TSTP Solution File: REL043+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : REL043+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : 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 : Sun May 5 08:53:09 EDT 2024
% Result : Theorem 37.16s 5.65s
% Output : Refutation 37.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 80
% Number of leaves : 17
% Syntax : Number of formulae : 274 ( 269 unt; 0 def)
% Number of atoms : 281 ( 280 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 15 ( 8 ~; 0 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 426 ( 420 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f291177,plain,
$false,
inference(trivial_inequality_removal,[],[f291031]) ).
fof(f291031,plain,
complement(sK0) != complement(sK0),
inference(superposition,[],[f44,f253182]) ).
fof(f253182,plain,
complement(sK0) = join(complement(sK0),composition(complement(sK2),sK1)),
inference(superposition,[],[f141044,f162501]) ).
fof(f162501,plain,
! [X0,X1] : join(complement(X0),X1) = join(meet(X0,X1),complement(X0)),
inference(forward_demodulation,[],[f162467,f142742]) ).
fof(f142742,plain,
! [X2,X0,X1] : meet(X1,X0) = meet(meet(X1,X0),join(X2,X0)),
inference(superposition,[],[f137727,f115013]) ).
fof(f115013,plain,
! [X0,X1] : join(X1,meet(X0,X1)) = X1,
inference(superposition,[],[f114945,f1949]) ).
fof(f1949,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f1655,f1946]) ).
fof(f1946,plain,
! [X0] : meet(X0,X0) = X0,
inference(forward_demodulation,[],[f1945,f1666]) ).
fof(f1666,plain,
! [X0] : join(zero,meet(X0,meet(X0,X0))) = X0,
inference(superposition,[],[f387,f1655]) ).
fof(f387,plain,
! [X0] : join(zero,meet(X0,complement(complement(X0)))) = X0,
inference(superposition,[],[f271,f28]) ).
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/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f271,plain,
! [X0] : join(meet(X0,complement(complement(X0))),zero) = X0,
inference(forward_demodulation,[],[f258,f62]) ).
fof(f62,plain,
zero = complement(top),
inference(forward_demodulation,[],[f57,f26]) ).
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/benchmark/theBenchmark.p',def_zero) ).
fof(f57,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(superposition,[],[f31,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/benchmark/theBenchmark.p',def_top) ).
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/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f258,plain,
! [X0] : join(meet(X0,complement(complement(X0))),complement(top)) = X0,
inference(superposition,[],[f40,f27]) ).
fof(f40,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f33,f31]) ).
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/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f1945,plain,
! [X0] : meet(X0,X0) = join(zero,meet(X0,meet(X0,X0))),
inference(forward_demodulation,[],[f1944,f1764]) ).
fof(f1764,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(superposition,[],[f58,f31]) ).
fof(f58,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(superposition,[],[f31,f28]) ).
fof(f1944,plain,
! [X0] : meet(X0,X0) = join(zero,meet(meet(X0,X0),X0)),
inference(forward_demodulation,[],[f1932,f31]) ).
fof(f1932,plain,
! [X0] : meet(X0,X0) = join(zero,complement(join(complement(meet(X0,X0)),complement(X0)))),
inference(superposition,[],[f40,f1790]) ).
fof(f1790,plain,
! [X0] : zero = meet(meet(X0,X0),complement(X0)),
inference(superposition,[],[f1782,f1655]) ).
fof(f1782,plain,
! [X0] : zero = meet(complement(X0),X0),
inference(forward_demodulation,[],[f1761,f62]) ).
fof(f1761,plain,
! [X0] : complement(top) = meet(complement(X0),X0),
inference(superposition,[],[f58,f27]) ).
fof(f1655,plain,
! [X0] : complement(complement(X0)) = meet(X0,X0),
inference(superposition,[],[f31,f1531]) ).
fof(f1531,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f1492,f1515]) ).
fof(f1515,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f1463,f1487]) ).
fof(f1487,plain,
one = converse(one),
inference(superposition,[],[f1463,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/benchmark/theBenchmark.p',composition_identity) ).
fof(f1463,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f1435,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/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f1435,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f54,f25]) ).
fof(f54,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
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/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f1492,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(superposition,[],[f32,f1463]) ).
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/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f114945,plain,
! [X0,X1] : join(X0,meet(complement(X1),X0)) = X0,
inference(forward_demodulation,[],[f114919,f2128]) ).
fof(f2128,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,complement(X1))) = X0,
inference(backward_demodulation,[],[f40,f2117]) ).
fof(f2117,plain,
! [X0,X1] : meet(X1,complement(X0)) = complement(join(complement(X1),X0)),
inference(backward_demodulation,[],[f1984,f2114]) ).
fof(f2114,plain,
! [X0] : meet(X0,top) = X0,
inference(backward_demodulation,[],[f1978,f1949]) ).
fof(f1978,plain,
! [X0] : complement(complement(X0)) = meet(X0,top),
inference(backward_demodulation,[],[f67,f1947]) ).
fof(f1947,plain,
! [X0] : join(zero,X0) = X0,
inference(backward_demodulation,[],[f263,f1946]) ).
fof(f263,plain,
! [X0] : join(zero,meet(X0,X0)) = X0,
inference(forward_demodulation,[],[f248,f31]) ).
fof(f248,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[],[f40,f26]) ).
