TSTP Solution File: REL021+2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : REL021+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n029.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 : Thu Aug 31 13:45:06 EDT 2023
% Result : Theorem 37.11s 5.72s
% Output : Refutation 37.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 86
% Number of leaves : 27
% Syntax : Number of formulae : 327 ( 322 unt; 0 def)
% Number of atoms : 334 ( 333 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 0 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 15 con; 0-2 aty)
% Number of variables : 270 (; 266 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f259517,plain,
$false,
inference(trivial_inequality_removal,[],[f258827]) ).
fof(f258827,plain,
sF5 != sF5,
inference(backward_demodulation,[],[f54,f258825]) ).
fof(f258825,plain,
sF5 = sF10,
inference(forward_demodulation,[],[f258821,f69]) ).
fof(f69,plain,
sF10 = join(sF5,sF9),
inference(superposition,[],[f28,f53]) ).
fof(f53,plain,
join(sF9,sF5) = sF10,
introduced(function_definition,[]) ).
fof(f28,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',maddux1_join_commutativity) ).
fof(f258821,plain,
sF5 = join(sF5,sF9),
inference(backward_demodulation,[],[f127668,f258814]) ).
fof(f258814,plain,
sF9 = complement(join(sF2,complement(sF9))),
inference(forward_demodulation,[],[f258813,f9239]) ).
fof(f9239,plain,
! [X4] : complement(complement(X4)) = X4,
inference(forward_demodulation,[],[f9238,f676]) ).
fof(f676,plain,
! [X20] : complement(X20) = join(complement(X20),complement(X20)),
inference(forward_demodulation,[],[f675,f273]) ).
fof(f273,plain,
! [X2] : composition(one,X2) = X2,
inference(backward_demodulation,[],[f260,f268]) ).
fof(f268,plain,
one = converse(one),
inference(superposition,[],[f260,f25]) ).
fof(f25,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',composition_identity) ).
fof(f260,plain,
! [X2] : composition(converse(one),X2) = X2,
inference(forward_demodulation,[],[f242,f24]) ).
fof(f24,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',converse_idempotence) ).
fof(f242,plain,
! [X2] : composition(converse(one),X2) = converse(converse(X2)),
inference(superposition,[],[f84,f25]) ).
fof(f84,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f30,f24]) ).
fof(f30,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',converse_multiplicativity) ).
fof(f675,plain,
! [X20] : complement(X20) = join(complement(X20),complement(composition(one,X20))),
inference(forward_demodulation,[],[f655,f273]) ).
fof(f655,plain,
! [X20] : complement(X20) = join(complement(X20),composition(one,complement(composition(one,X20)))),
inference(superposition,[],[f59,f268]) ).
fof(f59,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(forward_demodulation,[],[f32,f28]) ).
fof(f32,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',converse_cancellativity) ).
fof(f9238,plain,
! [X4] : complement(join(complement(X4),complement(X4))) = X4,
inference(forward_demodulation,[],[f8985,f8955]) ).
fof(f8955,plain,
! [X150,X149] : join(X150,X149) = join(X150,complement(complement(X149))),
inference(backward_demodulation,[],[f4441,f8877]) ).
fof(f8877,plain,
! [X7] : join(zero,X7) = X7,
inference(superposition,[],[f6226,f818]) ).
fof(f818,plain,
! [X2] : join(zero,complement(complement(X2))) = X2,
inference(forward_demodulation,[],[f817,f58]) ).
fof(f58,plain,
zero = complement(top),
inference(backward_demodulation,[],[f41,f27]) ).
fof(f27,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',def_top) ).
fof(f41,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f26,f31]) ).
fof(f31,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',maddux4_definiton_of_meet) ).
fof(f26,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',def_zero) ).
fof(f817,plain,
! [X2] : join(complement(top),complement(complement(X2))) = X2,
inference(forward_demodulation,[],[f816,f676]) ).
fof(f816,plain,
! [X2] : join(complement(top),complement(join(complement(X2),complement(X2)))) = X2,
inference(forward_demodulation,[],[f784,f28]) ).
fof(f784,plain,
! [X2] : join(complement(join(complement(X2),complement(X2))),complement(top)) = X2,
inference(superposition,[],[f60,f27]) ).
fof(f60,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f33,f28]) ).
fof(f33,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',maddux3_a_kind_of_de_Morgan) ).
fof(f6226,plain,
! [X0] : join(zero,X0) = join(zero,join(zero,X0)),
inference(superposition,[],[f34,f6172]) ).
fof(f6172,plain,
zero = join(zero,zero),
inference(forward_demodulation,[],[f6171,f58]) ).
fof(f6171,plain,
zero = join(zero,complement(top)),
inference(forward_demodulation,[],[f6132,f2708]) ).
fof(f2708,plain,
top = composition(top,top),
inference(forward_demodulation,[],[f2693,f1162]) ).
fof(f1162,plain,
! [X2] : top = join(X2,converse(complement(converse(X2)))),
inference(backward_demodulation,[],[f124,f1161]) ).
fof(f1161,plain,
top = converse(top),
inference(forward_demodulation,[],[f1160,f24]) ).
fof(f1160,plain,
converse(top) = converse(converse(top)),
inference(forward_demodulation,[],[f1159,f1145]) ).
fof(f1145,plain,
converse(top) = join(top,converse(top)),
inference(superposition,[],[f1043,f124]) ).
fof(f1043,plain,
! [X0] : join(top,X0) = join(top,join(top,X0)),
inference(superposition,[],[f34,f1037]) ).
fof(f1037,plain,
top = join(top,top),
inference(forward_demodulation,[],[f1036,f705]) ).
fof(f705,plain,
join(top,top) = join(top,complement(composition(converse(sK0),sF2))),
inference(superposition,[],[f352,f700]) ).
fof(f700,plain,
top = join(zero,complement(composition(converse(sK0),sF2))),
inference(forward_demodulation,[],[f699,f64]) ).
fof(f64,plain,
top = join(top,zero),
inference(superposition,[],[f27,f58]) ).
fof(f699,plain,
join(top,zero) = join(zero,complement(composition(converse(sK0),sF2))),
inference(forward_demodulation,[],[f693,f28]) ).
fof(f693,plain,
join(zero,top) = join(zero,complement(composition(converse(sK0),sF2))),
inference(superposition,[],[f689,f27]) ).
fof(f689,plain,
! [X0] : join(zero,X0) = join(zero,join(composition(converse(sK0),sF2),X0)),
inference(superposition,[],[f34,f686]) ).
fof(f686,plain,
zero = join(zero,composition(converse(sK0),sF2)),
inference(forward_demodulation,[],[f685,f58]) ).
