TSTP Solution File: REL011-2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : REL011-2 : 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 : n002.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 02:35:21 EDT 2024
% Result : Unsatisfiable 5.05s 1.11s
% Output : Refutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 16
% Syntax : Number of formulae : 219 ( 219 unt; 0 def)
% Number of atoms : 219 ( 218 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 205 ( 205 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14711,plain,
$false,
inference(trivial_inequality_removal,[],[f14695]) ).
fof(f14695,plain,
zero != zero,
inference(superposition,[],[f114,f14450]) ).
fof(f14450,plain,
zero = meet(sk3,composition(sk2,sk1)),
inference(forward_demodulation,[],[f14449,f466]) ).
fof(f466,plain,
zero = join(zero,zero),
inference(forward_demodulation,[],[f458,f27]) ).
fof(f27,plain,
zero = complement(top),
inference(forward_demodulation,[],[f22,f13]) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f22,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(superposition,[],[f4,f12]) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f4,axiom,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f458,plain,
zero = join(zero,complement(top)),
inference(backward_demodulation,[],[f384,f456]) ).
fof(f456,plain,
top = join(top,top),
inference(forward_demodulation,[],[f449,f12]) ).
fof(f449,plain,
join(zero,complement(zero)) = join(top,top),
inference(superposition,[],[f424,f1]) ).
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f424,plain,
join(top,top) = join(complement(zero),zero),
inference(forward_demodulation,[],[f423,f27]) ).
fof(f423,plain,
join(top,top) = join(complement(zero),complement(top)),
inference(forward_demodulation,[],[f422,f416]) ).
fof(f416,plain,
top = join(top,complement(join(top,top))),
inference(forward_demodulation,[],[f415,f39]) ).
fof(f39,plain,
top = join(zero,top),
inference(superposition,[],[f31,f1]) ).
fof(f31,plain,
top = join(top,zero),
inference(superposition,[],[f12,f27]) ).
fof(f415,plain,
join(zero,top) = join(top,complement(join(top,top))),
inference(forward_demodulation,[],[f413,f1]) ).
fof(f413,plain,
join(top,zero) = join(top,complement(join(top,top))),
inference(superposition,[],[f157,f384]) ).
fof(f157,plain,
! [X0] : join(top,X0) = join(top,join(zero,X0)),
inference(superposition,[],[f2,f31]) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f422,plain,
join(top,top) = join(complement(zero),complement(join(top,complement(join(top,top))))),
inference(forward_demodulation,[],[f419,f1]) ).
fof(f419,plain,
join(top,top) = join(complement(zero),complement(join(complement(join(top,top)),top))),
inference(superposition,[],[f19,f411]) ).
fof(f411,plain,
complement(zero) = meet(join(top,top),top),
inference(superposition,[],[f32,f384]) ).
fof(f32,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[],[f28,f1]) ).
fof(f28,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(superposition,[],[f4,f27]) ).
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/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f384,plain,
zero = join(zero,complement(join(top,top))),
inference(forward_demodulation,[],[f383,f202]) ).
fof(f202,plain,
join(top,top) = join(top,complement(zero)),
inference(superposition,[],[f157,f12]) ).
fof(f383,plain,
zero = join(zero,complement(join(top,complement(zero)))),
inference(forward_demodulation,[],[f357,f1]) ).
fof(f357,plain,
zero = join(zero,complement(join(complement(zero),top))),
inference(superposition,[],[f19,f73]) ).
fof(f73,plain,
zero = meet(zero,top),
inference(forward_demodulation,[],[f62,f27]) ).
fof(f62,plain,
complement(top) = meet(zero,top),
inference(superposition,[],[f32,f12]) ).
fof(f14449,plain,
join(zero,zero) = meet(sk3,composition(sk2,sk1)),
inference(forward_demodulation,[],[f14448,f13171]) ).
fof(f13171,plain,
! [X0] : zero = meet(zero,X0),
inference(superposition,[],[f13105,f93]) ).
fof(f93,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(superposition,[],[f23,f4]) ).
fof(f23,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(superposition,[],[f4,f1]) ).