fof(f67,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[],[f63,f28]) ).
fof(f63,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(superposition,[],[f31,f62]) ).
fof(f1984,plain,
! [X0,X1] : complement(join(complement(X1),meet(X0,top))) = meet(X1,complement(X0)),
inference(backward_demodulation,[],[f91,f1947]) ).
fof(f91,plain,
! [X0,X1] : meet(X1,join(zero,complement(X0))) = complement(join(complement(X1),meet(X0,top))),
inference(superposition,[],[f31,f67]) ).
fof(f114919,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,complement(X1))) = join(X0,meet(complement(X1),X0)),
inference(backward_demodulation,[],[f114082,f114879]) ).
fof(f114879,plain,
! [X0,X1] : meet(X1,X0) = meet(X0,meet(X1,X0)),
inference(forward_demodulation,[],[f114658,f2167]) ).
fof(f2167,plain,
! [X0] : join(X0,zero) = X0,
inference(forward_demodulation,[],[f2140,f1946]) ).
fof(f2140,plain,
! [X0] : join(meet(X0,X0),zero) = X0,
inference(backward_demodulation,[],[f2023,f2115]) ).
fof(f2115,plain,
! [X0] : meet(top,X0) = X0,
inference(backward_demodulation,[],[f1977,f1949]) ).
fof(f1977,plain,
! [X0] : complement(complement(X0)) = meet(top,X0),
inference(backward_demodulation,[],[f64,f1947]) ).
fof(f64,plain,
! [X0] : meet(top,X0) = complement(join(zero,complement(X0))),
inference(superposition,[],[f31,f62]) ).
fof(f2023,plain,
! [X0] : join(meet(X0,meet(top,X0)),zero) = X0,
inference(backward_demodulation,[],[f271,f1977]) ).
fof(f114658,plain,
! [X0,X1] : join(meet(X1,X0),zero) = meet(X0,meet(X1,X0)),
inference(superposition,[],[f114077,f1947]) ).
fof(f114077,plain,
! [X2,X0,X1] : join(meet(X0,X1),X2) = join(X2,meet(X1,meet(X0,X1))),
inference(forward_demodulation,[],[f114074,f2355]) ).
fof(f2355,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f34,f2320]) ).
fof(f2320,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f1531,f1949]) ).
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/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f114074,plain,
! [X2,X0,X1] : join(X2,meet(X1,meet(X0,X1))) = join(meet(X0,X1),join(meet(X0,X1),X2)),
inference(backward_demodulation,[],[f20572,f114073]) ).
fof(f114073,plain,
! [X2,X0,X1] : join(meet(X0,X1),X2) = join(meet(X1,meet(X0,X1)),X2),
inference(forward_demodulation,[],[f114072,f1764]) ).
fof(f114072,plain,
! [X2,X0,X1] : join(meet(X0,X1),X2) = join(meet(meet(X0,X1),X1),X2),
inference(forward_demodulation,[],[f113986,f1947]) ).
fof(f113986,plain,
! [X2,X0,X1] : join(meet(X0,X1),X2) = join(meet(meet(X0,X1),X1),join(zero,X2)),
inference(superposition,[],[f2127,f112792]) ).
fof(f112792,plain,
! [X0,X1] : zero = meet(meet(X1,X0),complement(X0)),
inference(superposition,[],[f111263,f1764]) ).
fof(f111263,plain,
! [X0,X1] : zero = meet(meet(X0,X1),complement(X0)),
inference(superposition,[],[f110685,f261]) ).
fof(f261,plain,
! [X0,X1] : join(meet(X0,complement(X1)),meet(X0,X1)) = X0,
inference(superposition,[],[f40,f31]) ).
fof(f110685,plain,
! [X0,X1] : zero = meet(X0,complement(join(X1,X0))),
inference(forward_demodulation,[],[f109884,f2416]) ).
fof(f2416,plain,
zero = converse(zero),
inference(superposition,[],[f2227,f2167]) ).
fof(f2227,plain,
! [X0] : join(converse(zero),X0) = X0,
inference(forward_demodulation,[],[f2211,f24]) ).
fof(f2211,plain,
! [X0] : converse(converse(X0)) = join(converse(zero),X0),
inference(superposition,[],[f48,f1947]) ).
fof(f48,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/benchmark/theBenchmark.p',converse_additivity) ).
fof(f109884,plain,
! [X0,X1] : converse(zero) = meet(X0,complement(join(X1,X0))),
inference(superposition,[],[f24,f108595]) ).
fof(f108595,plain,
! [X0,X1] : zero = converse(meet(X0,complement(join(X1,X0)))),
inference(forward_demodulation,[],[f108594,f2416]) ).
fof(f108594,plain,
! [X0,X1] : converse(zero) = converse(meet(X0,complement(join(X1,X0)))),
inference(forward_demodulation,[],[f108593,f62]) ).
fof(f108593,plain,
! [X0,X1] : converse(complement(top)) = converse(meet(X0,complement(join(X1,X0)))),
inference(forward_demodulation,[],[f108592,f45452]) ).
fof(f45452,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(superposition,[],[f45036,f24]) ).
fof(f45036,plain,
! [X0] : complement(X0) = converse(complement(converse(X0))),
inference(forward_demodulation,[],[f45027,f1947]) ).
