TSTP Solution File: REL012+2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : REL012+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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:48:03 EDT 2024
% Result : Theorem 24.16s 3.82s
% Output : Refutation 24.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 16
% Syntax : Number of formulae : 200 ( 199 unt; 0 def)
% Number of atoms : 201 ( 200 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 279 ( 275 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f178788,plain,
$false,
inference(trivial_inequality_removal,[],[f178663]) ).
fof(f178663,plain,
complement(sK0) != complement(sK0),
inference(superposition,[],[f22,f156595]) ).
fof(f156595,plain,
! [X0,X1] : complement(X1) = join(composition(complement(composition(X1,X0)),converse(X0)),complement(X1)),
inference(forward_demodulation,[],[f156594,f23]) ).
fof(f23,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f156594,plain,
! [X0,X1] : converse(converse(complement(X1))) = join(composition(complement(composition(X1,X0)),converse(X0)),complement(X1)),
inference(forward_demodulation,[],[f156424,f48]) ).
fof(f48,plain,
! [X0,X1] : composition(X0,converse(X1)) = converse(composition(X1,converse(X0))),
inference(superposition,[],[f29,f23]) ).
fof(f29,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/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f156424,plain,
! [X0,X1] : converse(converse(complement(X1))) = join(converse(composition(X0,converse(complement(composition(X1,X0))))),complement(X1)),
inference(superposition,[],[f43,f154608]) ).
fof(f154608,plain,
! [X0,X1] : converse(complement(X1)) = join(composition(X0,converse(complement(composition(X1,X0)))),converse(complement(X1))),
inference(forward_demodulation,[],[f153670,f153669]) ).
fof(f153669,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(backward_demodulation,[],[f54586,f153192]) ).
fof(f153192,plain,
! [X0] : converse(complement(X0)) = join(zero,meet(converse(complement(X0)),complement(converse(X0)))),
inference(superposition,[],[f2593,f152870]) ).
fof(f152870,plain,
! [X0] : zero = meet(converse(X0),converse(complement(X0))),
inference(superposition,[],[f121121,f460]) ).
fof(f460,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f384,f27]) ).
fof(f27,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/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f384,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f249,f177]) ).
fof(f177,plain,
! [X0] : join(zero,meet(X0,X0)) = X0,
inference(forward_demodulation,[],[f161,f30]) ).
fof(f30,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/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f161,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[],[f39,f25]) ).
fof(f25,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
fof(f39,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f32,f30]) ).
fof(f32,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/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f249,plain,
! [X0] : join(zero,X0) = join(zero,join(zero,X0)),
inference(forward_demodulation,[],[f229,f57]) ).
fof(f57,plain,
zero = complement(top),
inference(forward_demodulation,[],[f52,f25]) ).
fof(f52,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(superposition,[],[f30,f26]) ).
fof(f26,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f229,plain,
! [X0] : join(zero,X0) = join(zero,join(complement(top),X0)),
inference(backward_demodulation,[],[f205,f224]) ).
fof(f224,plain,
top = join(top,top),
inference(forward_demodulation,[],[f217,f26]) ).
fof(f217,plain,
join(zero,complement(zero)) = join(top,top),
inference(superposition,[],[f212,f27]) ).
fof(f212,plain,
join(top,top) = join(complement(zero),zero),
inference(forward_demodulation,[],[f211,f57]) ).
fof(f211,plain,
join(top,top) = join(complement(zero),complement(top)),
inference(forward_demodulation,[],[f210,f206]) ).
fof(f206,plain,
top = join(top,complement(join(top,top))),
inference(forward_demodulation,[],[f204,f73]) ).
fof(f73,plain,
top = join(top,zero),
inference(superposition,[],[f26,f57]) ).
fof(f204,plain,
join(top,zero) = join(top,complement(join(top,top))),
inference(superposition,[],[f76,f188]) ).
fof(f188,plain,
zero = join(zero,complement(join(top,top))),
inference(forward_demodulation,[],[f187,f124]) ).
fof(f124,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[],[f76,f26]) ).