fof(f13105,plain,
! [X0] : zero = meet(X0,zero),
inference(backward_demodulation,[],[f12223,f13053]) ).
fof(f13053,plain,
! [X0] : zero = join(meet(zero,X0),zero),
inference(superposition,[],[f11093,f372]) ).
fof(f372,plain,
! [X0] : join(zero,meet(X0,X0)) = X0,
inference(forward_demodulation,[],[f350,f4]) ).
fof(f350,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[],[f19,f13]) ).
fof(f11093,plain,
! [X0,X1] : join(meet(X0,join(X0,X1)),zero) = X0,
inference(forward_demodulation,[],[f10778,f27]) ).
fof(f10778,plain,
! [X0,X1] : join(meet(X0,join(X0,X1)),complement(top)) = X0,
inference(backward_demodulation,[],[f2739,f10730]) ).
fof(f10730,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[],[f10311,f10300]) ).
fof(f10300,plain,
! [X0] : top = join(X0,top),
inference(backward_demodulation,[],[f5718,f10298]) ).
fof(f10298,plain,
! [X0,X1] : top = join(top,meet(X1,X0)),
inference(backward_demodulation,[],[f3469,f10297]) ).
fof(f10297,plain,
! [X0,X1] : top = join(meet(X0,X1),top),
inference(forward_demodulation,[],[f10281,f12]) ).
fof(f10281,plain,
! [X0,X1] : top = join(meet(X0,X1),join(meet(X1,meet(X0,X1)),complement(meet(X1,meet(X0,X1))))),
inference(superposition,[],[f160,f1922]) ).
fof(f1922,plain,
! [X0,X1] : meet(X1,meet(X0,X1)) = join(meet(X0,X1),meet(X1,meet(X0,X1))),
inference(forward_demodulation,[],[f1912,f6]) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f1912,plain,
! [X0,X1] : meet(X1,meet(X0,composition(X1,one))) = join(meet(X0,X1),meet(X1,meet(X0,composition(X1,one)))),
inference(backward_demodulation,[],[f720,f1888]) ).
fof(f1888,plain,
one = converse(one),
inference(superposition,[],[f1867,f6]) ).
fof(f1867,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f1841,f8]) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f1841,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f77,f6]) ).
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/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f720,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,[],[f719,f6]) ).
fof(f719,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,[],[f699,f93]) ).
fof(f699,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/sandbox2/benchmark/theBenchmark.p',modular_law_2_16) ).
fof(f160,plain,
! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))),
inference(superposition,[],[f2,f12]) ).
fof(f3469,plain,
! [X0,X1] : join(top,meet(X1,X0)) = join(meet(X0,X1),top),
inference(superposition,[],[f150,f2843]) ).
fof(f2843,plain,
! [X0,X1] : top = join(complement(meet(X1,X0)),meet(X0,X1)),
inference(backward_demodulation,[],[f26,f2819]) ).
fof(f2819,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X1,X0)),
inference(superposition,[],[f2731,f23]) ).
fof(f2731,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f2730,f970]) ).
fof(f970,plain,
! [X0] : join(zero,meet(X0,complement(complement(X0)))) = X0,
inference(superposition,[],[f385,f1]) ).
fof(f385,plain,
! [X0] : join(meet(X0,complement(complement(X0))),zero) = X0,
inference(forward_demodulation,[],[f365,f27]) ).
fof(f365,plain,
! [X0] : join(meet(X0,complement(complement(X0))),complement(top)) = X0,
inference(superposition,[],[f19,f12]) ).
fof(f2730,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[],[f2713,f93]) ).
fof(f2713,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(superposition,[],[f370,f102]) ).
fof(f102,plain,
! [X0] : zero = meet(complement(X0),X0),
inference(forward_demodulation,[],[f90,f27]) ).
fof(f90,plain,
! [X0] : complement(top) = meet(complement(X0),X0),
inference(superposition,[],[f23,f12]) ).
fof(f370,plain,
! [X0,X1] : join(meet(X0,complement(X1)),meet(X0,X1)) = X0,
inference(superposition,[],[f19,f4]) ).
