TSTP Solution File: REL041+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : REL041+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 : n013.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 08:53:08 EDT 2024
% Result : Theorem 94.12s 13.76s
% Output : Refutation 94.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 17
% Syntax : Number of formulae : 201 ( 195 unt; 0 def)
% Number of atoms : 209 ( 208 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 0 |; 4 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 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 : 258 ( 252 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1038640,plain,
$false,
inference(trivial_inequality_removal,[],[f1038441]) ).
fof(f1038441,plain,
zero != zero,
inference(superposition,[],[f24,f1037455]) ).
fof(f1037455,plain,
! [X0] : zero = meet(composition(sK0,X0),composition(sK0,complement(X0))),
inference(superposition,[],[f637505,f5878]) ).
fof(f5878,plain,
! [X0] : join(X0,zero) = X0,
inference(forward_demodulation,[],[f5877,f5819]) ).
fof(f5819,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f3887,f3755]) ).
fof(f3755,plain,
! [X0] : join(zero,meet(X0,X0)) = X0,
inference(forward_demodulation,[],[f3706,f32]) ).
fof(f32,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(f3706,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[],[f41,f28]) ).
fof(f28,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(f41,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f34,f32]) ).
fof(f34,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(f3887,plain,
! [X0] : join(zero,X0) = join(zero,join(zero,X0)),
inference(forward_demodulation,[],[f3886,f61]) ).
fof(f61,plain,
zero = complement(top),
inference(forward_demodulation,[],[f56,f28]) ).
fof(f56,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(superposition,[],[f32,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/sandbox/benchmark/theBenchmark.p',def_top) ).
fof(f3886,plain,
! [X0] : join(zero,X0) = join(zero,join(complement(top),X0)),
inference(forward_demodulation,[],[f3860,f3883]) ).
fof(f3883,plain,
top = join(top,top),
inference(forward_demodulation,[],[f3882,f65]) ).
fof(f65,plain,
top = join(top,zero),
inference(superposition,[],[f27,f61]) ).
fof(f3882,plain,
join(top,zero) = join(top,top),
inference(forward_demodulation,[],[f3858,f1193]) ).
fof(f1193,plain,
! [X0] : join(top,X0) = join(zero,join(top,X0)),
inference(superposition,[],[f35,f290]) ).
fof(f290,plain,
top = join(zero,top),
inference(forward_demodulation,[],[f263,f25]) ).
fof(f25,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(f263,plain,
join(zero,top) = converse(converse(top)),
inference(superposition,[],[f243,f65]) ).
fof(f243,plain,
! [X0,X1] : join(X1,X0) = converse(converse(join(X0,X1))),
inference(forward_demodulation,[],[f242,f25]) ).
fof(f242,plain,
! [X0,X1] : converse(converse(join(X0,X1))) = converse(converse(join(X1,X0))),
inference(forward_demodulation,[],[f208,f30]) ).
fof(f30,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(f208,plain,
! [X0,X1] : converse(converse(join(X0,X1))) = converse(join(converse(X1),converse(X0))),
inference(superposition,[],[f175,f30]) ).
fof(f175,plain,
! [X0,X1] : converse(join(X0,X1)) = converse(join(X1,X0)),
inference(superposition,[],[f48,f30]) ).
fof(f48,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(superposition,[],[f30,f29]) ).
fof(f29,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(f35,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(f3858,plain,
join(top,zero) = join(zero,join(top,top)),
inference(superposition,[],[f2422,f3770]) ).
fof(f3770,plain,
zero = join(zero,complement(join(top,top))),
inference(forward_demodulation,[],[f3719,f1232]) ).
fof(f1232,plain,
join(top,top) = join(complement(zero),top),
inference(forward_demodulation,[],[f1230,f25]) ).
fof(f1230,plain,
join(complement(zero),top) = converse(converse(join(top,top))),
inference(superposition,[],[f243,f1220]) ).
fof(f1220,plain,
join(top,top) = join(top,complement(zero)),
inference(superposition,[],[f1192,f27]) ).