fof(f685,plain,
complement(top) = join(complement(top),composition(converse(sK0),sF2)),
inference(forward_demodulation,[],[f665,f45]) ).
fof(f45,plain,
complement(sK0) = sF2,
introduced(function_definition,[]) ).
fof(f665,plain,
complement(top) = join(complement(top),composition(converse(sK0),complement(sK0))),
inference(superposition,[],[f59,f57]) ).
fof(f57,plain,
sK0 = composition(sK0,top),
inference(backward_demodulation,[],[f55,f56]) ).
fof(f56,plain,
sK0 = sF11,
inference(definition_folding,[],[f22,f55]) ).
fof(f22,plain,
sK0 = composition(sK0,top),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
( meet(sK0,sK1) != join(composition(meet(sK0,one),sK1),meet(sK0,sK1))
& sK0 = composition(sK0,top) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f20]) ).
fof(f20,plain,
( ? [X0,X1] :
( meet(X0,X1) != join(composition(meet(X0,one),X1),meet(X0,X1))
& composition(X0,top) = X0 )
=> ( meet(sK0,sK1) != join(composition(meet(sK0,one),sK1),meet(sK0,sK1))
& sK0 = composition(sK0,top) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
? [X0,X1] :
( meet(X0,X1) != join(composition(meet(X0,one),X1),meet(X0,X1))
& composition(X0,top) = X0 ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( composition(X0,top) = X0
=> meet(X0,X1) = join(composition(meet(X0,one),X1),meet(X0,X1)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X0,X1] :
( composition(X0,top) = X0
=> meet(X0,X1) = join(composition(meet(X0,one),X1),meet(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',goals) ).
fof(f55,plain,
composition(sK0,top) = sF11,
introduced(function_definition,[]) ).
fof(f352,plain,
! [X19] : join(top,join(zero,X19)) = join(top,X19),
inference(superposition,[],[f34,f64]) ).
fof(f1036,plain,
top = join(top,complement(composition(converse(sK0),sF2))),
inference(forward_demodulation,[],[f1035,f273]) ).
fof(f1035,plain,
top = join(top,complement(composition(one,composition(converse(sK0),sF2)))),
inference(forward_demodulation,[],[f1025,f273]) ).
fof(f1025,plain,
top = join(top,composition(one,complement(composition(one,composition(converse(sK0),sF2))))),
inference(superposition,[],[f828,f268]) ).
fof(f828,plain,
! [X0] : top = join(top,composition(converse(X0),complement(composition(X0,composition(converse(sK0),sF2))))),
inference(forward_demodulation,[],[f819,f700]) ).
fof(f819,plain,
! [X0] : join(zero,complement(composition(converse(sK0),sF2))) = join(top,composition(converse(X0),complement(composition(X0,composition(converse(sK0),sF2))))),
inference(superposition,[],[f706,f59]) ).
fof(f706,plain,
! [X0] : join(top,X0) = join(zero,join(complement(composition(converse(sK0),sF2)),X0)),
inference(superposition,[],[f34,f700]) ).
fof(f1159,plain,
converse(converse(top)) = join(top,converse(top)),
inference(forward_demodulation,[],[f1157,f28]) ).
fof(f1157,plain,
converse(converse(top)) = join(converse(top),top),
inference(superposition,[],[f74,f1145]) ).
fof(f74,plain,
! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[],[f29,f24]) ).
fof(f29,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',converse_additivity) ).
fof(f124,plain,
! [X2] : join(X2,converse(complement(converse(X2)))) = converse(top),
inference(superposition,[],[f73,f27]) ).
fof(f73,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f29,f24]) ).
fof(f2693,plain,
composition(top,top) = join(sK0,converse(complement(converse(sK0)))),
inference(backward_demodulation,[],[f1181,f2684]) ).
fof(f2684,plain,
converse(complement(converse(sK0))) = composition(converse(complement(converse(sK0))),top),
inference(superposition,[],[f1225,f2245]) ).
fof(f2245,plain,
complement(converse(sK0)) = composition(top,complement(converse(sK0))),
inference(backward_demodulation,[],[f1738,f2243]) ).
fof(f2243,plain,
top = join(one,top),
inference(forward_demodulation,[],[f2236,f1037]) ).
fof(f2236,plain,
join(one,top) = join(top,top),
inference(superposition,[],[f2013,f2171]) ).
fof(f2171,plain,
top = join(top,converse(sF6)),
inference(forward_demodulation,[],[f2168,f1161]) ).
fof(f2168,plain,
converse(top) = join(top,converse(sF6)),
inference(superposition,[],[f1223,f1987]) ).
fof(f1987,plain,
top = join(top,sF6),
inference(forward_demodulation,[],[f1984,f63]) ).
fof(f63,plain,
top = join(one,sF6),
inference(superposition,[],[f27,f49]) ).
fof(f49,plain,
complement(one) = sF6,
introduced(function_definition,[]) ).
fof(f1984,plain,
join(one,sF6) = join(top,sF6),
inference(superposition,[],[f349,f1863]) ).
fof(f1863,plain,
sF6 = join(sF6,sF6),
inference(forward_demodulation,[],[f1862,f49]) ).
fof(f1862,plain,
sF6 = join(sF6,complement(one)),
inference(forward_demodulation,[],[f1846,f273]) ).
fof(f1846,plain,
sF6 = join(sF6,composition(one,complement(one))),
inference(superposition,[],[f670,f268]) ).
fof(f670,plain,
! [X0] : sF6 = join(sF6,composition(converse(X0),complement(X0))),
inference(forward_demodulation,[],[f642,f25]) ).
fof(f642,plain,
! [X0] : sF6 = join(sF6,composition(converse(X0),complement(composition(X0,one)))),
inference(superposition,[],[f59,f49]) ).
fof(f349,plain,
! [X14] : join(one,join(sF6,X14)) = join(top,X14),
inference(superposition,[],[f34,f63]) ).
fof(f1223,plain,
! [X0] : converse(join(top,X0)) = join(top,converse(X0)),
inference(superposition,[],[f29,f1161]) ).
fof(f2013,plain,
! [X1] : join(top,X1) = join(one,join(X1,converse(sF6))),
inference(superposition,[],[f1171,f28]) ).
fof(f1171,plain,
! [X15] : join(one,join(converse(sF6),X15)) = join(top,X15),
inference(backward_demodulation,[],[f350,f1161]) ).
fof(f350,plain,
! [X15] : join(one,join(converse(sF6),X15)) = join(converse(top),X15),
inference(superposition,[],[f34,f292]) ).
fof(f292,plain,
converse(top) = join(one,converse(sF6)),
inference(forward_demodulation,[],[f285,f49]) ).
