(converse(sk1)))),
inference(backward_demodulation,[],[f4848,f4868]) ).
fof(f4868,plain,
! [X0] : join(one,converse(X0)) = converse(join(one,X0)),
inference(superposition,[],[f9,f4744]) ).
fof(f4848,plain,
join(converse(top),converse(complement(converse(sk1)))) = converse(join(one,top)),
inference(backward_demodulation,[],[f4335,f4841]) ).
fof(f4335,plain,
converse(join(top,top)) = join(converse(top),converse(complement(converse(sk1)))),
inference(forward_demodulation,[],[f4320,f9]) ).
fof(f4320,plain,
join(converse(top),converse(top)) = join(converse(top),converse(complement(converse(sk1)))),
inference(superposition,[],[f4017,f128]) ).
fof(f4017,plain,
! [X0] : join(converse(top),X0) = join(converse(top),join(sk1,X0)),
inference(superposition,[],[f2,f4002]) ).
fof(f4002,plain,
converse(top) = join(converse(top),sk1),
inference(superposition,[],[f38,f3978]) ).
fof(f3978,plain,
top = join(top,converse(sk1)),
inference(superposition,[],[f3963,f1]) ).
fof(f3963,plain,
top = join(converse(sk1),top),
inference(forward_demodulation,[],[f3930,f8]) ).
fof(f3930,plain,
converse(converse(top)) = join(converse(sk1),top),
inference(superposition,[],[f38,f178]) ).
fof(f178,plain,
converse(top) = join(sk1,converse(top)),
inference(superposition,[],[f161,f128]) ).
fof(f161,plain,
! [X0] : join(one,X0) = join(sk1,join(one,X0)),
inference(superposition,[],[f2,f17]) ).
fof(f11583,plain,
join(converse(top),converse(top)) = join(converse(top),converse(complement(converse(sk1)))),
inference(superposition,[],[f4318,f11115]) ).
fof(f11115,plain,
! [X0] : converse(top) = join(converse(complement(converse(X0))),X0),
inference(forward_demodulation,[],[f10940,f6930]) ).
fof(f10940,plain,
! [X0] : join(converse(complement(converse(X0))),X0) = join(zero,converse(top)),
inference(superposition,[],[f9078,f128]) ).
fof(f9078,plain,
! [X0,X1] : join(X1,X0) = join(zero,join(X0,X1)),
inference(superposition,[],[f164,f6930]) ).
fof(f4318,plain,
! [X0] : join(converse(top),X0) = join(converse(top),join(X0,sk1)),
inference(superposition,[],[f4017,f1]) ).
fof(f163,plain,
! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))),
inference(superposition,[],[f2,f12]) ).
fof(f11713,plain,
converse(top) = join(top,converse(top)),
inference(superposition,[],[f37,f11706]) ).
fof(f74434,plain,
! [X0] : zero = composition(converse(X0),complement(composition(X0,top))),
inference(superposition,[],[f24628,f7279]) ).
fof(f7279,plain,
! [X0] : join(X0,zero) = X0,
inference(backward_demodulation,[],[f6218,f7219]) ).
fof(f6218,plain,
! [X0] : join(meet(X0,X0),zero) = X0,
inference(backward_demodulation,[],[f307,f6216]) ).
fof(f24628,plain,
! [X0,X1] : join(composition(converse(X1),complement(composition(X1,top))),X0) = X0,
inference(forward_demodulation,[],[f24539,f6930]) ).
fof(f24539,plain,
! [X0,X1] : join(zero,X0) = join(composition(converse(X1),complement(composition(X1,top))),join(zero,X0)),
inference(superposition,[],[f894,f31]) ).
fof(f894,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(f75368,plain,
! [X0] : composition(top,complement(composition(top,top))) = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f75367,f15787]) ).
fof(f15787,plain,
! [X0] : top = join(X0,top),
inference(backward_demodulation,[],[f9351,f15786]) ).
fof(f15786,plain,
! [X0] : top = join(one,join(sk1,join(complement(one),X0))),
inference(forward_demodulation,[],[f15785,f6930]) ).
fof(f15785,plain,
! [X0] : top = join(one,join(sk1,join(zero,join(complement(one),X0)))),
inference(forward_demodulation,[],[f15764,f164]) ).
fof(f15764,plain,
! [X0] : top = join(one,join(sk1,join(complement(one),join(X0,zero)))),
inference(backward_demodulation,[],[f2703,f15734]) ).
fof(f15734,plain,
! [X0] : zero = complement(join(top,X0)),
inference(superposition,[],[f15312,f7219]) ).
fof(f15312,plain,
! [X0,X1] : zero = complement(join(top,meet(X0,X1))),
inference(backward_demodulation,[],[f13859,f15292]) ).
fof(f15292,plain,
! [X0] : zero = meet(zero,complement(X0)),
inference(forward_demodulation,[],[f15266,f31]) ).
fof(f15266,plain,
! [X0] : complement(top) = meet(zero,complement(X0)),
inference(superposition,[],[f6216,f15197]) ).
fof(f15197,plain,
! [X0] : top = complement(meet(zero,complement(X0))),
inference(forward_demodulation,[],[f15194,f6493]) ).
fof(f6493,plain,
! [X0] : top = join(complement(X0),X0),
inference(superposition,[],[f12,f6216]) ).
fof(f15194,plain,
! [X0] : join(complement(X0),X0) = complement(meet(zero,complement(X0))),
inference(backward_demodulation,[],[f13897,f15133]) ).
fof(f15133,plain,
! [X0] : join(X0,meet(zero,complement(X0))) = X0,
inference(superposition,[],[f15086,f1]) ).
fof(f15086,plain,
! [X0] : join(meet(zero,complement(X0)),X0) = X0,
inference(superposition,[],[f15039,f6216]) ).
fof(f15039,plain,
! [X0] : complement(X0) = join(meet(zero,X0),complement(X0)),
inference(forward_demodulation,[],[f14978,f6930]) ).
fof(f14978,plain,
! [X0] : join(zero,complement(X0)) = join(meet(zero,X0),complement(X0)),
inference(superposition,[],[f6585,f7584]) ).
fof(f7584,plain,
! [X0] : join(meet(zero,X0),X0) = X0,
inference(superposition,[],[f7090,f93]) ).
fof(f7090,plain,
! [X0] : join(meet(X0,zero),X0) = X0,
inference(backward_demodulation,[],[f6191,f7088]) ).
fof(f7088,plain,
! [X0] : meet(X0,top) = X0,
inference(forward_demodulation,[],[f6993,f6216]) ).
fof(f6993,plain,
! [X0] : complement(complement(X0)) = meet(X0,top),
inference(backward_demodulation,[],[f36,f6930]) ).
fof(f6191,plain,
! [X0] : join(meet(X0,zero),meet(X0,top)) = X0,
inference(superposition,[],[f293,f31]) ).
fof(f13897,plain,
! [X0] : complement(meet(zero,complement(X0))) = join(complement(join(X0,meet(zero,complement(X0)))),X0),
inference(forward_demodulation,[],[f13895,f93]) ).
fof(f13895,plain,
! [X0] : complement(meet(zero,complement(X0))) = join(complement(join(X0,meet(complement(X0),zero))),X0),
inference(backward_demodulation,[],[f13415,f13856]) ).
fof(f13856,plain,
! [X2,X0,X1] : meet(complement(X0),complement(meet(X2,X1))) = complement(join(X0,meet(X1,X2))),
inference(superposition,[],[f6506,f6216]) ).