fof(f1192,plain,
! [X0] : join(top,X0) = join(top,join(zero,X0)),
inference(superposition,[],[f35,f65]) ).
fof(f3719,plain,
zero = join(zero,complement(join(complement(zero),top))),
inference(superposition,[],[f41,f95]) ).
fof(f95,plain,
zero = meet(zero,top),
inference(forward_demodulation,[],[f86,f61]) ).
fof(f86,plain,
complement(top) = meet(zero,top),
inference(superposition,[],[f66,f27]) ).
fof(f66,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[],[f62,f29]) ).
fof(f62,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(superposition,[],[f32,f61]) ).
fof(f2422,plain,
! [X0,X1] : join(top,X1) = join(join(X1,complement(X0)),X0),
inference(forward_demodulation,[],[f2401,f25]) ).
fof(f2401,plain,
! [X0,X1] : converse(converse(join(top,X1))) = join(join(X1,complement(X0)),X0),
inference(superposition,[],[f243,f1499]) ).
fof(f1499,plain,
! [X0,X1] : join(top,X1) = join(X0,join(X1,complement(X0))),
inference(superposition,[],[f1165,f29]) ).
fof(f1165,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f35,f27]) ).
fof(f3860,plain,
! [X0] : join(zero,X0) = join(zero,join(complement(join(top,top)),X0)),
inference(superposition,[],[f35,f3770]) ).
fof(f5877,plain,
! [X0] : join(zero,X0) = join(join(zero,X0),zero),
inference(forward_demodulation,[],[f5864,f25]) ).
fof(f5864,plain,
! [X0] : join(join(zero,X0),zero) = converse(converse(join(zero,X0))),
inference(superposition,[],[f243,f3887]) ).
fof(f637505,plain,
! [X0] : zero = join(meet(composition(sK0,X0),composition(sK0,complement(X0))),zero),
inference(forward_demodulation,[],[f637504,f705]) ).
fof(f705,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(superposition,[],[f57,f32]) ).
fof(f57,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(superposition,[],[f32,f29]) ).
fof(f637504,plain,
! [X0] : zero = join(meet(composition(sK0,complement(X0)),composition(sK0,X0)),zero),
inference(forward_demodulation,[],[f637290,f281504]) ).
fof(f281504,plain,
! [X0] : zero = composition(X0,zero),
inference(forward_demodulation,[],[f281473,f281457]) ).
fof(f281457,plain,
! [X0] : zero = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f281456,f281395]) ).
fof(f281395,plain,
zero = composition(top,complement(composition(top,top))),
inference(forward_demodulation,[],[f281352,f6480]) ).
fof(f6480,plain,
top = complement(converse(zero)),
inference(forward_demodulation,[],[f6455,f4887]) ).
fof(f4887,plain,
top = converse(top),
inference(superposition,[],[f4859,f101]) ).
fof(f101,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f46,f27]) ).
fof(f46,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f30,f25]) ).
fof(f4859,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[],[f4828,f65]) ).
fof(f4828,plain,
! [X0] : join(top,zero) = join(top,X0),
inference(superposition,[],[f3790,f316]) ).
fof(f316,plain,
! [X0] : zero = meet(complement(X0),X0),
inference(forward_demodulation,[],[f309,f61]) ).
fof(f309,plain,
! [X0] : complement(top) = meet(complement(X0),X0),
inference(superposition,[],[f32,f281]) ).
fof(f281,plain,
! [X0] : top = join(complement(X0),X0),
inference(forward_demodulation,[],[f252,f25]) ).
fof(f252,plain,
! [X0] : join(complement(X0),X0) = converse(converse(top)),
inference(superposition,[],[f243,f27]) ).
fof(f3790,plain,
! [X0,X1] : join(top,X1) = join(top,meet(X0,X1)),
inference(forward_demodulation,[],[f3747,f1165]) ).
fof(f3747,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,meet(X0,X1)),
inference(superposition,[],[f2422,f41]) ).