fof(f26,plain,
! [X0,X1] : top = join(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(superposition,[],[f12,f4]) ).
fof(f150,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f12]) ).
fof(f5718,plain,
! [X0] : join(X0,top) = join(top,meet(X0,X0)),
inference(superposition,[],[f5266,f2733]) ).
fof(f2733,plain,
! [X0] : join(meet(X0,X0),zero) = X0,
inference(backward_demodulation,[],[f385,f2731]) ).
fof(f5266,plain,
! [X0] : join(top,X0) = join(join(X0,zero),top),
inference(forward_demodulation,[],[f5212,f2098]) ).
fof(f2098,plain,
! [X0] : join(top,X0) = join(sk1,join(top,X0)),
inference(backward_demodulation,[],[f801,f1999]) ).
fof(f1999,plain,
! [X0] : join(top,X0) = join(sk1,join(X0,top)),
inference(backward_demodulation,[],[f1352,f1929]) ).
fof(f1929,plain,
top = join(sk1,top),
inference(backward_demodulation,[],[f1615,f1928]) ).
fof(f1928,plain,
top = join(top,complement(meet(sk1,join(sk1,top)))),
inference(forward_demodulation,[],[f1894,f1910]) ).
fof(f1910,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f1867,f1888]) ).
fof(f1894,plain,
top = join(top,complement(composition(one,meet(sk1,join(sk1,top))))),
inference(superposition,[],[f689,f1867]) ).
fof(f689,plain,
! [X0] : top = join(top,composition(converse(X0),complement(composition(X0,meet(sk1,join(sk1,top)))))),
inference(forward_demodulation,[],[f686,f578]) ).
fof(f578,plain,
top = join(sk1,complement(meet(sk1,join(sk1,top)))),
inference(forward_demodulation,[],[f568,f39]) ).
fof(f568,plain,
join(zero,top) = join(sk1,complement(meet(sk1,join(sk1,top)))),
inference(superposition,[],[f556,f12]) ).
fof(f556,plain,
! [X0] : join(sk1,X0) = join(zero,join(meet(sk1,join(sk1,top)),X0)),
inference(backward_demodulation,[],[f396,f554]) ).
fof(f554,plain,
complement(join(complement(sk1),composition(converse(sk2),sk3))) = meet(sk1,join(sk1,top)),
inference(forward_demodulation,[],[f550,f93]) ).
fof(f550,plain,
complement(join(complement(sk1),composition(converse(sk2),sk3))) = meet(join(sk1,top),sk1),
inference(superposition,[],[f23,f404]) ).
fof(f404,plain,
join(complement(sk1),composition(converse(sk2),sk3)) = join(complement(sk1),complement(join(sk1,top))),
inference(forward_demodulation,[],[f403,f397]) ).
fof(f397,plain,
join(top,complement(join(complement(sk1),composition(converse(sk2),sk3)))) = join(sk1,top),
inference(forward_demodulation,[],[f395,f1]) ).
fof(f395,plain,
join(top,complement(join(complement(sk1),composition(converse(sk2),sk3)))) = join(top,sk1),
inference(superposition,[],[f157,f358]) ).
fof(f358,plain,
sk1 = join(zero,complement(join(complement(sk1),composition(converse(sk2),sk3)))),
inference(superposition,[],[f19,f17]) ).
fof(f17,axiom,
zero = meet(sk1,composition(converse(sk2),sk3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f403,plain,
join(complement(sk1),composition(converse(sk2),sk3)) = join(complement(sk1),complement(join(top,complement(join(complement(sk1),composition(converse(sk2),sk3)))))),
inference(forward_demodulation,[],[f400,f1]) ).
fof(f400,plain,
join(complement(sk1),composition(converse(sk2),sk3)) = join(complement(sk1),complement(join(complement(join(complement(sk1),composition(converse(sk2),sk3))),top))),
inference(superposition,[],[f19,f393]) ).
fof(f393,plain,
complement(sk1) = meet(join(complement(sk1),composition(converse(sk2),sk3)),top),
inference(superposition,[],[f32,f358]) ).