fof(f45027,plain,
! [X0] : join(zero,complement(X0)) = converse(complement(converse(X0))),
inference(backward_demodulation,[],[f24399,f44939]) ).
fof(f44939,plain,
! [X0] : zero = meet(X0,converse(complement(converse(X0)))),
inference(superposition,[],[f44758,f24]) ).
fof(f44758,plain,
! [X0] : zero = meet(converse(X0),converse(complement(X0))),
inference(superposition,[],[f42879,f2167]) ).
fof(f42879,plain,
! [X0] : zero = join(meet(converse(X0),converse(complement(X0))),zero),
inference(forward_demodulation,[],[f42878,f1515]) ).
fof(f42878,plain,
! [X0] : zero = join(meet(converse(X0),composition(one,converse(complement(X0)))),zero),
inference(forward_demodulation,[],[f42877,f1764]) ).
fof(f42877,plain,
! [X0] : zero = join(meet(composition(one,converse(complement(X0))),converse(X0)),zero),
inference(forward_demodulation,[],[f42876,f5230]) ).
fof(f5230,plain,
! [X0] : zero = meet(zero,X0),
inference(forward_demodulation,[],[f5206,f62]) ).
fof(f5206,plain,
! [X0] : complement(top) = meet(zero,X0),
inference(superposition,[],[f1949,f5153]) ).
fof(f5153,plain,
! [X0] : top = complement(meet(zero,X0)),
inference(superposition,[],[f5080,f2167]) ).
fof(f5080,plain,
! [X0,X1] : top = join(complement(meet(X0,X1)),X0),
inference(superposition,[],[f5044,f261]) ).
fof(f5044,plain,
! [X0,X1] : top = join(complement(X0),join(X1,X0)),
inference(forward_demodulation,[],[f5043,f2825]) ).
fof(f2825,plain,
top = converse(top),
inference(backward_demodulation,[],[f907,f2808]) ).
fof(f2808,plain,
! [X0] : top = join(X0,converse(top)),
inference(backward_demodulation,[],[f2605,f2747]) ).
fof(f2747,plain,
! [X0] : top = join(top,X0),
inference(superposition,[],[f2651,f28]) ).
fof(f2651,plain,
! [X0] : top = join(X0,top),
inference(forward_demodulation,[],[f2603,f2649]) ).
fof(f2649,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f2599,f27]) ).
fof(f2599,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[],[f99,f2320]) ).
fof(f99,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f34,f27]) ).
fof(f2603,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(superposition,[],[f99,f27]) ).
fof(f2605,plain,
! [X0] : join(X0,converse(top)) = join(top,converse(complement(converse(complement(X0))))),
inference(superposition,[],[f99,f822]) ).
fof(f822,plain,
! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
inference(superposition,[],[f47,f27]) ).
fof(f47,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f29,f24]) ).
fof(f907,plain,
converse(top) = join(composition(sK0,converse(sK1)),converse(top)),
inference(superposition,[],[f129,f822]) ).
fof(f129,plain,
! [X0] : join(top,X0) = join(composition(sK0,converse(sK1)),join(top,X0)),
inference(superposition,[],[f34,f118]) ).
fof(f118,plain,
top = join(composition(sK0,converse(sK1)),top),
inference(superposition,[],[f103,f27]) ).
fof(f103,plain,
! [X0] : join(sK2,X0) = join(composition(sK0,converse(sK1)),join(sK2,X0)),
inference(superposition,[],[f34,f22]) ).
fof(f22,plain,
sK2 = join(composition(sK0,converse(sK1)),sK2),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
( complement(sK0) != join(composition(complement(sK2),sK1),complement(sK0))
& sK2 = join(composition(sK0,converse(sK1)),sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f19,f20]) ).
fof(f20,plain,
( ? [X0,X1,X2] :
( complement(X0) != join(composition(complement(X2),X1),complement(X0))
& join(composition(X0,converse(X1)),X2) = X2 )
=> ( complement(sK0) != join(composition(complement(sK2),sK1),complement(sK0))
& sK2 = join(composition(sK0,converse(sK1)),sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
? [X0,X1,X2] :
( complement(X0) != join(composition(complement(X2),X1),complement(X0))
& join(composition(X0,converse(X1)),X2) = X2 ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( join(composition(X0,converse(X1)),X2) = X2
=> complement(X0) = join(composition(complement(X2),X1),complement(X0)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( join(composition(X0,converse(X1)),X2) = X2
=> complement(X0) = join(composition(complement(X2),X1),complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f5043,plain,
! [X0,X1] : converse(top) = join(complement(X0),join(X1,X0)),
inference(forward_demodulation,[],[f4975,f24]) ).
fof(f4975,plain,
! [X0,X1] : converse(top) = join(complement(X0),converse(converse(join(X1,X0)))),
inference(superposition,[],[f47,f4459]) ).
fof(f4459,plain,
! [X0,X1] : top = join(converse(complement(X0)),converse(join(X1,X0))),
inference(superposition,[],[f4140,f1949]) ).
fof(f4140,plain,
! [X0,X1] : top = join(converse(X0),converse(join(X1,complement(X0)))),
inference(superposition,[],[f3919,f28]) ).
fof(f3919,plain,
! [X0,X1] : top = join(converse(X0),converse(join(complement(X0),X1))),
inference(superposition,[],[f2852,f24]) ).