fof(f6455,plain,
converse(top) = complement(converse(zero)),
inference(superposition,[],[f25,f6010]) ).
fof(f6010,plain,
top = converse(complement(converse(zero))),
inference(forward_demodulation,[],[f5906,f4887]) ).
fof(f5906,plain,
converse(top) = converse(complement(converse(zero))),
inference(superposition,[],[f5819,f101]) ).
fof(f281352,plain,
zero = composition(top,complement(composition(complement(converse(zero)),top))),
inference(superposition,[],[f281049,f6010]) ).
fof(f281049,plain,
! [X0] : zero = composition(converse(X0),complement(composition(X0,top))),
inference(superposition,[],[f7068,f5878]) ).
fof(f7068,plain,
! [X0] : zero = join(composition(converse(X0),complement(composition(X0,top))),zero),
inference(superposition,[],[f33,f61]) ).
fof(f33,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(f281456,plain,
! [X0] : composition(top,complement(composition(top,top))) = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f281455,f4874]) ).
fof(f4874,plain,
! [X0] : top = join(X0,top),
inference(superposition,[],[f4859,f1970]) ).
fof(f1970,plain,
! [X0] : join(top,join(zero,X0)) = join(X0,top),
inference(superposition,[],[f1165,f1886]) ).
fof(f1886,plain,
! [X0] : top = join(complement(X0),join(zero,X0)),
inference(superposition,[],[f1713,f29]) ).
fof(f1713,plain,
! [X0] : top = join(complement(X0),join(X0,zero)),
inference(forward_demodulation,[],[f1637,f61]) ).
fof(f1637,plain,
! [X0] : top = join(complement(X0),join(X0,complement(top))),
inference(superposition,[],[f1197,f281]) ).
fof(f1197,plain,
! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))),
inference(superposition,[],[f35,f27]) ).
fof(f281455,plain,
! [X0] : composition(join(X0,top),complement(composition(top,top))) = composition(X0,complement(composition(top,top))),
inference(forward_demodulation,[],[f281445,f5878]) ).
fof(f281445,plain,
! [X0] : composition(join(X0,top),complement(composition(top,top))) = join(composition(X0,complement(composition(top,top))),zero),
inference(superposition,[],[f37,f281395]) ).
fof(f37,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(f281473,plain,
! [X0,X1] : zero = composition(X0,composition(X1,complement(composition(top,top)))),
inference(superposition,[],[f281457,f36]) ).
fof(f36,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(f637290,plain,
! [X0] : composition(meet(sK0,composition(composition(sK0,X0),converse(complement(X0)))),zero) = join(meet(composition(sK0,complement(X0)),composition(sK0,X0)),composition(meet(sK0,composition(composition(sK0,X0),converse(complement(X0)))),zero)),
inference(superposition,[],[f40,f556768]) ).
fof(f556768,plain,
! [X0] : zero = meet(complement(X0),composition(converse(sK0),composition(sK0,X0))),
inference(superposition,[],[f14913,f537719]) ).
fof(f537719,plain,
! [X0] : join(X0,composition(converse(sK0),composition(sK0,X0))) = X0,
inference(forward_demodulation,[],[f537718,f481]) ).
fof(f481,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f468,f474]) ).
fof(f474,plain,
one = converse(one),
inference(superposition,[],[f468,f26]) ).
fof(f26,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(f468,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f447,f25]) ).
fof(f447,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f53,f26]) ).
fof(f53,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f31,f25]) ).
fof(f31,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(f537718,plain,
! [X0] : composition(one,X0) = join(X0,composition(converse(sK0),composition(sK0,X0))),
inference(forward_demodulation,[],[f537717,f36]) ).
fof(f537717,plain,
! [X0] : composition(one,X0) = join(X0,composition(composition(converse(sK0),sK0),X0)),
inference(forward_demodulation,[],[f537716,f53]) ).
fof(f537716,plain,
! [X0] : composition(one,X0) = join(X0,composition(converse(composition(converse(sK0),sK0)),X0)),
inference(forward_demodulation,[],[f537188,f448323]) ).