fof(f6506,plain,
! [X2,X0,X1] : complement(join(complement(X2),meet(X0,X1))) = meet(X2,complement(meet(X1,X0))),
inference(backward_demodulation,[],[f25,f6485]) ).
fof(f6485,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X1,X0)),
inference(superposition,[],[f6216,f27]) ).
fof(f25,plain,
! [X2,X0,X1] : meet(X2,join(complement(X0),complement(X1))) = complement(join(complement(X2),meet(X0,X1))),
inference(superposition,[],[f4,f4]) ).
fof(f13415,plain,
! [X0] : complement(meet(zero,complement(X0))) = join(meet(complement(X0),complement(meet(zero,complement(X0)))),X0),
inference(forward_demodulation,[],[f13389,f93]) ).
fof(f13389,plain,
! [X0] : complement(meet(zero,complement(X0))) = join(meet(complement(meet(zero,complement(X0))),complement(X0)),X0),
inference(superposition,[],[f293,f13355]) ).
fof(f13355,plain,
! [X0] : meet(complement(meet(zero,complement(X0))),X0) = X0,
inference(forward_demodulation,[],[f13312,f6216]) ).
fof(f13312,plain,
! [X0] : complement(complement(X0)) = meet(complement(meet(zero,complement(X0))),X0),
inference(superposition,[],[f6505,f7090]) ).
fof(f6505,plain,
! [X2,X0,X1] : complement(join(meet(X0,X1),complement(X2))) = meet(complement(meet(X1,X0)),X2),
inference(backward_demodulation,[],[f24,f6485]) ).
fof(f24,plain,
! [X2,X0,X1] : meet(join(complement(X0),complement(X1)),X2) = complement(join(meet(X0,X1),complement(X2))),
inference(superposition,[],[f4,f4]) ).
fof(f13859,plain,
! [X0,X1] : meet(zero,complement(meet(X1,X0))) = complement(join(top,meet(X0,X1))),
inference(superposition,[],[f6506,f6489]) ).
fof(f6489,plain,
top = complement(zero),
inference(superposition,[],[f6216,f31]) ).
fof(f2703,plain,
! [X0] : top = join(one,join(sk1,join(complement(one),join(X0,complement(join(top,X0)))))),
inference(forward_demodulation,[],[f2679,f2]) ).
fof(f2679,plain,
! [X0] : top = join(one,join(sk1,join(join(complement(one),X0),complement(join(top,X0))))),
inference(superposition,[],[f1194,f1913]) ).
fof(f9351,plain,
! [X0] : join(X0,top) = join(one,join(sk1,join(complement(one),X0))),
inference(forward_demodulation,[],[f9020,f2]) ).
fof(f9020,plain,
! [X0] : join(X0,top) = join(one,join(join(sk1,complement(one)),X0)),
inference(superposition,[],[f164,f1874]) ).
fof(f75367,plain,
! [X0] : composition(join(X0,top),complement(composition(top,top))) = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f75312,f7279]) ).
fof(f75312,plain,
! [X0] : composition(join(X0,top),complement(composition(top,top))) = join(composition(X0,complement(composition(top,top))),zero),
inference(superposition,[],[f7,f74864]) ).
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(f42973,plain,
! [X0] : top = join(composition(top,top),converse(join(complement(composition(top,top)),X0))),
inference(superposition,[],[f16189,f40277]) ).
fof(f40277,plain,
composition(top,top) = converse(composition(top,top)),
inference(superposition,[],[f37199,f11776]) ).
fof(f37199,plain,
! [X0] : composition(top,X0) = converse(composition(converse(X0),top)),
inference(superposition,[],[f8,f12054]) ).
fof(f12054,plain,
! [X0] : composition(converse(X0),top) = converse(composition(top,X0)),
inference(superposition,[],[f10,f11776]) ).
fof(f16189,plain,
! [X0,X1] : top = join(X0,converse(join(complement(converse(X0)),X1))),
inference(backward_demodulation,[],[f12080,f15985]) ).
fof(f15985,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[],[f15798,f15787]) ).
fof(f15798,plain,
! [X0] : join(top,X0) = join(one,top),
inference(backward_demodulation,[],[f5381,f15787]) ).
fof(f12080,plain,
! [X0,X1] : join(X0,converse(join(complement(converse(X0)),X1))) = join(top,converse(X1)),
inference(backward_demodulation,[],[f5102,f12052]) ).
fof(f12052,plain,
! [X0] : converse(join(top,X0)) = join(top,converse(X0)),
inference(superposition,[],[f9,f11776]) ).
fof(f5102,plain,
! [X0,X1] : converse(join(top,X1)) = join(X0,converse(join(complement(converse(X0)),X1))),
inference(superposition,[],[f37,f152]) ).
fof(f40476,plain,
! [X0] : join(composition(top,top),converse(X0)) = converse(join(X0,composition(top,top))),
inference(superposition,[],[f39,f40277]) ).
fof(f39,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(superposition,[],[f9,f1]) ).
fof(f40465,plain,
! [X0] : converse(join(X0,composition(top,top))) = join(converse(X0),composition(top,top)),
inference(superposition,[],[f9,f40277]) ).
fof(f40512,plain,
! [X0] : composition(top,top) = join(converse(meet(composition(top,top),X0)),composition(top,top)),
inference(superposition,[],[f19375,f40277]) ).
fof(f19375,plain,
! [X0,X1] : join(converse(meet(converse(X0),X1)),X0) = X0,
inference(forward_demodulation,[],[f19352,f8]) ).
fof(f19352,plain,
! [X0,X1] : converse(converse(X0)) = join(converse(meet(converse(X0),X1)),X0),
inference(superposition,[],[f38,f19269]) ).
fof(f19269,plain,
! [X0,X1] : join(meet(X0,X1),X0) = X0,
inference(backward_demodulation,[],[f15044,f19216]) ).
fof(f19216,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(superposition,[],[f19142,f93]) ).
fof(f15044,plain,
! [X0,X1] : join(meet(X0,X1),X0) = join(X0,meet(X1,X0)),
inference(forward_demodulation,[],[f14983,f6216]) ).
fof(f14983,plain,
! [X0,X1] : join(meet(X0,X1),X0) = join(X0,meet(complement(complement(X1)),X0)),
inference(superposition,[],[f6585,f6580]) ).
fof(f6580,plain,
! [X0,X1] : join(meet(X0,X1),meet(complement(X1),X0)) = X0,
inference(backward_demodulation,[],[f289,f6490]) ).
fof(f6490,plain,
! [X0,X1] : complement(join(X0,complement(X1))) = meet(complement(X0),X1),
inference(superposition,[],[f4,f6216]) ).
fof(f289,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(X1,complement(X0)))) = X0,
inference(superposition,[],[f19,f1]) ).
fof(f78686,plain,
! [X0] : meet(X0,composition(X0,composition(top,top))) = join(meet(top,X0),meet(X0,composition(X0,composition(top,top)))),
inference(forward_demodulation,[],[f78685,f11776]) ).
fof(f78685,plain,
! [X0] : meet(X0,composition(X0,composition(converse(top),top))) = join(meet(top,X0),meet(X0,composition(X0,composition(converse(top),top)))),
inference(forward_demodulation,[],[f78684,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(f78684,plain,
! [X0] : meet(X0,composition(composition(X0,converse(top)),top)) = join(meet(top,X0),meet(X0,composition(composition(X0,converse(top)),top))),
inference(forward_demodulation,[],[f78683,f7084]) ).