fof(f2852,plain,
! [X0,X1] : top = join(X0,converse(join(complement(converse(X0)),X1))),
inference(backward_demodulation,[],[f2774,f2825]) ).
fof(f2774,plain,
! [X0,X1] : converse(top) = join(X0,converse(join(complement(converse(X0)),X1))),
inference(backward_demodulation,[],[f2630,f2747]) ).
fof(f2630,plain,
! [X0,X1] : join(X0,converse(join(complement(converse(X0)),X1))) = converse(join(top,X1)),
inference(superposition,[],[f47,f99]) ).
fof(f42876,plain,
! [X0] : meet(zero,converse(X0)) = join(meet(composition(one,converse(complement(X0))),converse(X0)),meet(zero,converse(X0))),
inference(forward_demodulation,[],[f42875,f1764]) ).
fof(f42875,plain,
! [X0] : meet(converse(X0),zero) = join(meet(composition(one,converse(complement(X0))),converse(X0)),meet(converse(X0),zero)),
inference(forward_demodulation,[],[f42874,f42432]) ).
fof(f42432,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[],[f42338,f2416]) ).
fof(f42338,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(superposition,[],[f54,f41849]) ).
fof(f41849,plain,
! [X0] : zero = composition(X0,zero),
inference(forward_demodulation,[],[f41848,f41311]) ).
fof(f41311,plain,
zero = composition(top,zero),
inference(superposition,[],[f41115,f1947]) ).
fof(f41115,plain,
zero = join(zero,composition(top,zero)),
inference(forward_demodulation,[],[f41114,f2825]) ).
fof(f41114,plain,
zero = join(zero,composition(converse(top),zero)),
inference(forward_demodulation,[],[f41068,f62]) ).
fof(f41068,plain,
complement(top) = join(complement(top),composition(converse(top),complement(top))),
inference(superposition,[],[f349,f40807]) ).
fof(f40807,plain,
top = composition(top,top),
inference(superposition,[],[f40554,f8884]) ).
fof(f8884,plain,
! [X0,X1] : top = join(join(complement(X0),X1),X0),
inference(superposition,[],[f8556,f1949]) ).
fof(f8556,plain,
! [X0,X1] : top = join(join(X1,X0),complement(X1)),
inference(superposition,[],[f8480,f28]) ).
fof(f8480,plain,
! [X0,X1] : top = join(join(X1,X0),complement(X0)),
inference(superposition,[],[f5424,f2320]) ).
fof(f5424,plain,
! [X2,X0,X1] : top = join(join(X1,X0),join(complement(X0),X2)),
inference(forward_demodulation,[],[f5292,f2747]) ).
fof(f5292,plain,
! [X2,X0,X1] : join(top,X2) = join(join(X1,X0),join(complement(X0),X2)),
inference(superposition,[],[f100,f5044]) ).
fof(f100,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(superposition,[],[f34,f28]) ).
fof(f40554,plain,
! [X0] : top = composition(join(X0,one),top),
inference(forward_demodulation,[],[f40553,f3518]) ).
fof(f3518,plain,
top = join(composition(top,top),converse(complement(composition(top,top)))),
inference(superposition,[],[f2827,f3452]) ).
fof(f3452,plain,
composition(top,top) = converse(composition(top,top)),
inference(superposition,[],[f3171,f2825]) ).
fof(f3171,plain,
! [X0] : composition(top,X0) = converse(composition(converse(X0),top)),
inference(superposition,[],[f24,f2879]) ).
fof(f2879,plain,
! [X0] : composition(converse(X0),top) = converse(composition(top,X0)),
inference(superposition,[],[f30,f2825]) ).
fof(f2827,plain,
! [X0] : top = join(X0,converse(complement(converse(X0)))),
inference(backward_demodulation,[],[f822,f2825]) ).
fof(f40553,plain,
! [X0] : join(composition(top,top),converse(complement(composition(top,top)))) = composition(join(X0,one),top),
inference(forward_demodulation,[],[f40552,f2651]) ).
fof(f40552,plain,
! [X0] : join(composition(join(X0,top),top),converse(complement(composition(top,top)))) = composition(join(X0,one),top),
inference(forward_demodulation,[],[f40508,f1539]) ).
fof(f1539,plain,
! [X0,X1] : join(composition(X1,X0),X0) = composition(join(X1,one),X0),
inference(forward_demodulation,[],[f1500,f1487]) ).
fof(f1500,plain,
! [X0,X1] : composition(join(X1,converse(one)),X0) = join(composition(X1,X0),X0),
inference(superposition,[],[f36,f1463]) ).