fof(f448323,plain,
! [X0] : converse(X0) = complement(converse(complement(X0))),
inference(forward_demodulation,[],[f448014,f447403]) ).
fof(f447403,plain,
! [X0] : converse(X0) = join(complement(converse(complement(X0))),converse(X0)),
inference(superposition,[],[f447241,f25]) ).
fof(f447241,plain,
! [X0] : join(complement(converse(complement(converse(X0)))),X0) = X0,
inference(forward_demodulation,[],[f446862,f25]) ).
fof(f446862,plain,
! [X0] : converse(converse(X0)) = join(complement(converse(complement(converse(X0)))),X0),
inference(superposition,[],[f243,f437197]) ).
fof(f437197,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(forward_demodulation,[],[f437196,f5819]) ).
fof(f437196,plain,
! [X0] : join(zero,X0) = join(X0,complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f436617,f6011]) ).
fof(f6011,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f5921,f5893]) ).
fof(f5893,plain,
! [X0] : meet(top,X0) = X0,
inference(superposition,[],[f5819,f5205]) ).
fof(f5205,plain,
! [X0] : join(zero,meet(top,X0)) = X0,
inference(superposition,[],[f5160,f29]) ).
fof(f5160,plain,
! [X0] : join(meet(top,X0),zero) = X0,
inference(superposition,[],[f5051,f87]) ).
fof(f87,plain,
! [X0] : meet(X0,top) = meet(top,X0),
inference(superposition,[],[f66,f63]) ).
fof(f63,plain,
! [X0] : meet(top,X0) = complement(join(zero,complement(X0))),
inference(superposition,[],[f32,f61]) ).
fof(f5051,plain,
! [X0] : join(meet(X0,top),zero) = X0,
inference(forward_demodulation,[],[f5023,f61]) ).
fof(f5023,plain,
! [X0] : join(meet(X0,top),complement(top)) = X0,
inference(superposition,[],[f41,f4874]) ).
fof(f5921,plain,
! [X0] : complement(complement(X0)) = meet(top,X0),
inference(superposition,[],[f63,f5819]) ).
fof(f436617,plain,
! [X0] : join(zero,complement(complement(X0))) = join(complement(complement(X0)),complement(converse(complement(converse(X0))))),
inference(superposition,[],[f240871,f156169]) ).
fof(f156169,plain,
! [X0] : zero = meet(complement(X0),complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f156168,f5819]) ).
fof(f156168,plain,
! [X0] : zero = meet(join(zero,complement(X0)),complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f155935,f5891]) ).
fof(f5891,plain,
! [X0] : meet(X0,top) = X0,
inference(superposition,[],[f5819,f5168]) ).
fof(f5168,plain,
! [X0] : join(zero,meet(X0,top)) = X0,
inference(superposition,[],[f5051,f29]) ).
fof(f155935,plain,
! [X0] : zero = meet(join(zero,complement(X0)),complement(converse(complement(converse(meet(X0,top)))))),
inference(superposition,[],[f43041,f66]) ).
fof(f43041,plain,
! [X0] : zero = meet(X0,complement(converse(complement(converse(complement(X0)))))),
inference(forward_demodulation,[],[f42765,f61]) ).
fof(f42765,plain,
! [X0] : complement(top) = meet(X0,complement(converse(complement(converse(complement(X0)))))),
inference(superposition,[],[f6226,f19803]) ).
fof(f19803,plain,
! [X0] : top = join(X0,converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f19802,f4874]) ).
fof(f19802,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = join(X0,top),
inference(forward_demodulation,[],[f19499,f4887]) ).
fof(f19499,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = join(X0,converse(top)),
inference(superposition,[],[f18188,f282]) ).
fof(f282,plain,
! [X0] : converse(top) = join(converse(complement(converse(X0))),X0),
inference(forward_demodulation,[],[f255,f25]) ).
fof(f255,plain,
! [X0] : join(converse(complement(converse(X0))),X0) = converse(converse(converse(top))),
inference(superposition,[],[f243,f101]) ).