fof(f396,plain,
! [X0] : join(zero,join(complement(join(complement(sk1),composition(converse(sk2),sk3))),X0)) = join(sk1,X0),
inference(superposition,[],[f2,f358]) ).
fof(f686,plain,
! [X0] : join(sk1,complement(meet(sk1,join(sk1,top)))) = join(top,composition(converse(X0),complement(composition(X0,meet(sk1,join(sk1,top)))))),
inference(superposition,[],[f657,f11]) ).
fof(f11,axiom,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f657,plain,
! [X0] : join(top,X0) = join(sk1,join(X0,complement(meet(sk1,join(sk1,top))))),
inference(superposition,[],[f583,f1]) ).
fof(f583,plain,
! [X0] : join(top,X0) = join(sk1,join(complement(meet(sk1,join(sk1,top))),X0)),
inference(superposition,[],[f2,f578]) ).
fof(f1615,plain,
top = join(sk1,join(top,complement(meet(sk1,join(sk1,top))))),
inference(forward_demodulation,[],[f1614,f150]) ).
fof(f1614,plain,
top = join(sk1,join(top,join(complement(top),complement(meet(sk1,join(sk1,top)))))),
inference(forward_demodulation,[],[f1613,f456]) ).
fof(f1613,plain,
top = join(sk1,join(top,join(complement(join(top,top)),complement(meet(sk1,join(sk1,top)))))),
inference(forward_demodulation,[],[f1580,f1]) ).
fof(f1580,plain,
top = join(sk1,join(top,join(complement(meet(sk1,join(sk1,top))),complement(join(top,top))))),
inference(superposition,[],[f1315,f583]) ).
fof(f1315,plain,
! [X0] : top = join(sk1,join(top,join(X0,complement(join(sk1,join(X0,top)))))),
inference(superposition,[],[f827,f12]) ).
fof(f827,plain,
! [X0,X1] : join(join(sk1,join(X0,top)),X1) = join(sk1,join(top,join(X0,X1))),
inference(forward_demodulation,[],[f824,f2]) ).
fof(f824,plain,
! [X0,X1] : join(join(sk1,join(X0,top)),X1) = join(sk1,join(join(top,X0),X1)),
inference(superposition,[],[f2,f801]) ).
fof(f1352,plain,
! [X0] : join(join(sk1,top),X0) = join(sk1,join(X0,top)),
inference(forward_demodulation,[],[f1351,f215]) ).
fof(f215,plain,
! [X0] : join(X0,top) = join(zero,join(X0,top)),
inference(superposition,[],[f158,f1]) ).
fof(f158,plain,
! [X0] : join(top,X0) = join(zero,join(top,X0)),
inference(superposition,[],[f2,f39]) ).
fof(f1351,plain,
! [X0] : join(join(sk1,top),X0) = join(sk1,join(zero,join(X0,top))),
inference(forward_demodulation,[],[f1311,f161]) ).
fof(f161,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f2,f1]) ).
fof(f1311,plain,
! [X0] : join(join(sk1,top),X0) = join(sk1,join(top,join(zero,X0))),
inference(superposition,[],[f827,f39]) ).
fof(f801,plain,
! [X0] : join(sk1,join(top,X0)) = join(sk1,join(X0,top)),
inference(superposition,[],[f555,f580]) ).
fof(f580,plain,
! [X0] : join(top,join(meet(sk1,join(sk1,top)),X0)) = join(sk1,join(X0,top)),
inference(forward_demodulation,[],[f574,f161]) ).
fof(f574,plain,
! [X0] : join(top,join(meet(sk1,join(sk1,top)),X0)) = join(top,join(sk1,X0)),
inference(superposition,[],[f157,f556]) ).
fof(f555,plain,
! [X0] : join(sk1,join(top,X0)) = join(top,join(meet(sk1,join(sk1,top)),X0)),
inference(backward_demodulation,[],[f549,f554]) ).
fof(f549,plain,
! [X0] : join(top,join(complement(join(complement(sk1),composition(converse(sk2),sk3))),X0)) = join(sk1,join(top,X0)),
inference(forward_demodulation,[],[f548,f2]) ).