fof(f78683,plain,
! [X0] : meet(X0,composition(meet(top,composition(X0,converse(top))),top)) = join(meet(top,X0),meet(X0,composition(meet(top,composition(X0,converse(top))),top))),
inference(forward_demodulation,[],[f78612,f93]) ).
fof(f78612,plain,
! [X0] : meet(composition(meet(top,composition(X0,converse(top))),top),X0) = join(meet(top,X0),meet(composition(meet(top,composition(X0,converse(top))),top),X0)),
inference(superposition,[],[f16,f78104]) ).
fof(f19299,plain,
! [X0,X1] : join(meet(X1,X0),X0) = X0,
inference(superposition,[],[f19269,f93]) ).
fof(f300811,plain,
! [X2,X0,X1] : zero = meet(X0,meet(X2,complement(join(X0,X1)))),
inference(forward_demodulation,[],[f300316,f6216]) ).
fof(f300316,plain,
! [X2,X0,X1] : zero = meet(complement(complement(X0)),meet(X2,complement(join(X0,X1)))),
inference(superposition,[],[f193042,f261267]) ).
fof(f261267,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(X0)),
inference(forward_demodulation,[],[f260828,f6930]) ).
fof(f260828,plain,
! [X0,X1] : join(zero,complement(X0)) = join(complement(join(X0,X1)),complement(X0)),
inference(superposition,[],[f9078,f189871]) ).
fof(f189871,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(forward_demodulation,[],[f189281,f6930]) ).
fof(f189281,plain,
! [X0,X1] : join(zero,complement(X0)) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f177475,f185843]) ).
fof(f185843,plain,
! [X0,X1] : zero = meet(X0,complement(join(X0,X1))),
inference(superposition,[],[f184221,f19859]) ).
fof(f19859,plain,
! [X0,X1] : meet(X0,join(X0,X1)) = X0,
inference(superposition,[],[f15775,f7279]) ).
fof(f15775,plain,
! [X0,X1] : join(meet(X0,join(X0,X1)),zero) = X0,
inference(backward_demodulation,[],[f6223,f15734]) ).
fof(f6223,plain,
! [X0,X1] : join(meet(X0,join(X0,X1)),complement(join(top,X1))) = X0,
inference(backward_demodulation,[],[f5077,f6216]) ).
fof(f5077,plain,
! [X0,X1] : join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))) = X0,
inference(superposition,[],[f19,f152]) ).
fof(f184221,plain,
! [X0,X1] : zero = meet(meet(X1,X0),complement(X0)),
inference(superposition,[],[f184036,f6216]) ).
fof(f184036,plain,
! [X0,X1] : zero = meet(meet(X1,complement(X0)),X0),
inference(forward_demodulation,[],[f183848,f31]) ).
fof(f183848,plain,
! [X0,X1] : complement(top) = meet(meet(X1,complement(X0)),X0),
inference(superposition,[],[f6504,f183687]) ).
fof(f183687,plain,
! [X0,X1] : top = complement(meet(X1,meet(X0,complement(X1)))),
inference(forward_demodulation,[],[f183484,f12]) ).
fof(f183484,plain,
! [X0,X1] : join(meet(X0,complement(X1)),complement(meet(X0,complement(X1)))) = complement(meet(X1,meet(X0,complement(X1)))),
inference(superposition,[],[f182180,f19580]) ).
fof(f19580,plain,
! [X0,X1] : meet(X1,X0) = meet(meet(X1,X0),X0),
inference(forward_demodulation,[],[f19557,f6216]) ).
fof(f19557,plain,
! [X0,X1] : meet(meet(X1,X0),X0) = complement(complement(meet(X1,X0))),
inference(superposition,[],[f6504,f19271]) ).
fof(f19271,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,meet(X0,X1)),
inference(backward_demodulation,[],[f4778,f19216]) ).
fof(f182180,plain,
! [X0,X1] : complement(meet(X1,X0)) = join(meet(X0,complement(X1)),complement(X0)),
inference(forward_demodulation,[],[f182179,f19216]) ).
fof(f182179,plain,
! [X0,X1] : complement(meet(X1,X0)) = join(meet(X0,complement(join(X1,meet(X0,X1)))),complement(X0)),
inference(backward_demodulation,[],[f26017,f182178]) ).
fof(f182178,plain,
! [X2,X3,X0,X1] : meet(meet(complement(X0),X1),complement(meet(X3,X2))) = meet(X1,complement(join(X0,meet(X2,X3)))),
inference(forward_demodulation,[],[f182177,f6491]) ).
fof(f182177,plain,
! [X2,X3,X0,X1] : meet(meet(complement(X0),X1),complement(meet(X3,X2))) = complement(join(complement(X1),join(X0,meet(X2,X3)))),
inference(forward_demodulation,[],[f181958,f2]) ).
fof(f181958,plain,
! [X2,X3,X0,X1] : meet(meet(complement(X0),X1),complement(meet(X3,X2))) = complement(join(join(complement(X1),X0),meet(X2,X3))),
inference(superposition,[],[f6506,f177398]) ).
fof(f177398,plain,
! [X0,X1] : join(complement(X0),X1) = complement(meet(complement(X1),X0)),
inference(forward_demodulation,[],[f177397,f72220]) ).
fof(f72220,plain,
! [X0,X1] : join(complement(X1),meet(X0,X1)) = join(complement(X1),X0),
inference(superposition,[],[f19281,f6580]) ).
fof(f19281,plain,
! [X2,X0,X1] : join(X0,X2) = join(X0,join(X2,meet(X0,X1))),
inference(backward_demodulation,[],[f15041,f19230]) ).
fof(f19230,plain,
! [X2,X0,X1] : join(X0,X2) = join(X0,join(meet(X0,X1),X2)),
inference(superposition,[],[f2,f19142]) ).
fof(f15041,plain,
! [X2,X0,X1] : join(X0,join(X2,meet(X0,X1))) = join(X0,join(meet(X0,X1),X2)),
inference(forward_demodulation,[],[f15040,f6216]) ).
fof(f15040,plain,
! [X2,X0,X1] : join(X0,join(meet(X0,complement(complement(X1))),X2)) = join(X0,join(X2,meet(X0,X1))),
inference(forward_demodulation,[],[f14979,f164]) ).
fof(f14979,plain,
! [X2,X0,X1] : join(X0,join(meet(X0,complement(complement(X1))),X2)) = join(meet(X0,X1),join(X0,X2)),
inference(superposition,[],[f6585,f6585]) ).
fof(f177397,plain,
! [X0,X1] : join(complement(X0),meet(X1,X0)) = complement(meet(complement(X1),X0)),
inference(forward_demodulation,[],[f176903,f72925]) ).
fof(f72925,plain,
! [X2,X0,X1] : complement(meet(complement(X0),X1)) = join(complement(meet(complement(X0),X1)),meet(X2,X0)),
inference(superposition,[],[f72538,f19445]) ).
fof(f19445,plain,
! [X0,X1] : meet(complement(meet(complement(X1),X0)),X1) = X1,
inference(forward_demodulation,[],[f19399,f6216]) ).
fof(f19399,plain,
! [X0,X1] : complement(complement(X1)) = meet(complement(meet(complement(X1),X0)),X1),
inference(superposition,[],[f6505,f19299]) ).
fof(f72538,plain,
! [X2,X0,X1] : join(X1,meet(X0,meet(X1,X2))) = X1,
inference(forward_demodulation,[],[f72228,f19142]) ).