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/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f40508,plain,
! [X0] : join(composition(join(X0,top),top),converse(complement(composition(top,top)))) = join(composition(X0,top),top),
inference(superposition,[],[f442,f3518]) ).
fof(f442,plain,
! [X2,X3,X0,X1] : join(composition(X0,X1),join(composition(X2,X1),X3)) = join(composition(join(X0,X2),X1),X3),
inference(superposition,[],[f34,f36]) ).
fof(f349,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(superposition,[],[f32,f28]) ).
fof(f41848,plain,
! [X0] : composition(X0,zero) = composition(top,zero),
inference(forward_demodulation,[],[f41847,f2747]) ).
fof(f41847,plain,
! [X0] : composition(X0,zero) = composition(join(top,X0),zero),
inference(forward_demodulation,[],[f41794,f1947]) ).
fof(f41794,plain,
! [X0] : composition(join(top,X0),zero) = join(zero,composition(X0,zero)),
inference(superposition,[],[f36,f41311]) ).
fof(f42874,plain,
! [X0] : meet(converse(X0),composition(zero,converse(complement(X0)))) = join(meet(composition(one,converse(complement(X0))),converse(X0)),meet(converse(X0),composition(zero,converse(complement(X0))))),
inference(forward_demodulation,[],[f42754,f1764]) ).
fof(f42754,plain,
! [X0] : meet(composition(zero,converse(complement(X0))),converse(X0)) = join(meet(composition(one,converse(complement(X0))),converse(X0)),meet(composition(zero,converse(complement(X0))),converse(X0))),
inference(superposition,[],[f622,f37767]) ).
fof(f37767,plain,
! [X0] : zero = meet(one,composition(converse(X0),complement(X0))),
inference(superposition,[],[f37652,f24]) ).
fof(f37652,plain,
! [X0] : zero = meet(one,composition(X0,complement(converse(X0)))),
inference(superposition,[],[f35219,f2167]) ).
fof(f35219,plain,
! [X0] : zero = join(meet(one,composition(X0,complement(converse(X0)))),zero),
inference(forward_demodulation,[],[f35218,f1764]) ).
fof(f35218,plain,
! [X0] : zero = join(meet(composition(X0,complement(converse(X0))),one),zero),
inference(forward_demodulation,[],[f35217,f33824]) ).
fof(f33824,plain,
! [X0] : zero = meet(one,composition(X0,zero)),
inference(forward_demodulation,[],[f33823,f5220]) ).
fof(f5220,plain,
! [X0] : zero = meet(X0,zero),
inference(forward_demodulation,[],[f5200,f62]) ).
fof(f5200,plain,
! [X0] : complement(top) = meet(X0,zero),
inference(superposition,[],[f2083,f5153]) ).
fof(f2083,plain,
! [X0,X1] : meet(X0,X1) = complement(complement(meet(X1,X0))),
inference(backward_demodulation,[],[f31,f2082]) ).
fof(f2082,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X1,X0)),
inference(backward_demodulation,[],[f2068,f2081]) ).
fof(f2081,plain,
! [X0,X1] : complement(X0) = join(meet(complement(X0),X1),complement(join(X0,X1))),
inference(forward_demodulation,[],[f1990,f2031]) ).
fof(f2031,plain,
! [X0,X1] : join(X0,X1) = join(meet(top,X0),X1),
inference(backward_demodulation,[],[f1976,f1977]) ).
fof(f1976,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),X1),
inference(backward_demodulation,[],[f1743,f1947]) ).
fof(f1743,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),join(zero,X1)),
inference(superposition,[],[f34,f1699]) ).
fof(f1699,plain,
! [X0] : join(complement(complement(X0)),zero) = X0,
inference(forward_demodulation,[],[f1698,f62]) ).
fof(f1698,plain,
! [X0] : join(complement(complement(X0)),complement(top)) = X0,
inference(forward_demodulation,[],[f1697,f27]) ).
fof(f1697,plain,
! [X0] : join(complement(complement(X0)),complement(join(X0,complement(X0)))) = X0,
inference(forward_demodulation,[],[f1680,f28]) ).
fof(f1680,plain,
! [X0] : join(complement(complement(X0)),complement(join(complement(X0),X0))) = X0,
inference(superposition,[],[f40,f1655]) ).
fof(f1990,plain,
! [X0,X1] : complement(X0) = join(meet(complement(X0),X1),complement(join(meet(top,X0),X1))),
inference(backward_demodulation,[],[f255,f1947]) ).
fof(f255,plain,
! [X0,X1] : join(zero,complement(X0)) = join(meet(join(zero,complement(X0)),X1),complement(join(meet(top,X0),X1))),
inference(superposition,[],[f40,f64]) ).
fof(f2068,plain,
! [X2,X0,X1] : join(complement(X0),complement(X1)) = join(meet(complement(meet(X1,X0)),X2),complement(join(meet(X1,X0),X2))),
inference(backward_demodulation,[],[f1772,f2063]) ).
fof(f2063,plain,
! [X2,X0,X1] : meet(join(complement(X0),complement(X1)),X2) = meet(complement(meet(X1,X0)),X2),
inference(backward_demodulation,[],[f1769,f2061]) ).
fof(f2061,plain,
! [X0,X1] : complement(join(X0,complement(X1))) = meet(complement(X0),X1),
inference(forward_demodulation,[],[f1981,f2031]) ).
fof(f1981,plain,
! [X0,X1] : complement(join(meet(top,X0),complement(X1))) = meet(complement(X0),X1),
inference(backward_demodulation,[],[f73,f1947]) ).
fof(f73,plain,
! [X0,X1] : meet(join(zero,complement(X0)),X1) = complement(join(meet(top,X0),complement(X1))),
inference(superposition,[],[f31,f64]) ).
fof(f1769,plain,
! [X2,X0,X1] : meet(join(complement(X0),complement(X1)),X2) = complement(join(meet(X1,X0),complement(X2))),
inference(superposition,[],[f31,f58]) ).