fof(f18188,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,X0)),
inference(superposition,[],[f13562,f35]) ).
fof(f13562,plain,
! [X0,X1] : join(X0,X1) = join(join(X0,X1),X0),
inference(forward_demodulation,[],[f13494,f25]) ).
fof(f13494,plain,
! [X0,X1] : converse(converse(join(X0,X1))) = join(join(X0,X1),X0),
inference(superposition,[],[f243,f7377]) ).
fof(f7377,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f35,f7337]) ).
fof(f7337,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f7090,f6011]) ).
fof(f7090,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f7089,f481]) ).
fof(f7089,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(forward_demodulation,[],[f7050,f481]) ).
fof(f7050,plain,
! [X0] : complement(X0) = join(composition(one,complement(composition(one,X0))),complement(X0)),
inference(superposition,[],[f33,f474]) ).
fof(f6226,plain,
! [X0,X1] : complement(join(complement(X1),X0)) = meet(X1,complement(X0)),
inference(superposition,[],[f32,f6011]) ).
fof(f240871,plain,
! [X0,X1] : join(complement(X0),X1) = join(meet(X0,X1),complement(X0)),
inference(forward_demodulation,[],[f240870,f21000]) ).
fof(f21000,plain,
! [X2,X0,X1] : meet(X1,X0) = meet(meet(X1,X0),join(X2,X0)),
inference(superposition,[],[f14738,f13770]) ).
fof(f13770,plain,
! [X0,X1] : join(X1,meet(X0,X1)) = X1,
inference(superposition,[],[f13622,f29]) ).
fof(f13622,plain,
! [X0,X1] : join(meet(X1,X0),X0) = X0,
inference(superposition,[],[f13380,f705]) ).
fof(f13380,plain,
! [X0,X1] : join(meet(X0,X1),X0) = X0,
inference(superposition,[],[f7377,f41]) ).
fof(f14738,plain,
! [X2,X0,X1] : meet(X2,join(X0,join(X1,X2))) = X2,
inference(superposition,[],[f14590,f35]) ).
fof(f14590,plain,
! [X0,X1] : meet(X0,join(X1,X0)) = X0,
inference(superposition,[],[f9001,f5878]) ).
fof(f9001,plain,
! [X0,X1] : join(meet(X0,join(X1,X0)),zero) = X0,
inference(forward_demodulation,[],[f9000,f6011]) ).
fof(f9000,plain,
! [X0,X1] : join(meet(X0,join(X1,complement(complement(X0)))),zero) = X0,
inference(forward_demodulation,[],[f8952,f61]) ).
fof(f8952,plain,
! [X0,X1] : join(meet(X0,join(X1,complement(complement(X0)))),complement(top)) = X0,
inference(superposition,[],[f41,f7742]) ).
fof(f7742,plain,
! [X0,X1] : top = join(X0,join(X1,complement(X0))),
inference(superposition,[],[f6294,f35]) ).
fof(f6294,plain,
! [X0,X1] : top = join(join(X0,X1),complement(X0)),
inference(forward_demodulation,[],[f6249,f4859]) ).
fof(f6249,plain,
! [X0,X1] : join(top,X1) = join(join(X0,X1),complement(X0)),
inference(superposition,[],[f1523,f6011]) ).
fof(f1523,plain,
! [X0,X1] : join(top,X1) = join(join(complement(X0),X1),X0),
inference(forward_demodulation,[],[f1509,f25]) ).
fof(f1509,plain,
! [X0,X1] : join(join(complement(X0),X1),X0) = converse(converse(join(top,X1))),
inference(superposition,[],[f243,f1165]) ).
fof(f240870,plain,
! [X0,X1] : join(complement(X0),X1) = join(meet(meet(X0,X1),join(complement(X0),X1)),complement(X0)),
inference(forward_demodulation,[],[f240059,f705]) ).