fof(f72228,plain,
! [X2,X0,X1] : join(X1,meet(X0,meet(X1,X2))) = join(X1,meet(X1,X2)),
inference(superposition,[],[f19281,f19299]) ).
fof(f176903,plain,
! [X0,X1] : join(complement(X0),meet(X1,X0)) = join(complement(meet(complement(X1),X0)),meet(X0,X1)),
inference(superposition,[],[f26015,f6580]) ).
fof(f26015,plain,
! [X2,X0,X1] : join(complement(X2),meet(X1,X0)) = join(complement(join(meet(X1,X0),X2)),meet(X0,X1)),
inference(forward_demodulation,[],[f26014,f13887]) ).
fof(f13887,plain,
! [X2,X0,X1] : join(complement(X0),meet(X1,X2)) = complement(meet(X0,complement(meet(X2,X1)))),
inference(superposition,[],[f6216,f6506]) ).
fof(f26014,plain,
! [X2,X0,X1] : complement(meet(X2,complement(meet(X0,X1)))) = join(complement(join(meet(X1,X0),X2)),meet(X0,X1)),
inference(forward_demodulation,[],[f26013,f19216]) ).
fof(f26013,plain,
! [X2,X0,X1] : complement(meet(X2,complement(meet(X0,X1)))) = join(complement(join(meet(X1,X0),join(X2,meet(complement(meet(X0,X1)),X2)))),meet(X0,X1)),
inference(forward_demodulation,[],[f26012,f2]) ).
fof(f26012,plain,
! [X2,X0,X1] : complement(meet(X2,complement(meet(X0,X1)))) = join(complement(join(join(meet(X1,X0),X2),meet(complement(meet(X0,X1)),X2))),meet(X0,X1)),
inference(forward_demodulation,[],[f26011,f13856]) ).
fof(f26011,plain,
! [X2,X0,X1] : complement(meet(X2,complement(meet(X0,X1)))) = join(meet(complement(join(meet(X1,X0),X2)),complement(meet(X2,complement(meet(X0,X1))))),meet(X0,X1)),
inference(forward_demodulation,[],[f26010,f93]) ).
fof(f26010,plain,
! [X2,X0,X1] : complement(meet(X2,complement(meet(X0,X1)))) = join(meet(complement(meet(X2,complement(meet(X0,X1)))),complement(join(meet(X1,X0),X2))),meet(X0,X1)),
inference(forward_demodulation,[],[f25823,f6216]) ).
fof(f25823,plain,
! [X2,X0,X1] : complement(meet(X2,complement(meet(X0,X1)))) = join(meet(complement(meet(X2,complement(meet(X0,X1)))),complement(join(meet(X1,X0),X2))),complement(complement(meet(X0,X1)))),
inference(superposition,[],[f6525,f6525]) ).
fof(f6525,plain,
! [X2,X0,X1] : complement(meet(X1,X0)) = join(meet(complement(meet(X1,X0)),X2),complement(join(meet(X0,X1),X2))),
inference(backward_demodulation,[],[f283,f6485]) ).
fof(f283,plain,
! [X2,X0,X1] : join(complement(X0),complement(X1)) = join(meet(join(complement(X0),complement(X1)),X2),complement(join(meet(X0,X1),X2))),
inference(superposition,[],[f19,f4]) ).
fof(f26017,plain,
! [X0,X1] : complement(meet(X1,X0)) = join(meet(meet(complement(X1),X0),complement(meet(X1,X0))),complement(X0)),
inference(forward_demodulation,[],[f25825,f93]) ).
fof(f25825,plain,
! [X0,X1] : complement(meet(X1,X0)) = join(meet(complement(meet(X1,X0)),meet(complement(X1),X0)),complement(X0)),
inference(superposition,[],[f6525,f6580]) ).
fof(f6504,plain,
! [X0,X1] : meet(X0,X1) = complement(complement(meet(X1,X0))),
inference(backward_demodulation,[],[f4,f6485]) ).
fof(f193042,plain,
! [X2,X0,X1] : zero = meet(complement(join(X1,X2)),meet(X0,X1)),
inference(superposition,[],[f186829,f19565]) ).
fof(f19565,plain,
! [X2,X0,X1] : join(X0,X2) = join(meet(X1,X0),join(meet(X0,complement(meet(X1,X0))),X2)),
inference(superposition,[],[f6585,f19271]) ).
fof(f186829,plain,
! [X0,X1] : zero = meet(complement(join(X0,X1)),X0),
inference(superposition,[],[f185358,f19859]) ).
fof(f185358,plain,
! [X0,X1] : zero = meet(complement(X0),meet(X1,X0)),
inference(superposition,[],[f184077,f6216]) ).
fof(f184077,plain,
! [X0,X1] : zero = meet(X0,meet(X1,complement(X0))),
inference(forward_demodulation,[],[f183925,f31]) ).
fof(f183925,plain,
! [X0,X1] : complement(top) = meet(X0,meet(X1,complement(X0))),
inference(superposition,[],[f6216,f183687]) ).
fof(f177475,plain,
! [X0,X1] : join(complement(X0),X1) = join(meet(X0,X1),complement(X0)),
inference(forward_demodulation,[],[f177414,f22797]) ).
fof(f22797,plain,
! [X2,X0,X1] : meet(X1,X0) = meet(meet(X1,X0),join(X2,X0)),
inference(superposition,[],[f20017,f19216]) ).
fof(f20017,plain,
! [X2,X0,X1] : meet(X0,join(X1,join(X2,X0))) = X0,
inference(superposition,[],[f19859,f164]) ).
fof(f177414,plain,
! [X0,X1] : join(complement(X0),X1) = join(meet(meet(X0,X1),join(complement(X0),X1)),complement(X0)),
inference(backward_demodulation,[],[f26016,f177398]) ).
fof(f26016,plain,
! [X0,X1] : complement(meet(complement(X1),X0)) = join(meet(meet(X0,X1),complement(meet(complement(X1),X0))),complement(X0)),
inference(forward_demodulation,[],[f25824,f93]) ).
fof(f25824,plain,
! [X0,X1] : complement(meet(complement(X1),X0)) = join(meet(complement(meet(complement(X1),X0)),meet(X0,X1)),complement(X0)),
inference(superposition,[],[f6525,f293]) ).
fof(f1052516,plain,
meet(complement(composition(sk1,top)),one) = meet(join(complement(sk1),meet(one,complement(composition(sk1,top)))),one),
inference(superposition,[],[f26050,f647590]) ).
fof(f647590,plain,
one = join(meet(one,complement(composition(sk1,top))),sk1),
inference(forward_demodulation,[],[f647429,f17]) ).
fof(f647429,plain,
join(sk1,one) = join(meet(one,complement(composition(sk1,top))),sk1),
inference(superposition,[],[f8994,f647318]) ).
fof(f647318,plain,
sk1 = join(meet(one,composition(sk1,top)),sk1),
inference(forward_demodulation,[],[f647317,f19859]) ).
fof(f647317,plain,
meet(sk1,join(sk1,complement(one))) = join(meet(one,composition(sk1,top)),meet(sk1,join(sk1,complement(one)))),
inference(forward_demodulation,[],[f647316,f20626]) ).
fof(f20626,plain,
! [X0] : meet(sk1,X0) = meet(one,meet(sk1,X0)),
inference(superposition,[],[f20177,f19295]) ).
fof(f19295,plain,
! [X0] : one = join(meet(sk1,X0),one),
inference(forward_demodulation,[],[f19266,f20]) ).