fof(f187,plain,
zero = join(zero,complement(join(top,complement(zero)))),
inference(forward_demodulation,[],[f166,f27]) ).
fof(f166,plain,
zero = join(zero,complement(join(complement(zero),top))),
inference(superposition,[],[f39,f107]) ).
fof(f107,plain,
zero = meet(zero,top),
inference(forward_demodulation,[],[f96,f57]) ).
fof(f96,plain,
complement(top) = meet(zero,top),
inference(superposition,[],[f75,f26]) ).
fof(f75,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[],[f71,f27]) ).
fof(f71,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(superposition,[],[f30,f57]) ).
fof(f76,plain,
! [X0] : join(top,X0) = join(top,join(zero,X0)),
inference(superposition,[],[f33,f73]) ).
fof(f33,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/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f210,plain,
join(top,top) = join(complement(zero),complement(join(top,complement(join(top,top))))),
inference(forward_demodulation,[],[f209,f27]) ).
fof(f209,plain,
join(top,top) = join(complement(zero),complement(join(complement(join(top,top)),top))),
inference(superposition,[],[f39,f202]) ).
fof(f202,plain,
complement(zero) = meet(join(top,top),top),
inference(superposition,[],[f75,f188]) ).
fof(f205,plain,
! [X0] : join(zero,X0) = join(zero,join(complement(join(top,top)),X0)),
inference(superposition,[],[f33,f188]) ).
fof(f121121,plain,
! [X0] : zero = join(meet(converse(X0),converse(complement(X0))),zero),
inference(backward_demodulation,[],[f56951,f120840]) ).
fof(f120840,plain,
! [X2] : zero = composition(zero,X2),
inference(forward_demodulation,[],[f120804,f120794]) ).
fof(f120794,plain,
! [X0,X1] : zero = composition(converse(X1),composition(zero,X0)),
inference(backward_demodulation,[],[f2038,f120791]) ).
fof(f120791,plain,
! [X0,X1] : zero = converse(composition(X0,composition(zero,X1))),
inference(forward_demodulation,[],[f120738,f119843]) ).
fof(f119843,plain,
! [X0] : zero = composition(X0,zero),
inference(forward_demodulation,[],[f119842,f119809]) ).
fof(f119809,plain,
! [X0] : zero = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f119808,f119466]) ).
fof(f119466,plain,
zero = composition(top,complement(composition(top,top))),
inference(superposition,[],[f119209,f1262]) ).
fof(f1262,plain,
top = converse(top),
inference(backward_demodulation,[],[f1248,f1256]) ).
fof(f1256,plain,
top = join(top,converse(top)),
inference(superposition,[],[f1255,f27]) ).
fof(f1255,plain,
top = join(converse(top),top),
inference(forward_demodulation,[],[f1253,f23]) ).
fof(f1253,plain,
converse(converse(top)) = join(converse(top),top),
inference(superposition,[],[f43,f1248]) ).
fof(f1248,plain,
converse(top) = join(top,converse(top)),
inference(superposition,[],[f276,f147]) ).
fof(f147,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f42,f26]) ).
fof(f42,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f28,f23]) ).
fof(f28,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/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
fof(f276,plain,
! [X0] : join(top,X0) = join(top,join(top,X0)),
inference(superposition,[],[f33,f224]) ).
fof(f119209,plain,
! [X0] : zero = composition(X0,complement(composition(converse(X0),top))),
inference(superposition,[],[f7678,f460]) ).
fof(f7678,plain,
! [X0] : zero = join(composition(X0,complement(composition(converse(X0),top))),zero),
inference(superposition,[],[f259,f57]) ).
fof(f259,plain,
! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)),
inference(superposition,[],[f31,f23]) ).
fof(f31,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/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f119808,plain,
! [X0] : composition(top,complement(composition(top,top))) = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f119807,f2765]) ).
fof(f2765,plain,
! [X0] : top = join(X0,top),
inference(forward_demodulation,[],[f2649,f2664]) ).
fof(f2664,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f2645,f26]) ).
fof(f2645,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[],[f58,f2472]) ).
fof(f2472,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f2102,f2223]) ).