fof(f1772,plain,
! [X2,X0,X1] : join(complement(X0),complement(X1)) = join(meet(join(complement(X0),complement(X1)),X2),complement(join(meet(X1,X0),X2))),
inference(superposition,[],[f40,f58]) ).
fof(f33823,plain,
! [X0] : meet(one,composition(X0,zero)) = meet(meet(one,composition(X0,zero)),zero),
inference(forward_demodulation,[],[f33822,f2416]) ).
fof(f33822,plain,
! [X0] : meet(one,composition(X0,zero)) = meet(meet(one,composition(X0,zero)),converse(zero)),
inference(forward_demodulation,[],[f33721,f62]) ).
fof(f33721,plain,
! [X0] : meet(one,composition(X0,zero)) = meet(meet(one,composition(X0,zero)),converse(complement(top))),
inference(superposition,[],[f24201,f33350]) ).
fof(f33350,plain,
! [X0] : top = converse(complement(meet(one,composition(X0,zero)))),
inference(forward_demodulation,[],[f33349,f2313]) ).
fof(f2313,plain,
! [X0,X1] : complement(meet(X0,X1)) = complement(meet(X1,X0)),
inference(superposition,[],[f1949,f2083]) ).
fof(f33349,plain,
! [X0] : top = converse(complement(meet(composition(X0,zero),one))),
inference(forward_demodulation,[],[f33284,f2082]) ).
fof(f33284,plain,
! [X0] : top = converse(join(complement(one),complement(composition(X0,zero)))),
inference(superposition,[],[f30344,f49]) ).
fof(f49,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(superposition,[],[f29,f28]) ).
fof(f30344,plain,
! [X0] : top = join(converse(complement(composition(X0,zero))),converse(complement(one))),
inference(superposition,[],[f4459,f30281]) ).
fof(f30281,plain,
! [X0] : complement(one) = join(complement(one),composition(X0,zero)),
inference(forward_demodulation,[],[f30280,f7049]) ).
fof(f7049,plain,
complement(one) = join(composition(top,zero),complement(one)),
inference(forward_demodulation,[],[f7015,f62]) ).
fof(f7015,plain,
complement(one) = join(composition(top,complement(top)),complement(one)),
inference(superposition,[],[f341,f2825]) ).
fof(f341,plain,
! [X0] : complement(one) = join(composition(converse(X0),complement(X0)),complement(one)),
inference(superposition,[],[f32,f25]) ).
fof(f30280,plain,
! [X0] : join(composition(top,zero),complement(one)) = join(complement(one),composition(X0,zero)),
inference(forward_demodulation,[],[f30279,f2651]) ).
fof(f30279,plain,
! [X0] : join(composition(join(X0,top),zero),complement(one)) = join(complement(one),composition(X0,zero)),
inference(forward_demodulation,[],[f30163,f28]) ).
fof(f30163,plain,
! [X0] : join(composition(join(X0,top),zero),complement(one)) = join(composition(X0,zero),complement(one)),
inference(superposition,[],[f442,f7049]) ).
fof(f24201,plain,
! [X0] : meet(X0,converse(complement(converse(complement(X0))))) = X0,
inference(superposition,[],[f2858,f2167]) ).
fof(f2858,plain,
! [X0] : join(meet(X0,converse(complement(converse(complement(X0))))),zero) = X0,
inference(forward_demodulation,[],[f2832,f62]) ).
fof(f2832,plain,
! [X0] : join(meet(X0,converse(complement(converse(complement(X0))))),complement(top)) = X0,
inference(backward_demodulation,[],[f900,f2825]) ).
fof(f900,plain,
! [X0] : join(meet(X0,converse(complement(converse(complement(X0))))),complement(converse(top))) = X0,
inference(superposition,[],[f40,f822]) ).
fof(f35217,plain,
! [X0] : meet(one,composition(X0,zero)) = join(meet(composition(X0,complement(converse(X0))),one),meet(one,composition(X0,zero))),
inference(forward_demodulation,[],[f35096,f1764]) ).
fof(f35096,plain,
! [X0] : meet(composition(X0,zero),one) = join(meet(composition(X0,complement(converse(X0))),one),meet(composition(X0,zero),one)),
inference(superposition,[],[f541,f1782]) ).
fof(f541,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,[],[f37,f25]) ).
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/benchmark/theBenchmark.p',modular_law_1) ).
fof(f622,plain,
! [X2,X0,X1] : meet(composition(meet(X1,composition(X2,X0)),converse(X0)),X2) = join(meet(composition(X1,converse(X0)),X2),meet(composition(meet(X1,composition(X2,X0)),converse(X0)),X2)),
inference(superposition,[],[f38,f24]) ).
fof(f38,plain,
! [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)),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1,X2] : 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) ).
fof(f24399,plain,
! [X0] : converse(complement(converse(X0))) = join(meet(X0,converse(complement(converse(X0)))),complement(X0)),
inference(forward_demodulation,[],[f24398,f1949]) ).
fof(f24398,plain,
! [X0] : converse(complement(converse(complement(complement(X0))))) = join(meet(X0,converse(complement(converse(complement(complement(X0)))))),complement(X0)),
inference(forward_demodulation,[],[f24355,f1764]) ).