fof(f19266,plain,
! [X0] : join(one,sk1) = join(meet(sk1,X0),one),
inference(superposition,[],[f8968,f19142]) ).
fof(f8968,plain,
! [X0] : join(one,join(sk1,X0)) = join(X0,one),
inference(superposition,[],[f164,f176]) ).
fof(f176,plain,
! [X0] : join(X0,one) = join(sk1,join(X0,one)),
inference(superposition,[],[f161,f1]) ).
fof(f20177,plain,
! [X0,X1] : meet(join(X0,X1),X0) = X0,
inference(forward_demodulation,[],[f20125,f6216]) ).
fof(f20125,plain,
! [X0,X1] : complement(complement(X0)) = meet(join(X0,X1),X0),
inference(superposition,[],[f6504,f19859]) ).
fof(f647316,plain,
meet(one,meet(sk1,join(sk1,complement(one)))) = join(meet(one,composition(sk1,top)),meet(one,meet(sk1,join(sk1,complement(one))))),
inference(forward_demodulation,[],[f647315,f603633]) ).
fof(f603633,plain,
! [X0] : meet(sk1,X0) = composition(sk1,meet(sk1,X0)),
inference(superposition,[],[f593194,f93]) ).
fof(f593194,plain,
! [X0] : meet(sk1,X0) = composition(sk1,meet(X0,sk1)),
inference(forward_demodulation,[],[f593000,f586671]) ).
fof(f586671,plain,
! [X0] : meet(sk1,X0) = meet(one,composition(sk1,meet(X0,sk1))),
inference(forward_demodulation,[],[f586670,f449775]) ).
fof(f449775,plain,
! [X2,X0,X1] : meet(X1,X0) = join(meet(X2,composition(sk1,meet(X0,X1))),meet(X0,X1)),
inference(forward_demodulation,[],[f449774,f6930]) ).
fof(f449774,plain,
! [X2,X0,X1] : join(zero,meet(X1,X0)) = join(meet(X2,composition(sk1,meet(X0,X1))),meet(X0,X1)),
inference(forward_demodulation,[],[f449773,f31]) ).
fof(f449773,plain,
! [X2,X0,X1] : join(complement(top),meet(X1,X0)) = join(meet(X2,composition(sk1,meet(X0,X1))),meet(X0,X1)),
inference(forward_demodulation,[],[f449489,f6216]) ).
fof(f449489,plain,
! [X2,X0,X1] : join(complement(top),meet(X1,X0)) = join(complement(complement(meet(X2,composition(sk1,meet(X0,X1))))),meet(X0,X1)),
inference(superposition,[],[f26015,f370724]) ).
fof(f370724,plain,
! [X0,X1] : top = join(X0,complement(meet(X1,composition(sk1,X0)))),
inference(superposition,[],[f172395,f182180]) ).
fof(f172395,plain,
! [X0,X1] : top = join(X0,join(X1,complement(composition(sk1,X0)))),
inference(superposition,[],[f145036,f1]) ).
fof(f145036,plain,
! [X0,X1] : top = join(X0,join(complement(composition(sk1,X0)),X1)),
inference(forward_demodulation,[],[f144630,f4776]) ).
fof(f144630,plain,
! [X0,X1] : top = join(composition(one,X0),join(complement(composition(sk1,X0)),X1)),
inference(superposition,[],[f22721,f7410]) ).
fof(f7410,plain,
one = join(meet(one,complement(sk1)),sk1),
inference(superposition,[],[f293,f7220]) ).
fof(f7220,plain,
sk1 = meet(one,sk1),
inference(superposition,[],[f6930,f6173]) ).
fof(f6173,plain,
sk1 = join(zero,meet(one,sk1)),
inference(superposition,[],[f5492,f1]) ).
fof(f5492,plain,
sk1 = join(meet(one,sk1),zero),
inference(forward_demodulation,[],[f5389,f31]) ).
fof(f5389,plain,
sk1 = join(meet(one,sk1),complement(top)),
inference(backward_demodulation,[],[f5337,f5358]) ).
fof(f5337,plain,
sk1 = join(meet(one,sk1),complement(join(one,top))),
inference(forward_demodulation,[],[f5319,f93]) ).
fof(f5319,plain,
sk1 = join(meet(sk1,one),complement(join(one,top))),
inference(superposition,[],[f19,f5204]) ).
fof(f5204,plain,
join(one,top) = join(complement(sk1),one),
inference(forward_demodulation,[],[f5058,f1]) ).
fof(f5058,plain,
join(complement(sk1),one) = join(top,one),
inference(superposition,[],[f152,f176]) ).
fof(f22721,plain,
! [X2,X3,X0,X1] : top = join(composition(join(X3,X0),X1),join(complement(composition(X0,X1)),X2)),
inference(forward_demodulation,[],[f22654,f15787]) ).
fof(f22654,plain,
! [X2,X3,X0,X1] : join(composition(X3,X1),top) = join(composition(join(X3,X0),X1),join(complement(composition(X0,X1)),X2)),
inference(superposition,[],[f445,f15986]) ).
fof(f15986,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(backward_demodulation,[],[f152,f15985]) ).
fof(f445,plain,
! [X2,X3,X0,X1] : join(composition(X0,X1),join(composition(X2,X1),X3)) = join(composition(join(X0,X2),X1),X3),
inference(superposition,[],[f2,f7]) ).
fof(f586670,plain,
! [X0] : meet(one,composition(sk1,meet(X0,sk1))) = join(meet(one,composition(sk1,meet(X0,sk1))),meet(X0,sk1)),
inference(forward_demodulation,[],[f586336,f534411]) ).
fof(f534411,plain,
sk1 = converse(sk1),
inference(superposition,[],[f76,f534223]) ).
fof(f534223,plain,
sk1 = composition(sk1,converse(sk1)),
inference(backward_demodulation,[],[f29838,f534221]) ).
fof(f534221,plain,
! [X0] : join(X0,composition(X0,converse(sk1))) = X0,
inference(forward_demodulation,[],[f534220,f8]) ).
fof(f534220,plain,
! [X0] : converse(converse(X0)) = join(X0,composition(X0,converse(sk1))),
inference(forward_demodulation,[],[f534077,f76]) ).
fof(f534077,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(composition(sk1,converse(X0)))),
inference(superposition,[],[f37,f533541]) ).
fof(f533541,plain,
! [X0] : join(X0,composition(sk1,X0)) = X0,
inference(forward_demodulation,[],[f533315,f6930]) ).
fof(f533315,plain,
! [X0] : join(zero,X0) = join(X0,composition(sk1,X0)),
inference(superposition,[],[f180650,f530794]) ).
fof(f530794,plain,
! [X0] : zero = meet(complement(X0),composition(sk1,X0)),
inference(superposition,[],[f482655,f7084]) ).
fof(f482655,plain,
! [X0] : zero = meet(top,meet(complement(X0),composition(sk1,X0))),
inference(forward_demodulation,[],[f482654,f93]) ).
fof(f482654,plain,
! [X0] : zero = meet(top,meet(composition(sk1,X0),complement(X0))),
inference(forward_demodulation,[],[f481342,f6491]) ).
fof(f481342,plain,
! [X0] : zero = meet(top,complement(join(complement(composition(sk1,X0)),X0))),
inference(superposition,[],[f188751,f172391]) ).
fof(f172391,plain,
! [X0] : top = join(X0,complement(composition(sk1,X0))),
inference(superposition,[],[f145036,f887]) ).