fof(f2223,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f2219,f457]) ).
fof(f457,plain,
! [X0] : meet(X0,X0) = X0,
inference(superposition,[],[f384,f177]) ).
fof(f2219,plain,
! [X0] : complement(complement(X0)) = meet(X0,X0),
inference(superposition,[],[f30,f2102]) ).
fof(f2102,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f2062,f2085]) ).
fof(f2085,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f2042,f2059]) ).
fof(f2059,plain,
one = converse(one),
inference(superposition,[],[f2042,f24]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f2042,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f2014,f23]) ).
fof(f2014,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f49,f24]) ).
fof(f49,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f29,f23]) ).
fof(f2062,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(superposition,[],[f31,f2042]) ).
fof(f58,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f33,f26]) ).
fof(f2649,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(superposition,[],[f58,f26]) ).
fof(f119807,plain,
! [X0] : composition(join(X0,top),complement(composition(top,top))) = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f119750,f460]) ).
fof(f119750,plain,
! [X0] : composition(join(X0,top),complement(composition(top,top))) = join(composition(X0,complement(composition(top,top))),zero),
inference(superposition,[],[f35,f119466]) ).
fof(f35,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/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f119842,plain,
! [X0,X1] : composition(X0,zero) = composition(join(composition(X0,X1),top),complement(composition(top,top))),
inference(forward_demodulation,[],[f119841,f119809]) ).
fof(f119841,plain,
! [X0,X1] : composition(join(composition(X0,X1),top),complement(composition(top,top))) = composition(X0,composition(X1,complement(composition(top,top)))),
inference(forward_demodulation,[],[f119762,f460]) ).
fof(f119762,plain,
! [X0,X1] : composition(join(composition(X0,X1),top),complement(composition(top,top))) = join(composition(X0,composition(X1,complement(composition(top,top)))),zero),
inference(superposition,[],[f320,f119466]) ).
fof(f320,plain,
! [X2,X3,X0,X1] : composition(join(composition(X0,X1),X3),X2) = join(composition(X0,composition(X1,X2)),composition(X3,X2)),
inference(superposition,[],[f35,f34]) ).
fof(f34,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/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
fof(f120738,plain,
! [X0,X1] : composition(converse(X1),zero) = converse(composition(X0,composition(zero,X1))),
inference(backward_demodulation,[],[f7637,f120737]) ).
fof(f120737,plain,
! [X0] : zero = composition(zero,converse(X0)),
inference(forward_demodulation,[],[f119844,f515]) ).
fof(f515,plain,
zero = converse(zero),
inference(superposition,[],[f510,f384]) ).
fof(f510,plain,
! [X0] : join(X0,converse(zero)) = X0,
inference(forward_demodulation,[],[f508,f23]) ).
fof(f508,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(zero)),
inference(superposition,[],[f42,f460]) ).
fof(f119844,plain,
! [X0] : converse(zero) = composition(zero,converse(X0)),
inference(backward_demodulation,[],[f539,f119843]) ).
fof(f539,plain,
! [X0] : converse(composition(X0,zero)) = composition(zero,converse(X0)),
inference(superposition,[],[f29,f515]) ).
fof(f7637,plain,
! [X0,X1] : converse(composition(X0,composition(zero,X1))) = composition(converse(X1),composition(zero,converse(X0))),
inference(forward_demodulation,[],[f7610,f34]) ).
fof(f7610,plain,
! [X0,X1] : converse(composition(composition(X0,zero),X1)) = composition(converse(X1),composition(zero,converse(X0))),
inference(superposition,[],[f29,f539]) ).
fof(f2038,plain,
! [X0,X1] : composition(converse(X1),composition(zero,X0)) = converse(composition(converse(X0),composition(zero,X1))),
inference(forward_demodulation,[],[f2006,f34]) ).
fof(f2006,plain,
! [X0,X1] : composition(converse(X1),composition(zero,X0)) = converse(composition(composition(converse(X0),zero),X1)),
inference(superposition,[],[f49,f538]) ).