fof(f285,plain,
converse(top) = join(one,converse(complement(one))),
inference(superposition,[],[f124,f268]) ).
fof(f1738,plain,
complement(converse(sK0)) = composition(join(one,top),complement(converse(sK0))),
inference(forward_demodulation,[],[f1737,f1161]) ).
fof(f1737,plain,
complement(converse(sK0)) = composition(join(one,converse(top)),complement(converse(sK0))),
inference(forward_demodulation,[],[f1718,f501]) ).
fof(f501,plain,
! [X6,X7] : composition(join(one,X7),X6) = join(X6,composition(X7,X6)),
inference(superposition,[],[f36,f273]) ).
fof(f36,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',composition_distributivity) ).
fof(f1718,plain,
complement(converse(sK0)) = join(complement(converse(sK0)),composition(converse(top),complement(converse(sK0)))),
inference(superposition,[],[f59,f1663]) ).
fof(f1663,plain,
converse(sK0) = composition(top,converse(sK0)),
inference(superposition,[],[f1226,f57]) ).
fof(f1226,plain,
! [X3] : composition(top,converse(X3)) = converse(composition(X3,top)),
inference(superposition,[],[f30,f1161]) ).
fof(f1225,plain,
! [X2] : composition(converse(X2),top) = converse(composition(top,X2)),
inference(superposition,[],[f30,f1161]) ).
fof(f1181,plain,
composition(top,top) = join(sK0,composition(converse(complement(converse(sK0))),top)),
inference(backward_demodulation,[],[f548,f1161]) ).
fof(f548,plain,
join(sK0,composition(converse(complement(converse(sK0))),top)) = composition(converse(top),top),
inference(superposition,[],[f503,f124]) ).
fof(f503,plain,
! [X11] : composition(join(sK0,X11),top) = join(sK0,composition(X11,top)),
inference(superposition,[],[f36,f57]) ).
fof(f6132,plain,
zero = join(zero,complement(composition(top,top))),
inference(superposition,[],[f2833,f58]) ).
fof(f2833,plain,
! [X4] : complement(X4) = join(complement(X4),complement(composition(top,X4))),
inference(backward_demodulation,[],[f1227,f2831]) ).
fof(f2831,plain,
! [X10] : complement(composition(top,X10)) = composition(top,complement(composition(top,X10))),
inference(forward_demodulation,[],[f2830,f2243]) ).
fof(f2830,plain,
! [X10] : complement(composition(top,X10)) = composition(join(one,top),complement(composition(top,X10))),
inference(forward_demodulation,[],[f2829,f1161]) ).
fof(f2829,plain,
! [X10] : complement(composition(top,X10)) = composition(join(one,converse(top)),complement(composition(top,X10))),
inference(forward_demodulation,[],[f2816,f501]) ).
fof(f2816,plain,
! [X10] : complement(composition(top,X10)) = join(complement(composition(top,X10)),composition(converse(top),complement(composition(top,X10)))),
inference(superposition,[],[f59,f2752]) ).
fof(f2752,plain,
! [X0] : composition(top,X0) = composition(top,composition(top,X0)),
inference(superposition,[],[f35,f2708]) ).
fof(f35,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',composition_associativity) ).
fof(f1227,plain,
! [X4] : complement(X4) = join(complement(X4),composition(top,complement(composition(top,X4)))),
inference(superposition,[],[f59,f1161]) ).
fof(f34,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',maddux2_join_associativity) ).
fof(f4441,plain,
! [X150,X149] : join(X150,X149) = join(zero,join(X150,complement(complement(X149)))),
inference(superposition,[],[f372,f818]) ).
fof(f372,plain,
! [X2,X3,X4] : join(X2,join(X3,X4)) = join(X3,join(X2,X4)),
inference(forward_demodulation,[],[f345,f34]) ).
fof(f345,plain,
! [X2,X3,X4] : join(X2,join(X3,X4)) = join(join(X3,X2),X4),
inference(superposition,[],[f34,f28]) ).
fof(f8985,plain,
! [X4] : complement(join(complement(X4),complement(complement(complement(X4))))) = X4,
inference(backward_demodulation,[],[f788,f8877]) ).
fof(f788,plain,
! [X4] : join(zero,complement(join(complement(X4),complement(complement(complement(X4)))))) = X4,
inference(forward_demodulation,[],[f767,f58]) ).
fof(f767,plain,
! [X4] : join(complement(top),complement(join(complement(X4),complement(complement(complement(X4)))))) = X4,
inference(superposition,[],[f60,f27]) ).
fof(f258813,plain,
complement(complement(sF9)) = complement(join(sF2,complement(sF9))),
inference(forward_demodulation,[],[f258812,f8877]) ).
fof(f258812,plain,
complement(complement(sF9)) = join(zero,complement(join(sF2,complement(sF9)))),
inference(forward_demodulation,[],[f258384,f58]) ).
fof(f258384,plain,
complement(complement(sF9)) = join(complement(top),complement(join(sF2,complement(sF9)))),
inference(superposition,[],[f13964,f70332]) ).
fof(f70332,plain,
top = join(sK0,complement(sF9)),
inference(forward_demodulation,[],[f70331,f8877]) ).
fof(f70331,plain,
top = join(zero,join(sK0,complement(sF9))),
inference(forward_demodulation,[],[f70264,f362]) ).
fof(f362,plain,
! [X6,X7,X5] : join(X5,join(X6,X7)) = join(X7,join(X5,X6)),
inference(superposition,[],[f34,f28]) ).
fof(f70264,plain,
top = join(sK0,join(complement(sF9),zero)),
inference(superposition,[],[f361,f70231]) ).
fof(f70231,plain,
zero = complement(join(sK0,complement(sF9))),
inference(forward_demodulation,[],[f70230,f8877]) ).
fof(f70230,plain,
zero = join(zero,complement(join(sK0,complement(sF9)))),
inference(forward_demodulation,[],[f70229,f28]) ).
fof(f70229,plain,
zero = join(complement(join(sK0,complement(sF9))),zero),
inference(forward_demodulation,[],[f70228,f10992]) ).
fof(f10992,plain,
! [X25] : zero = composition(zero,X25),
inference(backward_demodulation,[],[f10525,f10990]) ).
fof(f10990,plain,
zero = converse(zero),
inference(forward_demodulation,[],[f10945,f58]) ).
fof(f10945,plain,
complement(top) = converse(zero),
inference(superposition,[],[f9239,f10881]) ).
fof(f10881,plain,
top = complement(converse(zero)),
inference(forward_demodulation,[],[f10861,f1161]) ).