fof(f887,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(superposition,[],[f11,f1]) ).
fof(f188751,plain,
! [X0,X1] : zero = meet(join(X0,X1),complement(join(X1,X0))),
inference(superposition,[],[f185843,f33433]) ).
fof(f33433,plain,
! [X0,X1] : join(X1,X0) = join(join(X0,X1),X0),
inference(forward_demodulation,[],[f33130,f30190]) ).
fof(f30190,plain,
! [X0,X1] : join(X1,X0) = join(join(X0,X1),join(X1,X0)),
inference(superposition,[],[f18071,f11242]) ).
fof(f11242,plain,
! [X0,X1] : join(X1,X0) = join(join(X0,X1),zero),
inference(forward_demodulation,[],[f11062,f6930]) ).
fof(f11062,plain,
! [X0,X1] : join(join(X0,X1),zero) = join(zero,join(X1,X0)),
inference(superposition,[],[f9078,f9078]) ).
fof(f18071,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f2,f18045]) ).
fof(f33130,plain,
! [X0,X1] : join(join(X0,X1),X0) = join(join(X0,X1),join(X1,X0)),
inference(superposition,[],[f30329,f18146]) ).
fof(f18146,plain,
! [X0,X1] : join(X0,X1) = join(X1,join(X1,X0)),
inference(backward_demodulation,[],[f18125,f18126]) ).
fof(f18126,plain,
! [X0,X1] : join(X0,X1) = join(X1,join(X0,X1)),
inference(backward_demodulation,[],[f18064,f18071]) ).
fof(f18064,plain,
! [X0,X1] : join(X0,X1) = join(X1,join(X0,join(X0,X1))),
inference(superposition,[],[f18045,f153]) ).
fof(f153,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(superposition,[],[f2,f1]) ).
fof(f18125,plain,
! [X0,X1] : join(X0,X1) = join(X1,join(X0,join(X1,X0))),
inference(forward_demodulation,[],[f18063,f2]) ).
fof(f18063,plain,
! [X0,X1] : join(X0,X1) = join(X1,join(join(X0,X1),X0)),
inference(superposition,[],[f18045,f164]) ).
fof(f30329,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,X0)),
inference(superposition,[],[f18071,f164]) ).
fof(f180650,plain,
! [X0,X1] : join(X0,X1) = join(meet(complement(X0),X1),X0),
inference(superposition,[],[f177475,f6216]) ).
fof(f29838,plain,
composition(sk1,converse(sk1)) = join(sk1,composition(sk1,converse(sk1))),
inference(forward_demodulation,[],[f29837,f21609]) ).
fof(f21609,plain,
converse(sk1) = meet(one,converse(sk1)),
inference(superposition,[],[f20177,f21516]) ).
fof(f21516,plain,
one = join(converse(sk1),one),
inference(superposition,[],[f21394,f7220]) ).
fof(f21394,plain,
! [X0] : one = join(converse(meet(one,X0)),one),
inference(superposition,[],[f19375,f4744]) ).
fof(f29837,plain,
composition(sk1,meet(one,converse(sk1))) = join(sk1,composition(sk1,meet(one,converse(sk1)))),
inference(forward_demodulation,[],[f29773,f6]) ).
fof(f29773,plain,
composition(sk1,meet(one,composition(converse(sk1),one))) = join(sk1,composition(sk1,meet(one,composition(converse(sk1),one)))),
inference(superposition,[],[f4779,f20121]) ).
fof(f20121,plain,
sk1 = meet(sk1,one),
inference(superposition,[],[f19859,f8059]) ).
fof(f8059,plain,
one = join(sk1,meet(one,complement(sk1))),
inference(forward_demodulation,[],[f8035,f93]) ).
fof(f8035,plain,
one = join(sk1,meet(complement(sk1),one)),
inference(superposition,[],[f6580,f7220]) ).
fof(f4779,plain,
! [X0,X1] : composition(meet(X0,X1),meet(one,composition(converse(X0),X1))) = join(meet(X0,X1),composition(meet(X0,X1),meet(one,composition(converse(X0),X1)))),
inference(forward_demodulation,[],[f4768,f6]) ).
fof(f4768,plain,
! [X0,X1] : composition(meet(X0,composition(X1,one)),meet(one,composition(converse(X0),X1))) = join(meet(X0,X1),composition(meet(X0,composition(X1,one)),meet(one,composition(converse(X0),X1)))),
inference(backward_demodulation,[],[f2805,f4744]) ).
fof(f2805,plain,
! [X0,X1] : composition(meet(X0,composition(X1,converse(one))),meet(one,composition(converse(X0),X1))) = join(meet(X0,X1),composition(meet(X0,composition(X1,converse(one))),meet(one,composition(converse(X0),X1)))),
inference(superposition,[],[f14,f6]) ).
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(f76,plain,
! [X0,X1] : composition(X0,converse(X1)) = converse(composition(X1,converse(X0))),
inference(superposition,[],[f10,f8]) ).
fof(f586336,plain,
! [X0] : meet(one,composition(converse(sk1),meet(X0,sk1))) = join(meet(one,composition(converse(sk1),meet(X0,sk1))),meet(X0,sk1)),
inference(superposition,[],[f577489,f28853]) ).
fof(f28853,plain,
! [X0,X1] : meet(X1,X0) = meet(meet(X1,X0),composition(X0,meet(one,composition(converse(X0),meet(X1,X0))))),
inference(forward_demodulation,[],[f28782,f19142]) ).
fof(f28782,plain,
! [X0,X1] : meet(meet(X1,X0),composition(X0,meet(one,composition(converse(X0),meet(X1,X0))))) = join(meet(X1,X0),meet(meet(X1,X0),composition(X0,meet(one,composition(converse(X0),meet(X1,X0)))))),
inference(superposition,[],[f1387,f19271]) ).
fof(f1387,plain,
! [X0,X1] : meet(X1,composition(X0,meet(one,composition(converse(X0),X1)))) = join(meet(X0,X1),meet(X1,composition(X0,meet(one,composition(converse(X0),X1))))),
inference(forward_demodulation,[],[f1368,f93]) ).
fof(f1368,plain,
! [X0,X1] : meet(composition(X0,meet(one,composition(converse(X0),X1))),X1) = join(meet(X0,X1),meet(composition(X0,meet(one,composition(converse(X0),X1))),X1)),
inference(superposition,[],[f15,f6]) ).
fof(f15,axiom,
! [X2,X0,X1] : meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2) = join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_1_15) ).
fof(f577489,plain,
! [X0,X1] : join(X0,meet(X1,composition(sk1,X0))) = X0,
inference(superposition,[],[f72897,f533877]) ).
fof(f533877,plain,
! [X0] : composition(sk1,X0) = meet(composition(sk1,X0),X0),
inference(superposition,[],[f20013,f533541]) ).
fof(f20013,plain,
! [X0,X1] : meet(X0,join(X1,X0)) = X0,
inference(superposition,[],[f19859,f1]) ).
fof(f72897,plain,
! [X2,X0,X1] : join(X0,meet(X2,meet(X1,X0))) = X0,
inference(superposition,[],[f72538,f93]) ).
fof(f593000,plain,
! [X0] : composition(sk1,meet(X0,sk1)) = meet(one,composition(sk1,meet(X0,sk1))),
inference(superposition,[],[f20177,f577620]) ).
fof(f577620,plain,
! [X0] : one = join(composition(sk1,meet(X0,sk1)),one),
inference(superposition,[],[f73890,f533877]) ).