fof(f538,plain,
! [X0] : converse(composition(zero,X0)) = composition(converse(X0),zero),
inference(superposition,[],[f29,f515]) ).
fof(f120804,plain,
! [X2,X0,X1] : composition(zero,X2) = composition(converse(X1),composition(zero,composition(X0,X2))),
inference(backward_demodulation,[],[f10238,f120794]) ).
fof(f10238,plain,
! [X2,X0,X1] : composition(converse(X1),composition(zero,composition(X0,X2))) = composition(composition(converse(X1),composition(zero,X0)),X2),
inference(forward_demodulation,[],[f10237,f34]) ).
fof(f10237,plain,
! [X2,X0,X1] : composition(converse(X1),composition(zero,composition(X0,X2))) = composition(composition(composition(converse(X1),zero),X0),X2),
inference(forward_demodulation,[],[f10236,f538]) ).
fof(f10236,plain,
! [X2,X0,X1] : composition(converse(X1),composition(zero,composition(X0,X2))) = composition(composition(converse(composition(zero,X1)),X0),X2),
inference(forward_demodulation,[],[f10235,f49]) ).
fof(f10235,plain,
! [X2,X0,X1] : composition(converse(X1),composition(zero,composition(X0,X2))) = composition(converse(composition(converse(X0),composition(zero,X1))),X2),
inference(forward_demodulation,[],[f10234,f34]) ).
fof(f10234,plain,
! [X2,X0,X1] : composition(converse(composition(composition(converse(X0),zero),X1)),X2) = composition(converse(X1),composition(zero,composition(X0,X2))),
inference(forward_demodulation,[],[f10143,f34]) ).
fof(f10143,plain,
! [X2,X0,X1] : composition(converse(composition(composition(converse(X0),zero),X1)),X2) = composition(converse(X1),composition(composition(zero,X0),X2)),
inference(superposition,[],[f111,f1947]) ).
fof(f1947,plain,
! [X0] : composition(zero,X0) = converse(composition(converse(X0),zero)),
inference(superposition,[],[f23,f538]) ).
fof(f111,plain,
! [X2,X0,X1] : composition(converse(X0),composition(converse(X1),X2)) = composition(converse(composition(X1,X0)),X2),
inference(superposition,[],[f34,f29]) ).
fof(f56951,plain,
! [X0] : composition(zero,meet(converse(X0),converse(complement(X0)))) = join(meet(converse(X0),converse(complement(X0))),composition(zero,meet(converse(X0),converse(complement(X0))))),
inference(forward_demodulation,[],[f56950,f2085]) ).
fof(f56950,plain,
! [X0] : composition(zero,meet(converse(X0),converse(complement(X0)))) = join(meet(converse(X0),composition(one,converse(complement(X0)))),composition(zero,meet(converse(X0),converse(complement(X0))))),
inference(forward_demodulation,[],[f56949,f2568]) ).
fof(f2568,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(superposition,[],[f2334,f2223]) ).
fof(f2334,plain,
! [X0,X1] : meet(X0,X1) = complement(complement(meet(X1,X0))),
inference(backward_demodulation,[],[f53,f2332]) ).
fof(f2332,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(forward_demodulation,[],[f2331,f384]) ).
fof(f2331,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,complement(meet(X0,X1))),
inference(forward_demodulation,[],[f2329,f457]) ).
fof(f2329,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,meet(complement(meet(X0,X1)),complement(meet(X0,X1)))),
inference(backward_demodulation,[],[f355,f2327]) ).
fof(f2327,plain,
! [X2,X0,X1] : meet(join(complement(X0),complement(X1)),X2) = meet(complement(meet(X0,X1)),X2),
inference(backward_demodulation,[],[f50,f2272]) ).
fof(f2272,plain,
! [X0,X1] : complement(join(X0,complement(X1))) = meet(complement(X0),X1),
inference(backward_demodulation,[],[f404,f2226]) ).
fof(f2226,plain,
! [X0] : meet(top,X0) = X0,
inference(backward_demodulation,[],[f97,f2224]) ).
fof(f2224,plain,
! [X0] : meet(X0,top) = X0,
inference(backward_demodulation,[],[f401,f2223]) ).