fof(f548,plain,
! [X0] : join(top,join(complement(join(complement(sk1),composition(converse(sk2),sk3))),X0)) = join(join(sk1,top),X0),
inference(superposition,[],[f2,f397]) ).
fof(f5212,plain,
! [X0] : join(join(X0,zero),top) = join(sk1,join(top,X0)),
inference(superposition,[],[f4847,f203]) ).
fof(f203,plain,
! [X0] : join(top,X0) = join(top,join(X0,zero)),
inference(superposition,[],[f157,f1]) ).
fof(f4847,plain,
! [X0] : join(X0,top) = join(sk1,join(top,X0)),
inference(superposition,[],[f161,f1929]) ).
fof(f10311,plain,
! [X0] : join(top,X0) = join(top,top),
inference(backward_demodulation,[],[f1654,f10300]) ).
fof(f1654,plain,
! [X0] : join(top,X0) = join(top,join(X0,top)),
inference(backward_demodulation,[],[f1138,f1653]) ).
fof(f1653,plain,
! [X0] : join(top,X0) = join(sk1,join(top,join(complement(meet(sk1,join(sk1,top))),X0))),
inference(forward_demodulation,[],[f1650,f2]) ).
fof(f1650,plain,
! [X0] : join(top,X0) = join(sk1,join(join(top,complement(meet(sk1,join(sk1,top)))),X0)),
inference(superposition,[],[f2,f1615]) ).
fof(f1138,plain,
! [X0] : join(top,join(X0,top)) = join(sk1,join(top,join(complement(meet(sk1,join(sk1,top))),X0))),
inference(superposition,[],[f820,f583]) ).
fof(f820,plain,
! [X0,X1] : join(sk1,join(top,join(X0,X1))) = join(sk1,join(X0,join(X1,top))),
inference(superposition,[],[f801,f2]) ).
fof(f2739,plain,
! [X0,X1] : join(meet(X0,join(X0,X1)),complement(join(top,X1))) = X0,
inference(backward_demodulation,[],[f2313,f2731]) ).
fof(f2313,plain,
! [X0,X1] : join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))) = X0,
inference(superposition,[],[f19,f150]) ).
fof(f12223,plain,
! [X0] : meet(X0,zero) = join(meet(zero,meet(X0,zero)),zero),
inference(forward_demodulation,[],[f12222,f27]) ).
fof(f12222,plain,
! [X0] : meet(X0,zero) = join(meet(complement(top),meet(X0,zero)),zero),
inference(forward_demodulation,[],[f12209,f93]) ).
fof(f12209,plain,
! [X0] : meet(X0,zero) = join(meet(meet(X0,zero),complement(top)),zero),
inference(superposition,[],[f370,f12128]) ).
fof(f12128,plain,
! [X0] : zero = meet(meet(X0,zero),top),
inference(superposition,[],[f12124,f93]) ).
fof(f12124,plain,
! [X0] : zero = meet(meet(zero,X0),top),
inference(forward_demodulation,[],[f12103,f27]) ).
fof(f12103,plain,
! [X0] : complement(top) = meet(meet(zero,X0),top),
inference(superposition,[],[f32,f11984]) ).
fof(f11984,plain,
! [X0,X1] : top = join(X0,complement(meet(X0,X1))),
inference(superposition,[],[f10761,f2912]) ).
fof(f2912,plain,
! [X2,X0,X1] : join(X0,X2) = join(meet(X0,X1),join(meet(X0,complement(X1)),X2)),
inference(backward_demodulation,[],[f371,f2825]) ).
fof(f2825,plain,
! [X0,X1] : complement(join(complement(X1),X0)) = meet(X1,complement(X0)),
inference(superposition,[],[f4,f2731]) ).
fof(f371,plain,
! [X2,X0,X1] : join(X0,X2) = join(meet(X0,X1),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f2,f19]) ).
fof(f10761,plain,
! [X0,X1] : top = join(X0,join(X1,complement(X0))),
inference(backward_demodulation,[],[f2299,f10730]) ).
fof(f2299,plain,
! [X0,X1] : join(top,X1) = join(X0,join(X1,complement(X0))),
inference(superposition,[],[f150,f1]) ).