fof(f73890,plain,
! [X0,X1] : one = join(meet(X0,meet(X1,sk1)),one),
inference(forward_demodulation,[],[f73855,f20]) ).
fof(f73855,plain,
! [X0,X1] : join(one,sk1) = join(meet(X0,meet(X1,sk1)),one),
inference(superposition,[],[f8968,f72897]) ).
fof(f647315,plain,
meet(one,composition(sk1,meet(sk1,join(sk1,complement(one))))) = join(meet(one,composition(sk1,top)),meet(one,composition(sk1,meet(sk1,join(sk1,complement(one)))))),
inference(forward_demodulation,[],[f647314,f534411]) ).
fof(f647314,plain,
meet(one,composition(sk1,meet(converse(sk1),join(sk1,complement(one))))) = join(meet(one,composition(sk1,top)),meet(one,composition(sk1,meet(converse(sk1),join(sk1,complement(one)))))),
inference(forward_demodulation,[],[f647195,f93]) ).
fof(f647195,plain,
meet(one,composition(sk1,meet(join(sk1,complement(one)),converse(sk1)))) = join(meet(one,composition(sk1,top)),meet(one,composition(sk1,meet(join(sk1,complement(one)),converse(sk1))))),
inference(superposition,[],[f1399,f630793]) ).
fof(f630793,plain,
composition(sk1,top) = composition(sk1,join(sk1,complement(one))),
inference(forward_demodulation,[],[f630792,f11776]) ).
fof(f630792,plain,
composition(sk1,converse(top)) = composition(sk1,join(sk1,complement(one))),
inference(forward_demodulation,[],[f630791,f535906]) ).
fof(f535906,plain,
! [X0] : composition(sk1,converse(X0)) = converse(composition(X0,sk1)),
inference(superposition,[],[f10,f534411]) ).
fof(f630791,plain,
converse(composition(top,sk1)) = composition(sk1,join(sk1,complement(one))),
inference(forward_demodulation,[],[f630790,f12]) ).
fof(f630790,plain,
composition(sk1,join(sk1,complement(one))) = converse(composition(join(one,complement(one)),sk1)),
inference(forward_demodulation,[],[f630506,f532266]) ).
fof(f532266,plain,
! [X0] : composition(join(sk1,X0),sk1) = composition(join(one,X0),sk1),
inference(forward_demodulation,[],[f532248,f474949]) ).
fof(f474949,plain,
! [X0] : composition(join(one,X0),sk1) = join(composition(join(X0,one),sk1),sk1),
inference(forward_demodulation,[],[f474948,f6930]) ).
fof(f474948,plain,
! [X0] : join(composition(join(X0,one),sk1),sk1) = join(zero,composition(join(one,X0),sk1)),
inference(forward_demodulation,[],[f474697,f225433]) ).
fof(f225433,plain,
! [X2,X3,X0,X1] : join(composition(join(X0,X2),X1),X3) = join(X3,composition(join(X2,X0),X1)),
inference(forward_demodulation,[],[f223458,f7]) ).
fof(f223458,plain,
! [X2,X3,X0,X1] : join(composition(join(X0,X2),X1),X3) = join(X3,join(composition(X2,X1),composition(X0,X1))),
inference(superposition,[],[f8455,f445]) ).
fof(f8455,plain,
! [X2,X0,X1] : join(X2,join(X0,X1)) = join(X1,join(X0,X2)),
inference(superposition,[],[f153,f1]) ).
fof(f474697,plain,
! [X0] : join(composition(join(X0,one),sk1),sk1) = join(composition(join(X0,one),sk1),zero),
inference(superposition,[],[f194328,f185945]) ).
fof(f185945,plain,
! [X0] : zero = meet(sk1,complement(composition(join(X0,one),sk1))),
inference(superposition,[],[f184221,f33767]) ).
fof(f33767,plain,
! [X0] : sk1 = meet(sk1,composition(join(X0,one),sk1)),
inference(superposition,[],[f32422,f176]) ).
fof(f32422,plain,
! [X0] : sk1 = meet(sk1,composition(join(sk1,X0),sk1)),
inference(superposition,[],[f29876,f443]) ).
fof(f443,plain,
! [X2,X0,X1] : composition(join(X0,X2),X1) = join(composition(X2,X1),composition(X0,X1)),
inference(superposition,[],[f7,f1]) ).
fof(f29876,plain,
! [X0] : sk1 = meet(sk1,join(X0,composition(sk1,sk1))),
inference(superposition,[],[f20018,f29825]) ).
fof(f29825,plain,
composition(sk1,sk1) = join(sk1,composition(sk1,sk1)),
inference(forward_demodulation,[],[f29824,f7220]) ).
fof(f29824,plain,
composition(sk1,meet(one,sk1)) = join(sk1,composition(sk1,meet(one,sk1))),
inference(forward_demodulation,[],[f29823,f4776]) ).
fof(f29823,plain,
composition(sk1,meet(one,composition(one,sk1))) = join(sk1,composition(sk1,meet(one,composition(one,sk1)))),
inference(forward_demodulation,[],[f29767,f4744]) ).
fof(f29767,plain,
composition(sk1,meet(one,composition(converse(one),sk1))) = join(sk1,composition(sk1,meet(one,composition(converse(one),sk1)))),
inference(superposition,[],[f4779,f7220]) ).
fof(f20018,plain,
! [X2,X0,X1] : meet(X0,join(X2,join(X0,X1))) = X0,
inference(superposition,[],[f19859,f164]) ).
fof(f194328,plain,
! [X0,X1] : join(X1,X0) = join(X1,meet(X0,complement(X1))),
inference(superposition,[],[f19281,f292]) ).
fof(f292,plain,
! [X0,X1] : join(meet(X0,complement(X1)),meet(X1,X0)) = X0,
inference(superposition,[],[f19,f27]) ).
fof(f532248,plain,
! [X0] : composition(join(sk1,X0),sk1) = join(composition(join(X0,one),sk1),sk1),
inference(backward_demodulation,[],[f426191,f532197]) ).
fof(f532197,plain,
! [X0] : composition(join(X0,sk1),sk1) = composition(join(X0,one),sk1),
inference(forward_demodulation,[],[f532063,f4800]) ).
fof(f4800,plain,
! [X0,X1] : join(composition(X1,X0),X0) = composition(join(X1,one),X0),
inference(forward_demodulation,[],[f4753,f4744]) ).
fof(f4753,plain,
! [X0,X1] : composition(join(X1,converse(one)),X0) = join(composition(X1,X0),X0),
inference(superposition,[],[f7,f4724]) ).
fof(f532063,plain,
! [X0] : composition(join(X0,sk1),sk1) = join(composition(X0,sk1),sk1),
inference(superposition,[],[f7,f530983]) ).
fof(f530983,plain,
sk1 = composition(sk1,sk1),
inference(forward_demodulation,[],[f530973,f7279]) ).
fof(f530973,plain,
join(sk1,zero) = composition(sk1,sk1),
inference(backward_demodulation,[],[f29971,f530794]) ).
fof(f29971,plain,
composition(sk1,sk1) = join(sk1,meet(complement(sk1),composition(sk1,sk1))),
inference(superposition,[],[f6580,f29877]) ).
fof(f29877,plain,
sk1 = meet(composition(sk1,sk1),sk1),
inference(superposition,[],[f20177,f29825]) ).
fof(f426191,plain,
! [X0] : composition(join(sk1,X0),sk1) = join(composition(join(X0,sk1),sk1),sk1),
inference(forward_demodulation,[],[f426190,f6930]) ).