fof(f401,plain,
! [X0] : complement(complement(X0)) = meet(X0,top),
inference(backward_demodulation,[],[f75,f384]) ).
fof(f97,plain,
! [X0] : meet(X0,top) = meet(top,X0),
inference(superposition,[],[f75,f72]) ).
fof(f72,plain,
! [X0] : meet(top,X0) = complement(join(zero,complement(X0))),
inference(superposition,[],[f30,f57]) ).
fof(f404,plain,
! [X0,X1] : complement(join(meet(top,X0),complement(X1))) = meet(complement(X0),X1),
inference(backward_demodulation,[],[f82,f384]) ).
fof(f82,plain,
! [X0,X1] : meet(join(zero,complement(X0)),X1) = complement(join(meet(top,X0),complement(X1))),
inference(superposition,[],[f30,f72]) ).
fof(f50,plain,
! [X2,X0,X1] : meet(join(complement(X0),complement(X1)),X2) = complement(join(meet(X0,X1),complement(X2))),
inference(superposition,[],[f30,f30]) ).
fof(f355,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(zero,meet(join(complement(X0),complement(X1)),complement(meet(X0,X1)))),
inference(superposition,[],[f304,f30]) ).
fof(f304,plain,
! [X0] : join(zero,meet(X0,complement(complement(X0)))) = X0,
inference(superposition,[],[f189,f27]) ).
fof(f189,plain,
! [X0] : join(meet(X0,complement(complement(X0))),zero) = X0,
inference(forward_demodulation,[],[f172,f57]) ).
fof(f172,plain,
! [X0] : join(meet(X0,complement(complement(X0))),complement(top)) = X0,
inference(superposition,[],[f39,f26]) ).
fof(f53,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(superposition,[],[f30,f27]) ).
fof(f56949,plain,
! [X0] : composition(zero,meet(converse(X0),converse(complement(X0)))) = join(meet(composition(one,converse(complement(X0))),converse(X0)),composition(zero,meet(converse(X0),converse(complement(X0))))),
inference(forward_demodulation,[],[f56948,f2568]) ).
fof(f56948,plain,
! [X0] : composition(zero,meet(converse(complement(X0)),converse(X0))) = join(meet(composition(one,converse(complement(X0))),converse(X0)),composition(zero,meet(converse(complement(X0)),converse(X0)))),
inference(forward_demodulation,[],[f56947,f24]) ).
fof(f56947,plain,
! [X0] : composition(zero,meet(converse(complement(X0)),converse(composition(X0,one)))) = join(meet(composition(one,converse(complement(X0))),converse(X0)),composition(zero,meet(converse(complement(X0)),converse(composition(X0,one))))),
inference(forward_demodulation,[],[f56711,f29]) ).
fof(f56711,plain,
! [X0] : composition(zero,meet(converse(complement(X0)),composition(converse(one),converse(X0)))) = join(meet(composition(one,converse(complement(X0))),converse(X0)),composition(zero,meet(converse(complement(X0)),composition(converse(one),converse(X0))))),
inference(superposition,[],[f784,f14056]) ).
fof(f14056,plain,
! [X0] : zero = meet(one,composition(converse(X0),complement(X0))),
inference(forward_demodulation,[],[f13931,f2223]) ).
fof(f13931,plain,
! [X0] : zero = meet(complement(complement(one)),composition(converse(X0),complement(X0))),
inference(superposition,[],[f13413,f261]) ).
fof(f261,plain,
! [X0] : complement(one) = join(composition(converse(X0),complement(X0)),complement(one)),
inference(superposition,[],[f31,f24]) ).
fof(f13413,plain,
! [X0,X1] : zero = meet(complement(join(X0,X1)),X0),
inference(forward_demodulation,[],[f13310,f2223]) ).
fof(f13310,plain,
! [X0,X1] : complement(complement(zero)) = meet(complement(join(X0,X1)),X0),
inference(superposition,[],[f2334,f12949]) ).
fof(f12949,plain,
! [X0,X1] : zero = meet(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f12873,f57]) ).