fof(f10861,plain,
converse(top) = complement(converse(zero)),
inference(superposition,[],[f24,f10605]) ).
fof(f10605,plain,
top = converse(complement(converse(zero))),
inference(backward_demodulation,[],[f9054,f10579]) ).
fof(f10579,plain,
converse(zero) = composition(converse(sF2),sK0),
inference(superposition,[],[f84,f9048]) ).
fof(f9048,plain,
zero = composition(converse(sK0),sF2),
inference(backward_demodulation,[],[f686,f8877]) ).
fof(f9054,plain,
top = converse(complement(composition(converse(sF2),sK0))),
inference(backward_demodulation,[],[f1213,f8877]) ).
fof(f1213,plain,
top = join(zero,converse(complement(composition(converse(sF2),sK0)))),
inference(forward_demodulation,[],[f1212,f64]) ).
fof(f1212,plain,
join(top,zero) = join(zero,converse(complement(composition(converse(sF2),sK0)))),
inference(forward_demodulation,[],[f1185,f28]) ).
fof(f1185,plain,
join(zero,top) = join(zero,converse(complement(composition(converse(sF2),sK0)))),
inference(backward_demodulation,[],[f701,f1161]) ).
fof(f701,plain,
join(zero,converse(top)) = join(zero,converse(complement(composition(converse(sF2),sK0)))),
inference(forward_demodulation,[],[f696,f84]) ).
fof(f696,plain,
join(zero,converse(complement(converse(composition(converse(sK0),sF2))))) = join(zero,converse(top)),
inference(superposition,[],[f689,f124]) ).
fof(f10525,plain,
! [X25] : converse(zero) = composition(converse(zero),X25),
inference(superposition,[],[f84,f10255]) ).
fof(f10255,plain,
! [X1] : zero = composition(X1,zero),
inference(forward_demodulation,[],[f10240,f9051]) ).
fof(f9051,plain,
zero = composition(top,zero),
inference(backward_demodulation,[],[f2735,f8877]) ).
fof(f2735,plain,
zero = join(zero,composition(top,zero)),
inference(forward_demodulation,[],[f2720,f58]) ).
fof(f2720,plain,
zero = join(zero,composition(top,complement(top))),
inference(backward_demodulation,[],[f2172,f2708]) ).
fof(f2172,plain,
zero = join(zero,composition(top,complement(composition(top,top)))),
inference(backward_demodulation,[],[f1999,f2171]) ).
fof(f1999,plain,
zero = join(zero,composition(join(top,converse(sF6)),complement(composition(top,top)))),
inference(backward_demodulation,[],[f1239,f1992]) ).
fof(f1992,plain,
composition(top,top) = join(sK0,composition(sF7,top)),
inference(backward_demodulation,[],[f544,f1987]) ).
fof(f544,plain,
join(sK0,composition(sF7,top)) = composition(join(top,sF6),top),
inference(superposition,[],[f503,f418]) ).
fof(f418,plain,
join(top,sF6) = join(sK0,sF7),
inference(superposition,[],[f353,f50]) ).
fof(f50,plain,
join(sF2,sF6) = sF7,
introduced(function_definition,[]) ).
fof(f353,plain,
! [X20] : join(sK0,join(sF2,X20)) = join(top,X20),
inference(superposition,[],[f34,f65]) ).
fof(f65,plain,
top = join(sK0,sF2),
inference(superposition,[],[f27,f45]) ).
fof(f1239,plain,
zero = join(zero,composition(join(top,converse(sF6)),complement(join(sK0,composition(sF7,top))))),
inference(backward_demodulation,[],[f681,f1223]) ).
fof(f681,plain,
zero = join(zero,composition(converse(join(top,sF6)),complement(join(sK0,composition(sF7,top))))),
inference(forward_demodulation,[],[f661,f58]) ).
fof(f661,plain,
complement(top) = join(complement(top),composition(converse(join(top,sF6)),complement(join(sK0,composition(sF7,top))))),
inference(superposition,[],[f59,f544]) ).
fof(f10240,plain,
! [X1] : composition(top,zero) = composition(X1,zero),
inference(backward_demodulation,[],[f9816,f10222]) ).
fof(f10222,plain,
! [X9] : top = join(X9,top),
inference(forward_demodulation,[],[f10003,f9911]) ).
fof(f9911,plain,
! [X6] : top = join(top,X6),
inference(forward_demodulation,[],[f9852,f2064]) ).
fof(f2064,plain,
! [X14,X13] : join(top,X14) = join(X13,join(X14,complement(X13))),
inference(superposition,[],[f344,f28]) ).
fof(f344,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f34,f27]) ).
fof(f9852,plain,
! [X6] : top = join(X6,join(X6,complement(X6))),
inference(superposition,[],[f361,f9249]) ).
fof(f9249,plain,
! [X7] : join(X7,X7) = X7,
inference(forward_demodulation,[],[f9248,f9239]) ).
fof(f9248,plain,
! [X7] : complement(complement(X7)) = join(X7,complement(complement(X7))),
inference(forward_demodulation,[],[f9247,f2833]) ).
fof(f9247,plain,
! [X7] : complement(join(complement(X7),complement(composition(top,X7)))) = join(X7,complement(join(complement(X7),complement(composition(top,X7))))),
inference(forward_demodulation,[],[f9241,f2752]) ).
fof(f9241,plain,
! [X7] : complement(join(complement(X7),complement(composition(top,composition(top,X7))))) = join(X7,complement(join(complement(X7),complement(composition(top,composition(top,X7)))))),
inference(backward_demodulation,[],[f9230,f9239]) ).
fof(f9230,plain,
! [X7] : complement(join(complement(X7),complement(composition(top,complement(complement(composition(top,X7))))))) = join(X7,complement(join(complement(X7),complement(composition(top,complement(complement(composition(top,X7)))))))),
inference(forward_demodulation,[],[f9229,f8877]) ).
fof(f9229,plain,
! [X7] : complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(top,X7)))))))) = join(X7,complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(top,X7))))))))),
inference(forward_demodulation,[],[f8981,f8974]) ).
fof(f8974,plain,
! [X2,X1] : join(X1,X2) = join(complement(complement(X1)),X2),
inference(backward_demodulation,[],[f875,f8877]) ).
fof(f875,plain,
! [X2,X1] : join(X1,X2) = join(zero,join(complement(complement(X1)),X2)),
inference(superposition,[],[f34,f818]) ).
fof(f8981,plain,
! [X7] : complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(top,X7)))))))) = join(complement(complement(X7)),complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(top,X7))))))))),
inference(backward_demodulation,[],[f2737,f8877]) ).