fof(f24355,plain,
! [X0] : converse(complement(converse(complement(complement(X0))))) = join(meet(converse(complement(converse(complement(complement(X0))))),X0),complement(X0)),
inference(superposition,[],[f2062,f24201]) ).
fof(f2062,plain,
! [X0,X1] : join(meet(X0,X1),meet(complement(X1),X0)) = X0,
inference(backward_demodulation,[],[f259,f2061]) ).
fof(f259,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(X1,complement(X0)))) = X0,
inference(superposition,[],[f40,f28]) ).
fof(f108592,plain,
! [X0,X1] : complement(converse(top)) = converse(meet(X0,complement(join(X1,X0)))),
inference(forward_demodulation,[],[f108591,f2117]) ).
fof(f108591,plain,
! [X0,X1] : complement(converse(top)) = converse(complement(join(complement(X0),join(X1,X0)))),
inference(forward_demodulation,[],[f108144,f34]) ).
fof(f108144,plain,
! [X0,X1] : complement(converse(top)) = converse(complement(join(join(complement(X0),X1),X0))),
inference(superposition,[],[f107664,f2761]) ).
fof(f2761,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(backward_demodulation,[],[f99,f2747]) ).
fof(f107664,plain,
! [X0,X1] : complement(converse(join(X1,X0))) = converse(complement(join(X0,X1))),
inference(superposition,[],[f45452,f1090]) ).
fof(f1090,plain,
! [X0,X1] : converse(join(X0,X1)) = converse(join(X1,X0)),
inference(superposition,[],[f49,f29]) ).
fof(f2127,plain,
! [X2,X0,X1] : join(X0,X2) = join(meet(X0,X1),join(meet(X0,complement(X1)),X2)),
inference(backward_demodulation,[],[f262,f2117]) ).
fof(f262,plain,
! [X2,X0,X1] : join(X0,X2) = join(meet(X0,X1),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f34,f40]) ).
fof(f20572,plain,
! [X2,X0,X1] : join(meet(X0,X1),join(meet(X1,meet(X0,X1)),X2)) = join(X2,meet(X1,meet(X0,X1))),
inference(forward_demodulation,[],[f20531,f1764]) ).
fof(f20531,plain,
! [X2,X0,X1] : join(meet(X0,X1),join(meet(meet(X0,X1),X1),X2)) = join(X2,meet(meet(X0,X1),X1)),
inference(superposition,[],[f108,f1527]) ).
fof(f1527,plain,
! [X0,X1] : meet(meet(X0,X1),X1) = join(meet(X0,X1),meet(meet(X0,X1),X1)),
inference(forward_demodulation,[],[f1517,f25]) ).
fof(f1517,plain,
! [X0,X1] : meet(meet(X0,composition(X1,one)),X1) = join(meet(X0,X1),meet(meet(X0,composition(X1,one)),X1)),
inference(backward_demodulation,[],[f629,f1487]) ).
fof(f629,plain,
! [X0,X1] : meet(meet(X0,composition(X1,converse(one))),X1) = join(meet(X0,X1),meet(meet(X0,composition(X1,converse(one))),X1)),
inference(forward_demodulation,[],[f616,f25]) ).
fof(f616,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,[],[f38,f25]) ).
fof(f108,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f34,f28]) ).
fof(f114082,plain,
! [X0,X1] : join(meet(X0,X1),meet(complement(X1),meet(X0,complement(X1)))) = join(X0,meet(complement(X1),X0)),
inference(forward_demodulation,[],[f114078,f15158]) ).
fof(f15158,plain,
! [X0,X1] : join(meet(X0,X1),X0) = join(X0,meet(X1,X0)),
inference(forward_demodulation,[],[f15067,f1949]) ).
fof(f15067,plain,
! [X0,X1] : join(meet(X0,X1),X0) = join(X0,meet(complement(complement(X1)),X0)),
inference(superposition,[],[f2127,f2062]) ).
fof(f114078,plain,
! [X0,X1] : join(meet(X0,complement(X1)),X0) = join(meet(X0,X1),meet(complement(X1),meet(X0,complement(X1)))),
inference(backward_demodulation,[],[f20569,f114077]) ).
fof(f20569,plain,
! [X0,X1] : join(X0,meet(complement(X1),meet(X0,complement(X1)))) = join(meet(X0,X1),meet(complement(X1),meet(X0,complement(X1)))),
inference(forward_demodulation,[],[f20527,f1764]) ).
fof(f20527,plain,
! [X0,X1] : join(X0,meet(meet(X0,complement(X1)),complement(X1))) = join(meet(X0,X1),meet(meet(X0,complement(X1)),complement(X1))),
inference(superposition,[],[f2127,f1527]) ).
fof(f137727,plain,
! [X2,X0,X1] : meet(X2,join(X1,join(X0,X2))) = X2,
inference(superposition,[],[f136405,f100]) ).
fof(f136405,plain,
! [X0,X1] : meet(X0,join(X1,X0)) = X0,
inference(superposition,[],[f111423,f1947]) ).
fof(f111423,plain,
! [X0,X1] : join(zero,meet(X0,join(X1,X0))) = X0,
inference(superposition,[],[f261,f110685]) ).
fof(f162467,plain,
! [X0,X1] : join(complement(X0),X1) = join(meet(meet(X0,X1),join(complement(X0),X1)),complement(X0)),
inference(backward_demodulation,[],[f33638,f162118]) ).