fof(f14448,plain,
meet(sk3,composition(sk2,sk1)) = join(meet(zero,meet(sk3,composition(sk2,sk1))),zero),
inference(forward_demodulation,[],[f14432,f93]) ).
fof(f14432,plain,
meet(sk3,composition(sk2,sk1)) = join(meet(meet(sk3,composition(sk2,sk1)),zero),zero),
inference(backward_demodulation,[],[f13023,f14404]) ).
fof(f14404,plain,
! [X0] : zero = composition(X0,zero),
inference(forward_demodulation,[],[f14403,f466]) ).
fof(f14403,plain,
! [X0] : join(zero,zero) = composition(X0,zero),
inference(forward_demodulation,[],[f14402,f13171]) ).
fof(f14402,plain,
! [X0] : composition(X0,zero) = join(meet(zero,composition(X0,zero)),zero),
inference(forward_demodulation,[],[f14399,f93]) ).
fof(f14399,plain,
! [X0] : composition(X0,zero) = join(meet(composition(X0,zero),zero),zero),
inference(superposition,[],[f11093,f13338]) ).
fof(f13338,plain,
! [X0] : zero = join(composition(X0,zero),zero),
inference(forward_demodulation,[],[f13337,f13106]) ).
fof(f13106,plain,
zero = composition(top,zero),
inference(backward_demodulation,[],[f12926,f13053]) ).
fof(f12926,plain,
composition(top,zero) = join(meet(zero,composition(top,zero)),zero),
inference(forward_demodulation,[],[f12925,f27]) ).
fof(f12925,plain,
composition(top,zero) = join(meet(complement(top),composition(top,zero)),zero),
inference(forward_demodulation,[],[f12901,f93]) ).
fof(f12901,plain,
composition(top,zero) = join(meet(composition(top,zero),complement(top)),zero),
inference(superposition,[],[f370,f12888]) ).
fof(f12888,plain,
zero = meet(composition(top,zero),top),
inference(forward_demodulation,[],[f12877,f27]) ).
fof(f12877,plain,
complement(top) = meet(composition(top,zero),top),
inference(superposition,[],[f32,f12759]) ).
fof(f12759,plain,
top = join(zero,complement(composition(top,zero))),
inference(superposition,[],[f11926,f1]) ).
fof(f11926,plain,
top = join(complement(composition(top,zero)),zero),
inference(superposition,[],[f10360,f11618]) ).
fof(f11618,plain,
zero = join(zero,composition(top,zero)),
inference(forward_demodulation,[],[f11617,f2371]) ).
fof(f2371,plain,
top = converse(top),
inference(backward_demodulation,[],[f2161,f2362]) ).
fof(f2362,plain,
top = join(top,converse(top)),
inference(superposition,[],[f2361,f1]) ).
fof(f2361,plain,
top = join(converse(top),top),
inference(forward_demodulation,[],[f2359,f8]) ).
fof(f2359,plain,
converse(converse(top)) = join(converse(top),top),
inference(superposition,[],[f34,f2161]) ).
fof(f34,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/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f2161,plain,
converse(top) = join(top,converse(top)),
inference(backward_demodulation,[],[f998,f2159]) ).
fof(f2159,plain,
converse(top) = join(sk1,converse(top)),
inference(forward_demodulation,[],[f2103,f163]) ).
fof(f163,plain,
! [X0,X1] : converse(top) = join(X0,join(X1,converse(complement(converse(join(X0,X1)))))),
inference(superposition,[],[f2,f126]) ).
fof(f126,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f33,f12]) ).
fof(f33,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f9,f8]) ).
fof(f2103,plain,
! [X0] : converse(top) = join(sk1,join(top,join(X0,converse(complement(converse(join(top,X0))))))),
inference(backward_demodulation,[],[f1318,f1999]) ).
fof(f1318,plain,
! [X0] : converse(top) = join(sk1,join(top,join(X0,converse(complement(converse(join(sk1,join(X0,top)))))))),
inference(superposition,[],[f827,f126]) ).