fof(f12873,plain,
! [X0,X1] : complement(top) = meet(X0,complement(join(X0,X1))),
inference(superposition,[],[f2271,f2777]) ).
fof(f2777,plain,
! [X0,X1] : top = join(complement(X0),join(X0,X1)),
inference(backward_demodulation,[],[f1599,f2772]) ).
fof(f2772,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[],[f2766,f2472]) ).
fof(f2766,plain,
! [X0] : join(top,X0) = join(top,top),
inference(backward_demodulation,[],[f1930,f2765]) ).
fof(f1930,plain,
! [X0] : join(top,X0) = join(top,join(X0,top)),
inference(superposition,[],[f1577,f33]) ).
fof(f1577,plain,
! [X0] : join(top,X0) = join(join(top,X0),top),
inference(forward_demodulation,[],[f1529,f23]) ).
fof(f1529,plain,
! [X0] : join(join(top,X0),top) = converse(converse(join(top,X0))),
inference(superposition,[],[f1491,f276]) ).
fof(f1491,plain,
! [X0,X1] : join(X1,X0) = converse(converse(join(X0,X1))),
inference(forward_demodulation,[],[f1490,f23]) ).
fof(f1490,plain,
! [X0,X1] : converse(converse(join(X0,X1))) = join(X1,converse(converse(X0))),
inference(forward_demodulation,[],[f1431,f42]) ).
fof(f1431,plain,
! [X0,X1] : converse(converse(join(X0,X1))) = converse(join(converse(X1),converse(X0))),
inference(superposition,[],[f1295,f28]) ).
fof(f1295,plain,
! [X0,X1] : converse(join(X0,X1)) = converse(join(X1,X0)),
inference(superposition,[],[f44,f28]) ).
fof(f44,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(superposition,[],[f28,f27]) ).
fof(f1599,plain,
! [X0,X1] : join(top,X1) = join(complement(X0),join(X0,X1)),
inference(superposition,[],[f33,f1554]) ).
fof(f1554,plain,
! [X0] : top = join(complement(X0),X0),
inference(forward_demodulation,[],[f1505,f23]) ).
fof(f1505,plain,
! [X0] : join(complement(X0),X0) = converse(converse(top)),
inference(superposition,[],[f1491,f26]) ).
fof(f2271,plain,
! [X0,X1] : meet(X1,complement(X0)) = complement(join(complement(X1),X0)),
inference(backward_demodulation,[],[f403,f2226]) ).
fof(f403,plain,
! [X0,X1] : complement(join(complement(X1),meet(top,X0))) = meet(X1,complement(X0)),
inference(backward_demodulation,[],[f81,f384]) ).
fof(f81,plain,
! [X0,X1] : meet(X1,join(zero,complement(X0))) = complement(join(complement(X1),meet(top,X0))),
inference(superposition,[],[f30,f72]) ).
fof(f784,plain,
! [X2,X0,X1] : composition(meet(X1,composition(X2,X0)),meet(converse(X0),composition(converse(X1),X2))) = join(meet(composition(X1,converse(X0)),X2),composition(meet(X1,composition(X2,X0)),meet(converse(X0),composition(converse(X1),X2)))),
inference(superposition,[],[f38,f23]) ).
fof(f38,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/sandbox/benchmark/theBenchmark.p',dedekind_law) ).
fof(f2593,plain,
! [X0,X1] : join(meet(X1,X0),meet(X0,complement(X1))) = X0,
inference(superposition,[],[f2322,f2568]) ).
fof(f2322,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,complement(X1))) = X0,
inference(backward_demodulation,[],[f39,f2271]) ).
fof(f54586,plain,
! [X0] : complement(converse(X0)) = join(zero,meet(converse(complement(X0)),complement(converse(X0)))),
inference(forward_demodulation,[],[f54500,f2568]) ).
fof(f54500,plain,
! [X0] : complement(converse(X0)) = join(zero,meet(complement(converse(X0)),converse(complement(X0)))),
inference(superposition,[],[f175,f38174]) ).