fof(f2737,plain,
! [X7] : complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(top,X7)))))))) = join(complement(join(zero,complement(X7))),complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(top,X7))))))))),
inference(forward_demodulation,[],[f2722,f58]) ).
fof(f2722,plain,
! [X7] : complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(top,X7)))))))) = join(complement(join(complement(top),complement(X7))),complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(top,X7))))))))),
inference(backward_demodulation,[],[f2174,f2708]) ).
fof(f2174,plain,
! [X7] : complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(top,X7)))))))) = join(complement(join(complement(composition(top,top)),complement(X7))),complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(top,X7))))))))),
inference(backward_demodulation,[],[f1997,f2171]) ).
fof(f1997,plain,
! [X7] : complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(join(top,converse(sF6)),X7)))))))) = join(complement(join(complement(composition(top,top)),complement(X7))),complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(join(top,converse(sF6)),X7))))))))),
inference(backward_demodulation,[],[f1989,f1992]) ).
fof(f1989,plain,
! [X7] : complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(join(top,converse(sF6)),X7)))))))) = join(complement(join(complement(join(sK0,composition(sF7,top))),complement(X7))),complement(join(complement(X7),complement(composition(top,complement(join(zero,complement(composition(join(top,converse(sF6)),X7))))))))),
inference(backward_demodulation,[],[f1238,f1987]) ).
fof(f1238,plain,
! [X7] : complement(join(complement(X7),complement(composition(join(top,sF6),complement(join(zero,complement(composition(join(top,converse(sF6)),X7)))))))) = join(complement(join(complement(join(sK0,composition(sF7,top))),complement(X7))),complement(join(complement(X7),complement(composition(join(top,sF6),complement(join(zero,complement(composition(join(top,converse(sF6)),X7))))))))),
inference(backward_demodulation,[],[f935,f1223]) ).
fof(f935,plain,
! [X7] : complement(join(complement(X7),complement(composition(join(top,sF6),complement(join(zero,complement(composition(converse(join(top,sF6)),X7)))))))) = join(complement(join(complement(join(sK0,composition(sF7,top))),complement(X7))),complement(join(complement(X7),complement(composition(join(top,sF6),complement(join(zero,complement(composition(converse(join(top,sF6)),X7))))))))),
inference(forward_demodulation,[],[f890,f58]) ).
fof(f890,plain,
! [X7] : complement(join(complement(X7),complement(composition(join(top,sF6),complement(join(complement(top),complement(composition(converse(join(top,sF6)),X7)))))))) = join(complement(join(complement(join(sK0,composition(sF7,top))),complement(X7))),complement(join(complement(X7),complement(composition(join(top,sF6),complement(join(complement(top),complement(composition(converse(join(top,sF6)),X7))))))))),
inference(superposition,[],[f61,f544]) ).
fof(f61,plain,
! [X2,X0,X1] : complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2))))))))),
inference(forward_demodulation,[],[f42,f28]) ).
fof(f42,plain,
! [X2,X0,X1] : complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2)))),
inference(definition_unfolding,[],[f37,f31,f31,f31,f31,f31]) ).
fof(f37,plain,
! [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)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2] : 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/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',modular_law_1) ).
fof(f10003,plain,
! [X10,X9] : join(X9,top) = join(top,join(X9,join(sF8,X10))),
inference(backward_demodulation,[],[f7779,f9911]) ).
fof(f7779,plain,
! [X10,X9] : join(X9,join(top,X10)) = join(top,join(X9,join(sF8,X10))),
inference(forward_demodulation,[],[f7778,f34]) ).
fof(f7778,plain,
! [X10,X9] : join(join(X9,top),X10) = join(top,join(X9,join(sF8,X10))),
inference(forward_demodulation,[],[f7731,f34]) ).
fof(f7731,plain,
! [X10,X9] : join(join(X9,top),X10) = join(top,join(join(X9,sF8),X10)),
inference(superposition,[],[f34,f6425]) ).
fof(f6425,plain,
! [X3] : join(X3,top) = join(top,join(X3,sF8)),
inference(backward_demodulation,[],[f5292,f6414]) ).
fof(f6414,plain,
top = join(top,sK0),
inference(backward_demodulation,[],[f2706,f6413]) ).
fof(f6413,plain,
! [X1] : top = join(top,converse(complement(composition(top,X1)))),
inference(forward_demodulation,[],[f6398,f1161]) ).
fof(f6398,plain,
! [X1] : converse(top) = join(top,converse(complement(composition(top,X1)))),
inference(superposition,[],[f1223,f6189]) ).
fof(f6189,plain,
! [X3] : top = join(top,complement(composition(top,X3))),
inference(forward_demodulation,[],[f6145,f27]) ).
fof(f6145,plain,
! [X3] : join(X3,complement(X3)) = join(top,complement(composition(top,X3))),
inference(superposition,[],[f344,f2833]) ).
fof(f2706,plain,
join(top,sK0) = join(top,converse(complement(composition(top,converse(sF2))))),
inference(backward_demodulation,[],[f1242,f2694]) ).
fof(f2694,plain,
! [X0] : join(top,X0) = join(composition(top,top),X0),
inference(forward_demodulation,[],[f2692,f1170]) ).
fof(f1170,plain,
! [X8,X9] : join(X8,join(converse(complement(converse(X8))),X9)) = join(top,X9),
inference(backward_demodulation,[],[f347,f1161]) ).
fof(f347,plain,
! [X8,X9] : join(X8,join(converse(complement(converse(X8))),X9)) = join(converse(top),X9),
inference(superposition,[],[f34,f124]) ).
fof(f2692,plain,
! [X0] : join(composition(top,top),X0) = join(sK0,join(converse(complement(converse(sK0))),X0)),
inference(backward_demodulation,[],[f1182,f2684]) ).
fof(f1182,plain,
! [X0] : join(composition(top,top),X0) = join(sK0,join(composition(converse(complement(converse(sK0))),top),X0)),
inference(backward_demodulation,[],[f609,f1161]) ).
fof(f609,plain,
! [X0] : join(sK0,join(composition(converse(complement(converse(sK0))),top),X0)) = join(composition(converse(top),top),X0),
inference(superposition,[],[f34,f548]) ).
fof(f1242,plain,
join(top,sK0) = join(composition(top,top),converse(complement(composition(top,converse(sF2))))),
inference(backward_demodulation,[],[f1211,f1226]) ).
fof(f1211,plain,
join(top,sK0) = join(composition(top,top),converse(complement(converse(composition(sF2,top))))),
inference(forward_demodulation,[],[f1184,f28]) ).
fof(f1184,plain,
join(sK0,top) = join(composition(top,top),converse(complement(converse(composition(sF2,top))))),
inference(backward_demodulation,[],[f616,f1161]) ).