fof(f998,plain,
join(sk1,converse(top)) = join(top,join(sk1,converse(top))),
inference(superposition,[],[f949,f126]) ).
fof(f949,plain,
! [X0] : join(sk1,join(top,X0)) = join(top,join(sk1,join(top,X0))),
inference(forward_demodulation,[],[f943,f504]) ).
fof(f504,plain,
! [X0] : join(top,X0) = join(top,join(top,X0)),
inference(superposition,[],[f2,f456]) ).
fof(f943,plain,
! [X0] : join(sk1,join(top,join(top,X0))) = join(top,join(sk1,join(top,X0))),
inference(superposition,[],[f555,f591]) ).
fof(f591,plain,
! [X0] : join(sk1,join(top,X0)) = join(meet(sk1,join(sk1,top)),join(top,X0)),
inference(forward_demodulation,[],[f588,f2]) ).
fof(f588,plain,
! [X0] : join(join(sk1,top),X0) = join(meet(sk1,join(sk1,top)),join(top,X0)),
inference(superposition,[],[f2,f572]) ).
fof(f572,plain,
join(sk1,top) = join(meet(sk1,join(sk1,top)),top),
inference(superposition,[],[f556,f215]) ).
fof(f11617,plain,
zero = join(zero,composition(converse(top),zero)),
inference(forward_demodulation,[],[f11598,f27]) ).
fof(f11598,plain,
complement(top) = join(complement(top),composition(converse(top),complement(top))),
inference(superposition,[],[f541,f11487]) ).
fof(f11487,plain,
top = composition(top,top),
inference(superposition,[],[f11224,f2403]) ).
fof(f2403,plain,
top = join(one,converse(complement(one))),
inference(backward_demodulation,[],[f2240,f2371]) ).
fof(f2240,plain,
converse(top) = join(one,converse(complement(one))),
inference(superposition,[],[f126,f1888]) ).
fof(f11224,plain,
! [X0] : top = composition(join(one,X0),top),
inference(forward_demodulation,[],[f11223,f2371]) ).
fof(f11223,plain,
! [X0] : converse(top) = composition(join(one,X0),top),
inference(backward_demodulation,[],[f4433,f11048]) ).
fof(f11048,plain,
! [X0] : top = composition(top,join(one,converse(X0))),
inference(backward_demodulation,[],[f4432,f10730]) ).
fof(f4432,plain,
! [X0] : join(top,composition(top,converse(X0))) = composition(top,join(one,converse(X0))),
inference(forward_demodulation,[],[f4431,f2225]) ).
fof(f2225,plain,
! [X0] : converse(join(one,X0)) = join(one,converse(X0)),
inference(superposition,[],[f9,f1888]) ).
fof(f4431,plain,
! [X0] : join(top,composition(top,converse(X0))) = composition(top,converse(join(one,X0))),
inference(forward_demodulation,[],[f4430,f2422]) ).
fof(f2422,plain,
! [X0] : converse(composition(X0,top)) = composition(top,converse(X0)),
inference(superposition,[],[f10,f2371]) ).
fof(f4430,plain,
! [X0] : join(top,composition(top,converse(X0))) = converse(composition(join(one,X0),top)),
inference(forward_demodulation,[],[f4402,f2186]) ).
fof(f2186,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(forward_demodulation,[],[f1898,f1888]) ).
fof(f1898,plain,
! [X0,X1] : composition(join(converse(one),X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f7,f1867]) ).
fof(f7,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f4402,plain,
! [X0] : join(top,composition(top,converse(X0))) = converse(join(top,composition(X0,top))),
inference(superposition,[],[f3661,f3867]) ).
fof(f3867,plain,
! [X0] : composition(X0,top) = converse(composition(top,converse(X0))),
inference(superposition,[],[f8,f2422]) ).
fof(f3661,plain,
! [X0] : join(top,X0) = converse(join(top,converse(X0))),
inference(superposition,[],[f8,f2419]) ).
fof(f2419,plain,
! [X0] : join(top,converse(X0)) = converse(join(top,X0)),
inference(superposition,[],[f9,f2371]) ).