fof(f38174,plain,
! [X0] : zero = meet(complement(converse(X0)),complement(converse(complement(X0)))),
inference(superposition,[],[f25456,f23]) ).
fof(f25456,plain,
! [X0] : zero = meet(complement(X0),complement(converse(complement(converse(X0))))),
inference(superposition,[],[f12998,f2223]) ).
fof(f12998,plain,
! [X0] : zero = meet(X0,complement(converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[],[f12905,f57]) ).
fof(f12905,plain,
! [X0] : complement(top) = meet(X0,complement(converse(complement(converse(complement(X0)))))),
inference(superposition,[],[f2271,f1263]) ).
fof(f1263,plain,
! [X0] : top = join(X0,converse(complement(converse(X0)))),
inference(backward_demodulation,[],[f147,f1262]) ).
fof(f175,plain,
! [X0,X1] : join(meet(X0,complement(X1)),meet(X0,X1)) = X0,
inference(superposition,[],[f39,f30]) ).
fof(f153670,plain,
! [X0,X1] : converse(complement(X1)) = join(composition(X0,complement(converse(composition(X1,X0)))),converse(complement(X1))),
inference(backward_demodulation,[],[f274,f153669]) ).
fof(f274,plain,
! [X0,X1] : complement(converse(X1)) = join(composition(X0,complement(converse(composition(X1,X0)))),complement(converse(X1))),
inference(forward_demodulation,[],[f263,f23]) ).
fof(f263,plain,
! [X0,X1] : complement(converse(X1)) = join(composition(converse(converse(X0)),complement(converse(composition(X1,X0)))),complement(converse(X1))),
inference(superposition,[],[f31,f29]) ).
fof(f43,plain,
! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[],[f28,f23]) ).
fof(f22,plain,
complement(sK0) != join(composition(complement(composition(sK0,sK1)),converse(sK1)),complement(sK0)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
complement(sK0) != join(composition(complement(composition(sK0,sK1)),converse(sK1)),complement(sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f20]) ).
fof(f20,plain,
( ? [X0,X1] : complement(X0) != join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0))
=> complement(sK0) != join(composition(complement(composition(sK0,sK1)),converse(sK1)),complement(sK0)) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
? [X0,X1] : complement(X0) != join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0)),
inference(ennf_transformation,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] : complement(X0) = join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0)),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X0,X1] : complement(X0) = join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL012+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
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 00:21:46 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (24941)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (24944)WARNING: value z3 for option sas not known
% 0.14/0.38 % (24942)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (24943)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (24944)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (24946)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (24947)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (24948)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (24945)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.21/0.41 TRYING [3]
% 0.21/0.42 TRYING [3]
% 0.21/0.48 TRYING [4]
% 0.21/0.52 TRYING [4]
% 2.01/0.65 TRYING [5]
% 6.19/1.23 TRYING [5]
% 6.19/1.26 TRYING [6]
% 7.86/1.48 TRYING [1]
% 7.86/1.48 TRYING [2]
% 7.86/1.49 TRYING [3]
% 8.02/1.52 TRYING [4]
% 9.47/1.72 TRYING [5]
% 14.49/2.44 TRYING [6]
% 23.06/3.63 TRYING [7]
% 24.16/3.80 % (24947)First to succeed.
% 24.16/3.82 % (24947)Refutation found. Thanks to Tanya!
% 24.16/3.82 % SZS status Theorem for theBenchmark
% 24.16/3.82 % SZS output start Proof for theBenchmark
% See solution above
% 24.16/3.82 % (24947)------------------------------
% 24.16/3.82 % (24947)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 24.16/3.82 % (24947)Termination reason: Refutation
% 24.16/3.82
% 24.16/3.82 % (24947)Memory used [KB]: 62318
% 24.16/3.82 % (24947)Time elapsed: 3.437 s
% 24.16/3.82 % (24947)Instructions burned: 10602 (million)
% 24.16/3.82 % (24947)------------------------------
% 24.16/3.82 % (24947)------------------------------
% 24.16/3.82 % (24941)Success in time 3.392 s
%------------------------------------------------------------------------------