fof(f616,plain,
join(sK0,converse(top)) = join(composition(top,top),converse(complement(converse(composition(sF2,top))))),
inference(superposition,[],[f559,f124]) ).
fof(f559,plain,
! [X0] : join(sK0,join(composition(sF2,top),X0)) = join(composition(top,top),X0),
inference(superposition,[],[f34,f542]) ).
fof(f542,plain,
join(sK0,composition(sF2,top)) = composition(top,top),
inference(superposition,[],[f503,f65]) ).
fof(f5292,plain,
! [X3] : join(top,join(X3,sF8)) = join(X3,join(top,sK0)),
inference(superposition,[],[f372,f5257]) ).
fof(f5257,plain,
join(top,sK0) = join(top,sF8),
inference(forward_demodulation,[],[f5256,f28]) ).
fof(f5256,plain,
join(sK0,top) = join(top,sF8),
inference(forward_demodulation,[],[f5255,f51]) ).
fof(f51,plain,
complement(sF7) = sF8,
introduced(function_definition,[]) ).
fof(f5255,plain,
join(sK0,top) = join(top,complement(sF7)),
inference(forward_demodulation,[],[f5254,f50]) ).
fof(f5254,plain,
join(sK0,top) = join(top,complement(join(sF2,sF6))),
inference(forward_demodulation,[],[f5253,f28]) ).
fof(f5253,plain,
join(sK0,top) = join(top,complement(join(sF6,sF2))),
inference(forward_demodulation,[],[f5137,f1043]) ).
fof(f5137,plain,
join(sK0,top) = join(top,join(top,complement(join(sF6,sF2)))),
inference(superposition,[],[f353,f3946]) ).
fof(f3946,plain,
! [X1] : top = join(X1,join(top,complement(join(sF6,X1)))),
inference(forward_demodulation,[],[f3910,f28]) ).
fof(f3910,plain,
! [X1] : top = join(X1,join(complement(join(sF6,X1)),top)),
inference(superposition,[],[f2658,f362]) ).
fof(f2658,plain,
! [X39] : top = join(top,join(X39,complement(join(sF6,X39)))),
inference(forward_demodulation,[],[f2452,f2243]) ).
fof(f2452,plain,
! [X39] : join(one,top) = join(top,join(X39,complement(join(sF6,X39)))),
inference(superposition,[],[f349,f361]) ).
fof(f9816,plain,
! [X1] : composition(X1,zero) = composition(join(X1,top),zero),
inference(forward_demodulation,[],[f9815,f8877]) ).
fof(f9815,plain,
! [X1] : composition(join(X1,top),zero) = join(zero,composition(X1,zero)),
inference(forward_demodulation,[],[f9803,f28]) ).
fof(f9803,plain,
! [X1] : composition(join(X1,top),zero) = join(composition(X1,zero),zero),
inference(superposition,[],[f36,f9051]) ).
fof(f70228,plain,
composition(zero,complement(join(sF3,complement(composition(converse(sF8),sF2))))) = join(complement(join(sK0,complement(sF9))),composition(zero,complement(join(sF3,complement(composition(converse(sF8),sF2)))))),
inference(forward_demodulation,[],[f70226,f58]) ).
fof(f70226,plain,
composition(complement(top),complement(join(sF3,complement(composition(converse(sF8),sF2))))) = join(complement(join(sK0,complement(sF9))),composition(complement(top),complement(join(sF3,complement(composition(converse(sF8),sF2)))))),
inference(backward_demodulation,[],[f37426,f70225]) ).
fof(f70225,plain,
! [X4] : top = join(sF7,complement(composition(sF2,X4))),
inference(forward_demodulation,[],[f70183,f28]) ).
fof(f70183,plain,
! [X4] : top = join(complement(composition(sF2,X4)),sF7),
inference(superposition,[],[f16095,f10462]) ).
fof(f10462,plain,
! [X3] : join(X3,sF7) = join(sF2,join(X3,sF7)),
inference(superposition,[],[f372,f9251]) ).
fof(f9251,plain,
sF7 = join(sF2,sF7),
inference(backward_demodulation,[],[f2188,f9249]) ).
fof(f2188,plain,
join(sF7,sF7) = join(sF2,sF7),
inference(superposition,[],[f356,f2001]) ).
fof(f2001,plain,
sF7 = join(sF6,sF7),
inference(forward_demodulation,[],[f2000,f50]) ).
fof(f2000,plain,
join(sF2,sF6) = join(sF6,sF7),
inference(forward_demodulation,[],[f1985,f28]) ).
fof(f1985,plain,
join(sF2,sF6) = join(sF7,sF6),
inference(superposition,[],[f356,f1863]) ).
fof(f356,plain,
! [X23] : join(sF2,join(sF6,X23)) = join(sF7,X23),
inference(superposition,[],[f34,f50]) ).
fof(f16095,plain,
! [X36,X35] : top = join(sF2,join(complement(composition(sF2,X35)),X36)),
inference(forward_demodulation,[],[f16094,f8877]) ).
fof(f16094,plain,
! [X36,X35] : top = join(zero,join(sF2,join(complement(composition(sF2,X35)),X36))),
inference(forward_demodulation,[],[f16093,f3297]) ).
fof(f3297,plain,
! [X14,X15,X12,X13] : join(X15,join(X13,join(X14,X12))) = join(X13,join(X14,join(X15,X12))),
inference(forward_demodulation,[],[f2944,f34]) ).
fof(f2944,plain,
! [X14,X15,X12,X13] : join(join(X13,X14),join(X15,X12)) = join(X15,join(X13,join(X14,X12))),
inference(superposition,[],[f362,f362]) ).
fof(f16093,plain,
! [X36,X35] : top = join(sF2,join(complement(composition(sF2,X35)),join(zero,X36))),
inference(forward_demodulation,[],[f16016,f34]) ).
fof(f16016,plain,
! [X36,X35] : top = join(join(sF2,complement(composition(sF2,X35))),join(zero,X36)),
inference(superposition,[],[f9912,f11266]) ).
fof(f11266,plain,
! [X0] : zero = complement(join(sF2,complement(composition(sF2,X0)))),
inference(forward_demodulation,[],[f11265,f45]) ).
fof(f11265,plain,
! [X0] : zero = complement(join(complement(sK0),complement(composition(sF2,X0)))),
inference(forward_demodulation,[],[f11264,f28]) ).
fof(f11264,plain,
! [X0] : zero = complement(join(complement(composition(sF2,X0)),complement(sK0))),
inference(forward_demodulation,[],[f11263,f8877]) ).