fof(f240059,plain,
! [X0,X1] : join(complement(X0),X1) = join(meet(join(complement(X0),X1),meet(X0,X1)),complement(X0)),
inference(superposition,[],[f3735,f41]) ).
fof(f3735,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(X1,complement(X0)))) = X0,
inference(superposition,[],[f41,f29]) ).
fof(f448014,plain,
! [X0] : complement(converse(complement(X0))) = join(complement(converse(complement(X0))),converse(X0)),
inference(superposition,[],[f13821,f447294]) ).
fof(f447294,plain,
! [X0] : meet(X0,converse(complement(converse(complement(X0))))) = X0,
inference(forward_demodulation,[],[f447015,f6011]) ).
fof(f447015,plain,
! [X0] : complement(complement(X0)) = meet(X0,converse(complement(converse(complement(X0))))),
inference(superposition,[],[f32,f437197]) ).
fof(f13821,plain,
! [X0,X1] : join(X1,converse(meet(X0,converse(X1)))) = X1,
inference(forward_demodulation,[],[f13797,f25]) ).
fof(f13797,plain,
! [X0,X1] : converse(converse(X1)) = join(X1,converse(meet(X0,converse(X1)))),
inference(superposition,[],[f102,f13622]) ).
fof(f102,plain,
! [X0,X1] : join(X0,converse(X1)) = converse(join(X1,converse(X0))),
inference(superposition,[],[f46,f29]) ).
fof(f537188,plain,
! [X0] : composition(one,X0) = join(X0,composition(complement(converse(complement(composition(converse(sK0),sK0)))),X0)),
inference(superposition,[],[f13577,f447316]) ).
fof(f447316,plain,
one = join(one,complement(converse(complement(composition(converse(sK0),sK0))))),
inference(forward_demodulation,[],[f447315,f23]) ).
fof(f23,plain,
one = join(composition(converse(sK0),sK0),one),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( zero != meet(composition(sK0,sK1),composition(sK0,complement(sK1)))
& one = join(composition(converse(sK0),sK0),one) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f21,f20]) ).
fof(f20,plain,
( ? [X0] :
( ? [X1] : zero != meet(composition(X0,X1),composition(X0,complement(X1)))
& one = join(composition(converse(X0),X0),one) )
=> ( ? [X1] : zero != meet(composition(sK0,X1),composition(sK0,complement(X1)))
& one = join(composition(converse(sK0),sK0),one) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
( ? [X1] : zero != meet(composition(sK0,X1),composition(sK0,complement(X1)))
=> zero != meet(composition(sK0,sK1),composition(sK0,complement(sK1))) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
? [X0] :
( ? [X1] : zero != meet(composition(X0,X1),composition(X0,complement(X1)))
& one = join(composition(converse(X0),X0),one) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X0] :
( one = join(composition(converse(X0),X0),one)
=> ! [X1] : zero = meet(composition(X0,X1),composition(X0,complement(X1))) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X0] :
( one = join(composition(converse(X0),X0),one)
=> ! [X1] : zero = meet(composition(X0,X1),composition(X0,complement(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f447315,plain,
join(composition(converse(sK0),sK0),one) = join(one,complement(converse(complement(composition(converse(sK0),sK0))))),
inference(forward_demodulation,[],[f447073,f53]) ).
fof(f447073,plain,
join(composition(converse(sK0),sK0),one) = join(one,complement(converse(complement(converse(composition(converse(sK0),sK0)))))),
inference(superposition,[],[f209196,f437197]) ).
fof(f209196,plain,
! [X0] : join(one,X0) = join(join(composition(converse(sK0),sK0),X0),one),
inference(forward_demodulation,[],[f208992,f25]) ).
fof(f208992,plain,
! [X0] : converse(converse(join(one,X0))) = join(join(composition(converse(sK0),sK0),X0),one),
inference(superposition,[],[f243,f1178]) ).
fof(f1178,plain,
! [X0] : join(one,X0) = join(one,join(composition(converse(sK0),sK0),X0)),
inference(superposition,[],[f35,f42]) ).