fof(f426190,plain,
! [X0] : join(composition(join(X0,sk1),sk1),sk1) = join(zero,composition(join(sk1,X0),sk1)),
inference(forward_demodulation,[],[f425998,f225433]) ).
fof(f425998,plain,
! [X0] : join(composition(join(X0,sk1),sk1),sk1) = join(composition(join(X0,sk1),sk1),zero),
inference(superposition,[],[f194328,f185944]) ).
fof(f185944,plain,
! [X0] : zero = meet(sk1,complement(composition(join(X0,sk1),sk1))),
inference(superposition,[],[f184221,f32423]) ).
fof(f32423,plain,
! [X0] : sk1 = meet(sk1,composition(join(X0,sk1),sk1)),
inference(superposition,[],[f29876,f7]) ).
fof(f630506,plain,
composition(sk1,join(sk1,complement(one))) = converse(composition(join(sk1,complement(one)),sk1)),
inference(superposition,[],[f557815,f570665]) ).
fof(f570665,plain,
join(sk1,complement(one)) = converse(join(sk1,complement(one))),
inference(superposition,[],[f557384,f211404]) ).
fof(f211404,plain,
complement(one) = converse(complement(one)),
inference(superposition,[],[f129,f207887]) ).
fof(f207887,plain,
complement(one) = join(complement(one),converse(complement(one))),
inference(forward_demodulation,[],[f207707,f6930]) ).
fof(f207707,plain,
join(zero,complement(one)) = join(complement(one),converse(complement(one))),
inference(superposition,[],[f177475,f207336]) ).
fof(f207336,plain,
zero = meet(one,converse(complement(one))),
inference(superposition,[],[f207072,f93]) ).
fof(f207072,plain,
zero = meet(converse(complement(one)),one),
inference(superposition,[],[f202070,f6]) ).
fof(f202070,plain,
! [X0] : zero = meet(composition(converse(complement(X0)),X0),one),
inference(superposition,[],[f189581,f6216]) ).
fof(f189581,plain,
! [X0] : zero = meet(composition(converse(X0),complement(X0)),one),
inference(forward_demodulation,[],[f188985,f6216]) ).
fof(f188985,plain,
! [X0] : zero = meet(composition(converse(X0),complement(X0)),complement(complement(one))),
inference(superposition,[],[f185843,f878]) ).
fof(f878,plain,
! [X0] : complement(one) = join(composition(converse(X0),complement(X0)),complement(one)),
inference(superposition,[],[f11,f6]) ).
fof(f129,plain,
! [X0,X1] : join(X0,converse(X1)) = converse(join(X1,converse(X0))),
inference(superposition,[],[f37,f1]) ).
fof(f557384,plain,
! [X0] : join(sk1,X0) = converse(join(sk1,converse(X0))),
inference(superposition,[],[f8,f535903]) ).
fof(f535903,plain,
! [X0] : converse(join(sk1,X0)) = join(sk1,converse(X0)),
inference(superposition,[],[f9,f534411]) ).
fof(f557815,plain,
! [X0] : composition(sk1,X0) = converse(composition(converse(X0),sk1)),
inference(superposition,[],[f8,f535905]) ).
fof(f535905,plain,
! [X0] : composition(converse(X0),sk1) = converse(composition(sk1,X0)),
inference(superposition,[],[f10,f534411]) ).
fof(f1399,plain,
! [X0,X1] : meet(one,composition(X0,meet(X1,converse(X0)))) = join(meet(one,composition(X0,X1)),meet(one,composition(X0,meet(X1,converse(X0))))),
inference(forward_demodulation,[],[f1398,f93]) ).
fof(f1398,plain,
! [X0,X1] : meet(one,composition(X0,meet(X1,converse(X0)))) = join(meet(composition(X0,X1),one),meet(one,composition(X0,meet(X1,converse(X0))))),
inference(forward_demodulation,[],[f1377,f93]) ).
fof(f1377,plain,
! [X0,X1] : meet(composition(X0,meet(X1,converse(X0))),one) = join(meet(composition(X0,X1),one),meet(composition(X0,meet(X1,converse(X0))),one)),
inference(superposition,[],[f15,f6]) ).
fof(f8994,plain,
! [X2,X0,X1] : join(X2,X0) = join(meet(X0,complement(X1)),join(meet(X0,X1),X2)),
inference(superposition,[],[f164,f293]) ).
fof(f26050,plain,
! [X2,X0,X1] : meet(X0,X1) = meet(join(complement(X2),meet(X1,X0)),join(meet(X1,X0),X2)),
inference(forward_demodulation,[],[f26049,f6216]) ).
fof(f26049,plain,
! [X2,X0,X1] : complement(complement(meet(X0,X1))) = meet(join(complement(X2),meet(X1,X0)),join(meet(X1,X0),X2)),
inference(forward_demodulation,[],[f25851,f13887]) ).
fof(f25851,plain,
! [X2,X0,X1] : complement(complement(meet(X0,X1))) = meet(complement(meet(X2,complement(meet(X0,X1)))),join(meet(X1,X0),X2)),
inference(superposition,[],[f6505,f6525]) ).
fof(f18,axiom,
meet(complement(composition(sk1,top)),one) != meet(complement(sk1),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL027-3 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 08:04:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (9760)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (9767)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)
% 0.20/0.39 % (9763)WARNING: value z3 for option sas not known
% 0.20/0.39 % (9766)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)
% 0.20/0.39 % (9763)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)
% 0.20/0.39 % (9764)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.39 % (9765)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)
% 0.20/0.40 TRYING [1]
% 0.20/0.40 TRYING [2]
% 0.20/0.40 % (9761)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.40 % (9762)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.41 TRYING [1]
% 0.20/0.42 TRYING [2]
% 0.20/0.42 TRYING [3]
% 0.20/0.45 TRYING [3]
% 0.20/0.48 TRYING [4]
% 0.20/0.53 TRYING [4]
% 1.89/0.66 TRYING [5]
% 4.72/1.04 TRYING [5]
% 6.21/1.25 TRYING [6]
% 7.57/1.47 TRYING [1]
% 7.57/1.47 TRYING [2]
% 7.79/1.48 TRYING [3]
% 8.16/1.54 TRYING [4]
% 9.93/1.80 TRYING [5]
% 16.70/2.76 TRYING [6]
% 21.77/3.48 TRYING [7]
% 24.45/3.92 TRYING [6]
% 46.43/7.05 TRYING [7]
% 90.07/13.31 TRYING [8]
% 134.95/19.70 TRYING [8]
% 233.35/33.75 TRYING [7]
% 277.87/40.09 TRYING [9]
% 290.54/41.89 % (9766)First to succeed.
% 290.54/41.96 % (9766)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9760"
% 291.25/41.99 % (9766)Refutation found. Thanks to Tanya!
% 291.25/41.99 % SZS status Unsatisfiable for theBenchmark
% 291.25/41.99 % SZS output start Proof for theBenchmark
% See solution above
% 291.25/41.99 % (9766)------------------------------
% 291.25/41.99 % (9766)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 291.25/41.99 % (9766)Termination reason: Refutation
% 291.25/41.99
% 291.25/41.99 % (9766)Memory used [KB]: 444959
% 291.25/41.99 % (9766)Time elapsed: 41.574 s
% 291.25/41.99 % (9766)Instructions burned: 106667 (million)
% 291.25/41.99 % (9760)Success in time 41.204 s
%------------------------------------------------------------------------------