fof(f11263,plain,
! [X0] : zero = join(zero,complement(join(complement(composition(sF2,X0)),complement(sK0)))),
inference(forward_demodulation,[],[f11262,f28]) ).
fof(f11262,plain,
! [X0] : zero = join(complement(join(complement(composition(sF2,X0)),complement(sK0))),zero),
inference(forward_demodulation,[],[f11261,f10255]) ).
fof(f11261,plain,
! [X0] : composition(complement(join(complement(sF2),complement(composition(sK0,converse(X0))))),zero) = join(complement(join(complement(composition(sF2,X0)),complement(sK0))),composition(complement(join(complement(sF2),complement(composition(sK0,converse(X0))))),zero)),
inference(forward_demodulation,[],[f11260,f58]) ).
fof(f11260,plain,
! [X0] : composition(complement(join(complement(sF2),complement(composition(sK0,converse(X0))))),complement(top)) = join(complement(join(complement(composition(sF2,X0)),complement(sK0))),composition(complement(join(complement(sF2),complement(composition(sK0,converse(X0))))),complement(top))),
inference(forward_demodulation,[],[f11259,f9911]) ).
fof(f11259,plain,
! [X0] : composition(complement(join(complement(sF2),complement(composition(sK0,converse(X0))))),complement(join(top,complement(X0)))) = join(complement(join(complement(composition(sF2,X0)),complement(sK0))),composition(complement(join(complement(sF2),complement(composition(sK0,converse(X0))))),complement(join(top,complement(X0))))),
inference(forward_demodulation,[],[f11258,f28]) ).
fof(f11258,plain,
! [X0] : composition(complement(join(complement(sF2),complement(composition(sK0,converse(X0))))),complement(join(complement(X0),top))) = join(complement(join(complement(composition(sF2,X0)),complement(sK0))),composition(complement(join(complement(sF2),complement(composition(sK0,converse(X0))))),complement(join(complement(X0),top)))),
inference(forward_demodulation,[],[f11247,f9364]) ).
fof(f9364,plain,
top = complement(zero),
inference(backward_demodulation,[],[f9010,f9048]) ).
fof(f9010,plain,
top = complement(composition(converse(sK0),sF2)),
inference(backward_demodulation,[],[f700,f8877]) ).
fof(f11247,plain,
! [X0] : composition(complement(join(complement(sF2),complement(composition(sK0,converse(X0))))),complement(join(complement(X0),complement(zero)))) = join(complement(join(complement(composition(sF2,X0)),complement(sK0))),composition(complement(join(complement(sF2),complement(composition(sK0,converse(X0))))),complement(join(complement(X0),complement(zero))))),
inference(superposition,[],[f44,f10993]) ).
fof(f10993,plain,
zero = composition(converse(sF2),sK0),
inference(backward_demodulation,[],[f10579,f10990]) ).
fof(f44,plain,
! [X2,X0,X1] : composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2))))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2)))))),
inference(definition_unfolding,[],[f39,f31,f31,f31,f31,f31]) ).
fof(f39,plain,
! [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)))),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] : 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/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842',dedekind_law) ).
fof(f9912,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(backward_demodulation,[],[f344,f9911]) ).
fof(f37426,plain,
composition(complement(join(sF7,complement(composition(sF2,converse(sK1))))),complement(join(sF3,complement(composition(converse(sF8),sF2))))) = join(complement(join(sK0,complement(sF9))),composition(complement(join(sF7,complement(composition(sF2,converse(sK1))))),complement(join(sF3,complement(composition(converse(sF8),sF2)))))),
inference(forward_demodulation,[],[f37370,f28]) ).
fof(f37370,plain,
composition(complement(join(sF7,complement(composition(sF2,converse(sK1))))),complement(join(sF3,complement(composition(converse(sF8),sF2))))) = join(complement(join(complement(sF9),sK0)),composition(complement(join(sF7,complement(composition(sF2,converse(sK1))))),complement(join(sF3,complement(composition(converse(sF8),sF2)))))),
inference(superposition,[],[f9206,f9020]) ).
fof(f9020,plain,
sK0 = complement(sF2),
inference(backward_demodulation,[],[f870,f8877]) ).
fof(f870,plain,
sK0 = join(zero,complement(sF2)),
inference(superposition,[],[f818,f45]) ).
fof(f9206,plain,
! [X20] : composition(complement(join(sF7,complement(composition(X20,converse(sK1))))),complement(join(sF3,complement(composition(converse(sF8),X20))))) = join(complement(join(complement(sF9),complement(X20))),composition(complement(join(sF7,complement(composition(X20,converse(sK1))))),complement(join(sF3,complement(composition(converse(sF8),X20)))))),
inference(backward_demodulation,[],[f1438,f8973]) ).
fof(f8973,plain,
! [X0] : join(sF7,X0) = join(complement(sF8),X0),
inference(backward_demodulation,[],[f971,f8877]) ).
fof(f971,plain,
! [X0] : join(sF7,X0) = join(zero,join(complement(sF8),X0)),
inference(superposition,[],[f34,f873]) ).
fof(f873,plain,
sF7 = join(zero,complement(sF8)),
inference(superposition,[],[f818,f51]) ).
fof(f1438,plain,
! [X20] : composition(complement(join(complement(sF8),complement(composition(X20,converse(sK1))))),complement(join(sF3,complement(composition(converse(sF8),X20))))) = join(complement(join(complement(sF9),complement(X20))),composition(complement(join(complement(sF8),complement(composition(X20,converse(sK1))))),complement(join(sF3,complement(composition(converse(sF8),X20)))))),
inference(forward_demodulation,[],[f1360,f46]) ).
fof(f46,plain,
complement(sK1) = sF3,
introduced(function_definition,[]) ).
fof(f1360,plain,
! [X20] : composition(complement(join(complement(sF8),complement(composition(X20,converse(sK1))))),complement(join(complement(sK1),complement(composition(converse(sF8),X20))))) = join(complement(join(complement(sF9),complement(X20))),composition(complement(join(complement(sF8),complement(composition(X20,converse(sK1))))),complement(join(complement(sK1),complement(composition(converse(sF8),X20)))))),
inference(superposition,[],[f44,f52]) ).
fof(f52,plain,
composition(sF8,sK1) = sF9,
introduced(function_definition,[]) ).
fof(f361,plain,
! [X3,X4] : top = join(X3,join(X4,complement(join(X3,X4)))),
inference(superposition,[],[f34,f27]) ).
fof(f13964,plain,
! [X0] : complement(X0) = join(complement(join(sK0,X0)),complement(join(sF2,X0))),
inference(superposition,[],[f800,f9239]) ).