fof(f42,plain,
one = join(one,composition(converse(sK0),sK0)),
inference(superposition,[],[f23,f29]) ).
fof(f13577,plain,
! [X0,X1] : composition(join(one,X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f37,f481]) ).
fof(f14913,plain,
! [X0,X1] : zero = meet(complement(join(X1,X0)),X0),
inference(superposition,[],[f10593,f14590]) ).
fof(f10593,plain,
! [X0,X1] : zero = meet(complement(X0),meet(X1,X0)),
inference(forward_demodulation,[],[f10592,f5819]) ).
fof(f10592,plain,
! [X0,X1] : zero = meet(join(zero,complement(X0)),meet(X1,X0)),
inference(forward_demodulation,[],[f10542,f5891]) ).
fof(f10542,plain,
! [X0,X1] : zero = meet(join(zero,complement(X0)),meet(X1,meet(X0,top))),
inference(superposition,[],[f10006,f66]) ).
fof(f10006,plain,
! [X0,X1] : zero = meet(X0,meet(X1,complement(X0))),
inference(forward_demodulation,[],[f9947,f61]) ).
fof(f9947,plain,
! [X0,X1] : complement(top) = meet(X0,meet(X1,complement(X0))),
inference(superposition,[],[f32,f8745]) ).
fof(f8745,plain,
! [X0,X1] : top = join(X0,complement(meet(X1,X0))),
inference(superposition,[],[f7652,f705]) ).
fof(f7652,plain,
! [X0,X1] : top = join(X0,complement(meet(X0,X1))),
inference(superposition,[],[f6294,f41]) ).
fof(f40,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(f24,plain,
zero != meet(composition(sK0,sK1),composition(sK0,complement(sK1))),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : REL041+2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n013.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.17/0.31 % DateTime : Fri May 3 15:38:38 EDT 2024
% 0.17/0.32 % CPUTime :
% 0.17/0.32 % (21641)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.33 % (21644)WARNING: value z3 for option sas not known
% 0.17/0.33 % (21646)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)
% 0.17/0.33 % (21648)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)
% 0.17/0.33 % (21643)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.33 % (21644)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)
% 0.17/0.33 % (21645)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.33 % (21647)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)
% 0.17/0.34 % (21642)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.34 TRYING [1]
% 0.17/0.34 TRYING [2]
% 0.17/0.35 TRYING [1]
% 0.17/0.35 TRYING [2]
% 0.17/0.36 TRYING [3]
% 0.17/0.38 TRYING [3]
% 0.17/0.42 TRYING [4]
% 0.17/0.47 TRYING [4]
% 2.39/0.69 TRYING [5]
% 7.56/1.44 TRYING [1]
% 7.56/1.44 TRYING [2]
% 7.56/1.45 TRYING [3]
% 8.34/1.51 TRYING [5]
% 8.34/1.51 TRYING [4]
% 9.24/1.67 TRYING [6]
% 10.54/1.83 TRYING [5]
% 18.25/2.97 TRYING [6]
% 29.17/4.54 TRYING [7]
% 39.89/6.03 TRYING [7]
% 85.69/12.61 TRYING [6]
% 86.37/12.64 TRYING [8]
% 94.12/13.75 % (21648)First to succeed.
% 94.12/13.75 % (21648)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-21641"
% 94.12/13.76 % (21648)Refutation found. Thanks to Tanya!
% 94.12/13.76 % SZS status Theorem for theBenchmark
% 94.12/13.76 % SZS output start Proof for theBenchmark
% See solution above
% 94.12/13.77 % (21648)------------------------------
% 94.12/13.77 % (21648)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 94.12/13.77 % (21648)Termination reason: Refutation
% 94.12/13.77
% 94.12/13.77 % (21648)Memory used [KB]: 208221
% 94.12/13.77 % (21648)Time elapsed: 13.414 s
% 94.12/13.77 % (21648)Instructions burned: 43877 (million)
% 94.12/13.77 % (21641)Success in time 13.328 s
%------------------------------------------------------------------------------