fof(f4433,plain,
! [X0] : composition(join(one,X0),top) = converse(composition(top,join(one,converse(X0)))),
inference(backward_demodulation,[],[f4037,f4432]) ).
fof(f4037,plain,
! [X0] : converse(join(top,composition(top,converse(X0)))) = composition(join(one,X0),top),
inference(forward_demodulation,[],[f3991,f2186]) ).
fof(f3991,plain,
! [X0] : join(top,composition(X0,top)) = converse(join(top,composition(top,converse(X0)))),
inference(superposition,[],[f3661,f2422]) ).
fof(f541,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(superposition,[],[f11,f1]) ).
fof(f10360,plain,
! [X0,X1] : top = join(complement(X0),join(X1,X0)),
inference(backward_demodulation,[],[f4665,f10300]) ).
fof(f4665,plain,
! [X0,X1] : join(X1,top) = join(complement(X0),join(X1,X0)),
inference(superposition,[],[f161,f12]) ).
fof(f13337,plain,
! [X0] : composition(top,zero) = join(composition(X0,zero),zero),
inference(forward_demodulation,[],[f13303,f10730]) ).
fof(f13303,plain,
! [X0] : join(composition(X0,zero),zero) = composition(join(top,X0),zero),
inference(superposition,[],[f436,f13106]) ).
fof(f436,plain,
! [X2,X0,X1] : composition(join(X0,X2),X1) = join(composition(X2,X1),composition(X0,X1)),
inference(superposition,[],[f7,f1]) ).
fof(f13023,plain,
meet(sk3,composition(sk2,sk1)) = join(meet(meet(sk3,composition(sk2,sk1)),composition(meet(sk2,composition(sk3,converse(sk1))),zero)),zero),
inference(superposition,[],[f11093,f878]) ).
fof(f878,plain,
composition(meet(sk2,composition(sk3,converse(sk1))),zero) = join(meet(sk3,composition(sk2,sk1)),composition(meet(sk2,composition(sk3,converse(sk1))),zero)),
inference(forward_demodulation,[],[f868,f93]) ).
fof(f868,plain,
composition(meet(sk2,composition(sk3,converse(sk1))),zero) = join(meet(composition(sk2,sk1),sk3),composition(meet(sk2,composition(sk3,converse(sk1))),zero)),
inference(superposition,[],[f14,f17]) ).
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/sandbox2/benchmark/theBenchmark.p',dedekind_law_14) ).
fof(f114,plain,
zero != meet(sk3,composition(sk2,sk1)),
inference(superposition,[],[f18,f93]) ).
fof(f18,axiom,
zero != meet(composition(sk2,sk1),sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_18) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : REL011-2 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37 % Computer : n002.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Mon May 20 08:23:38 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % (1410)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (1413)WARNING: value z3 for option sas not known
% 0.14/0.39 % (1413)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)
% 0.14/0.39 % (1417)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)
% 0.14/0.39 % (1415)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)
% 0.14/0.39 % (1412)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (1414)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (1416)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)
% 0.14/0.39 % (1411)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.41 TRYING [1]
% 0.14/0.41 TRYING [2]
% 0.21/0.43 TRYING [3]
% 0.21/0.45 TRYING [3]
% 0.21/0.50 TRYING [4]
% 0.21/0.57 TRYING [4]
% 2.94/0.85 TRYING [5]
% 5.05/1.11 % (1416)First to succeed.
% 5.05/1.11 % (1416)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1410"
% 5.05/1.11 % (1416)Refutation found. Thanks to Tanya!
% 5.05/1.11 % SZS status Unsatisfiable for theBenchmark
% 5.05/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 5.05/1.12 % (1416)------------------------------
% 5.05/1.12 % (1416)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 5.05/1.12 % (1416)Termination reason: Refutation
% 5.05/1.12
% 5.05/1.12 % (1416)Memory used [KB]: 7643
% 5.05/1.12 % (1416)Time elapsed: 0.722 s
% 5.05/1.12 % (1416)Instructions burned: 1131 (million)
% 5.05/1.12 % (1410)Success in time 0.726 s
%------------------------------------------------------------------------------