fof(f800,plain,
! [X2] : join(complement(join(sK0,complement(X2))),complement(join(sF2,complement(X2)))) = X2,
inference(forward_demodulation,[],[f799,f28]) ).
fof(f799,plain,
! [X2] : join(complement(join(sF2,complement(X2))),complement(join(sK0,complement(X2)))) = X2,
inference(forward_demodulation,[],[f798,f28]) ).
fof(f798,plain,
! [X2] : join(complement(join(sF2,complement(X2))),complement(join(complement(X2),sK0))) = X2,
inference(forward_demodulation,[],[f797,f28]) ).
fof(f797,plain,
! [X2] : join(complement(join(complement(X2),sK0)),complement(join(sF2,complement(X2)))) = X2,
inference(forward_demodulation,[],[f779,f28]) ).
fof(f779,plain,
! [X2] : join(complement(join(complement(X2),sK0)),complement(join(complement(X2),sF2))) = X2,
inference(superposition,[],[f60,f45]) ).
fof(f127668,plain,
sF5 = join(sF5,complement(join(sF2,complement(sF9)))),
inference(superposition,[],[f20962,f127167]) ).
fof(f127167,plain,
join(sF2,complement(sF9)) = join(sF4,complement(sF9)),
inference(superposition,[],[f355,f126316]) ).
fof(f126316,plain,
complement(sF9) = join(sF3,complement(sF9)),
inference(forward_demodulation,[],[f126315,f46]) ).
fof(f126315,plain,
complement(sF9) = join(complement(sK1),complement(sF9)),
inference(forward_demodulation,[],[f125085,f28]) ).
fof(f125085,plain,
complement(sF9) = join(complement(sF9),complement(sK1)),
inference(superposition,[],[f24458,f21254]) ).
fof(f21254,plain,
sK1 = join(sK1,sF9),
inference(forward_demodulation,[],[f21253,f28]) ).
fof(f21253,plain,
sK1 = join(sF9,sK1),
inference(forward_demodulation,[],[f21233,f273]) ).
fof(f21233,plain,
composition(one,sK1) = join(sF9,composition(one,sK1)),
inference(superposition,[],[f531,f21199]) ).
fof(f21199,plain,
one = join(one,sF8),
inference(forward_demodulation,[],[f21156,f51]) ).
fof(f21156,plain,
one = join(one,complement(sF7)),
inference(superposition,[],[f20954,f2001]) ).
fof(f20954,plain,
! [X2] : one = join(one,complement(join(sF6,X2))),
inference(superposition,[],[f20803,f49]) ).
fof(f20803,plain,
! [X36,X35] : join(X35,complement(join(complement(X35),X36))) = X35,
inference(forward_demodulation,[],[f20607,f28]) ).
fof(f20607,plain,
! [X36,X35] : join(complement(join(complement(X35),X36)),X35) = X35,
inference(superposition,[],[f9851,f785]) ).
fof(f785,plain,
! [X3,X4] : join(complement(join(complement(X3),X4)),complement(join(complement(X4),complement(X3)))) = X3,
inference(superposition,[],[f60,f28]) ).
fof(f9851,plain,
! [X2,X3] : join(X2,X3) = join(X2,join(X2,X3)),
inference(superposition,[],[f34,f9249]) ).
fof(f531,plain,
! [X14] : join(sF9,composition(X14,sK1)) = composition(join(X14,sF8),sK1),
inference(forward_demodulation,[],[f513,f28]) ).
fof(f513,plain,
! [X14] : composition(join(X14,sF8),sK1) = join(composition(X14,sK1),sF9),
inference(superposition,[],[f36,f52]) ).
fof(f24458,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(superposition,[],[f20975,f9239]) ).
fof(f20975,plain,
! [X16,X17] : join(X16,complement(join(X17,complement(X16)))) = X16,
inference(superposition,[],[f20803,f28]) ).
fof(f355,plain,
! [X22] : join(sF2,join(sF3,X22)) = join(sF4,X22),
inference(superposition,[],[f34,f47]) ).
fof(f47,plain,
join(sF2,sF3) = sF4,
introduced(function_definition,[]) ).
fof(f20962,plain,
! [X10] : sF5 = join(sF5,complement(join(sF4,X10))),
inference(superposition,[],[f20803,f9022]) ).
fof(f9022,plain,
sF4 = complement(sF5),
inference(backward_demodulation,[],[f872,f8877]) ).
fof(f872,plain,
sF4 = join(zero,complement(sF5)),
inference(superposition,[],[f818,f48]) ).
fof(f48,plain,
complement(sF4) = sF5,
introduced(function_definition,[]) ).
fof(f54,plain,
sF5 != sF10,
inference(definition_folding,[],[f40,f53,f48,f47,f46,f45,f52,f51,f50,f49,f45,f48,f47,f46,f45]) ).
fof(f40,plain,
complement(join(complement(sK0),complement(sK1))) != join(composition(complement(join(complement(sK0),complement(one))),sK1),complement(join(complement(sK0),complement(sK1)))),
inference(definition_unfolding,[],[f23,f31,f31,f31]) ).
fof(f23,plain,
meet(sK0,sK1) != join(composition(meet(sK0,one),sK1),meet(sK0,sK1)),
inference(cnf_transformation,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL021+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.19/0.36 % Computer : n029.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Fri Aug 25 22:42:55 EDT 2023
% 0.19/0.37 % CPUTime :
% 0.19/0.37 This is a FOF_THM_RFO_PEQ problem
% 0.19/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.31FDDQAdiZ/Vampire---4.8_30842
% 0.19/0.37 % (30961)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.43 % (30963)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.19/0.43 % (30965)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.19/0.43 % (30966)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.19/0.43 % (30967)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.19/0.43 % (30962)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.19/0.43 % (30964)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.19/0.43 % (30968)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 37.11/5.71 % (30964)First to succeed.
% 37.11/5.72 % (30964)Refutation found. Thanks to Tanya!
% 37.11/5.72 % SZS status Theorem for Vampire---4
% 37.11/5.72 % SZS output start Proof for Vampire---4
% See solution above
% 37.11/5.72 % (30964)------------------------------
% 37.11/5.72 % (30964)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 37.11/5.72 % (30964)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 37.11/5.72 % (30964)Termination reason: Refutation
% 37.11/5.72
% 37.11/5.72 % (30964)Memory used [KB]: 202896
% 37.11/5.72 % (30964)Time elapsed: 5.270 s
% 37.11/5.72 % (30964)------------------------------
% 37.11/5.72 % (30964)------------------------------
% 37.11/5.72 % (30961)Success in time 5.324 s
% 37.11/5.73 % Vampire---4.8 exiting
%------------------------------------------------------------------------------