fof(f162118,plain,
! [X0,X1] : join(complement(X1),X0) = complement(meet(complement(X0),X1)),
inference(superposition,[],[f2082,f1949]) ).
fof(f33638,plain,
! [X0,X1] : complement(meet(complement(X1),X0)) = join(meet(meet(X0,X1),complement(meet(complement(X1),X0))),complement(X0)),
inference(forward_demodulation,[],[f33439,f1764]) ).
fof(f33439,plain,
! [X0,X1] : complement(meet(complement(X1),X0)) = join(meet(complement(meet(complement(X1),X0)),meet(X0,X1)),complement(X0)),
inference(superposition,[],[f2096,f261]) ).
fof(f2096,plain,
! [X2,X0,X1] : complement(meet(X1,X0)) = join(meet(complement(meet(X1,X0)),X2),complement(join(meet(X0,X1),X2))),
inference(backward_demodulation,[],[f2071,f2082]) ).
fof(f2071,plain,
! [X2,X0,X1] : join(complement(X0),complement(X1)) = join(meet(complement(meet(X1,X0)),X2),complement(join(meet(X0,X1),X2))),
inference(backward_demodulation,[],[f253,f2063]) ).
fof(f253,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,[],[f40,f31]) ).
fof(f141044,plain,
! [X0] : join(meet(sK0,composition(complement(sK2),sK1)),X0) = X0,
inference(forward_demodulation,[],[f141043,f1764]) ).
fof(f141043,plain,
! [X0] : join(meet(composition(complement(sK2),sK1),sK0),X0) = X0,
inference(forward_demodulation,[],[f141042,f1947]) ).
fof(f141042,plain,
! [X0] : join(zero,X0) = join(meet(composition(complement(sK2),sK1),sK0),join(zero,X0)),
inference(forward_demodulation,[],[f140941,f42432]) ).
fof(f140941,plain,
! [X0] : join(composition(zero,meet(sK1,composition(converse(complement(sK2)),sK0))),X0) = join(meet(composition(complement(sK2),sK1),sK0),join(composition(zero,meet(sK1,composition(converse(complement(sK2)),sK0))),X0)),
inference(superposition,[],[f746,f113261]) ).
fof(f113261,plain,
zero = meet(complement(sK2),composition(sK0,converse(sK1))),
inference(superposition,[],[f112625,f22]) ).
fof(f112625,plain,
! [X0,X1] : zero = meet(complement(join(X0,X1)),X0),
inference(forward_demodulation,[],[f112263,f1949]) ).
fof(f112263,plain,
! [X0,X1] : complement(complement(zero)) = meet(complement(join(X0,X1)),X0),
inference(superposition,[],[f2083,f111121]) ).
fof(f111121,plain,
! [X0,X1] : zero = meet(X1,complement(join(X1,X0))),
inference(superposition,[],[f110685,f28]) ).
fof(f746,plain,
! [X2,X3,X0,X1] : join(composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),X3) = join(meet(composition(X0,X1),X2),join(composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),X3)),
inference(superposition,[],[f34,f39]) ).
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/benchmark/theBenchmark.p',dedekind_law) ).
fof(f44,plain,
complement(sK0) != join(complement(sK0),composition(complement(sK2),sK1)),
inference(superposition,[],[f23,f28]) ).
fof(f23,plain,
complement(sK0) != join(composition(complement(sK2),sK1),complement(sK0)),
inference(cnf_transformation,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL043+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 15:38:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (17942)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (17946)WARNING: value z3 for option sas not known
% 0.15/0.38 % (17947)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (17943)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (17949)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)
% 0.15/0.38 % (17950)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)
% 0.15/0.38 % (17948)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)
% 0.15/0.38 % (17945)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (17946)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.22/0.42 TRYING [3]
% 0.22/0.43 TRYING [3]
% 0.22/0.48 TRYING [4]
% 0.22/0.53 TRYING [4]
% 2.00/0.65 TRYING [5]
% 6.26/1.27 TRYING [6]
% 6.26/1.27 TRYING [5]
% 7.88/1.48 TRYING [1]
% 7.88/1.48 TRYING [2]
% 7.88/1.49 TRYING [3]
% 8.17/1.52 TRYING [4]
% 9.46/1.73 TRYING [5]
% 14.61/2.44 TRYING [6]
% 23.54/3.75 TRYING [7]
% 35.05/5.40 TRYING [7]
% 37.07/5.63 % (17949)First to succeed.
% 37.16/5.64 % (17949)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17942"
% 37.16/5.65 % (17949)Refutation found. Thanks to Tanya!
% 37.16/5.65 % SZS status Theorem for theBenchmark
% 37.16/5.65 % SZS output start Proof for theBenchmark
% See solution above
% 37.16/5.65 % (17949)------------------------------
% 37.16/5.65 % (17949)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 37.16/5.65 % (17949)Termination reason: Refutation
% 37.16/5.65
% 37.16/5.65 % (17949)Memory used [KB]: 94238
% 37.16/5.65 % (17949)Time elapsed: 5.267 s
% 37.16/5.65 % (17949)Instructions burned: 16181 (million)
% 37.16/5.65 % (17942)Success in time 5.262 s
%------------------------------------------------------------------------------