TSTP Solution File: REL006-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : REL006-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 20:37:20 EDT 2024

% Result   : Unsatisfiable 2.85s 0.76s
% Output   : CNFRefutation 3.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   42
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  117 ( 117 unt;   0 def)
%            Number of atoms       :  117 ( 116 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    6 (   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   :  146 ( 146   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] : join(A,B) = join(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [A,B,C] : join(A,join(B,C)) = join(join(A,B),C),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [A,B] : A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A,B] : meet(A,B) = complement(join(complement(A),complement(B))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A] : composition(A,one) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A] : converse(converse(A)) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [A,B] : join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A] : top = join(A,complement(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [A] : zero = meet(A,complement(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,negated_conjecture,
    meet(converse(sk1),sk2) = zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,negated_conjecture,
    meet(sk1,converse(sk2)) != zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,plain,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f17,plain,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f18,plain,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f19,plain,
    ! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f21,plain,
    ! [X0] : composition(X0,one) = X0,
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f23,plain,
    ! [X0] : converse(converse(X0)) = X0,
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f24,plain,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f25,plain,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f26,plain,
    ! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f27,plain,
    ! [X0] : top = join(X0,complement(X0)),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f28,plain,
    ! [X0] : zero = meet(X0,complement(X0)),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f29,plain,
    meet(converse(sk1),sk2) = zero,
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f30,plain,
    meet(sk1,converse(sk2)) != zero,
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f34,plain,
    ! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
    inference(paramodulation,[status(thm)],[f23,f24]) ).

fof(f35,plain,
    ! [X0,X1] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
    inference(paramodulation,[status(thm)],[f23,f24]) ).

fof(f37,plain,
    ! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
    inference(paramodulation,[status(thm)],[f23,f25]) ).

fof(f160,plain,
    ! [X0] : converse(converse(X0)) = composition(converse(one),X0),
    inference(paramodulation,[status(thm)],[f21,f37]) ).

fof(f161,plain,
    ! [X0] : X0 = composition(converse(one),X0),
    inference(forward_demodulation,[status(thm)],[f23,f160]) ).

fof(f176,plain,
    ! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
    inference(paramodulation,[status(thm)],[f16,f19]) ).

fof(f177,plain,
    ! [X0,X1] : meet(X0,X1) = meet(X1,X0),
    inference(forward_demodulation,[status(thm)],[f19,f176]) ).

fof(f198,plain,
    ! [X0] : meet(X0,complement(X0)) = complement(top),
    inference(paramodulation,[status(thm)],[f27,f19]) ).

fof(f199,plain,
    zero = complement(top),
    inference(forward_demodulation,[status(thm)],[f28,f198]) ).

fof(f212,plain,
    one = converse(one),
    inference(paramodulation,[status(thm)],[f21,f161]) ).

fof(f224,plain,
    ! [X0] : X0 = composition(one,X0),
    inference(backward_demodulation,[status(thm)],[f212,f161]) ).

fof(f245,plain,
    ! [X0] : join(composition(converse(one),complement(X0)),complement(X0)) = complement(X0),
    inference(paramodulation,[status(thm)],[f224,f26]) ).

fof(f246,plain,
    ! [X0] : join(complement(X0),composition(converse(one),complement(X0))) = complement(X0),
    inference(forward_demodulation,[status(thm)],[f16,f245]) ).

fof(f247,plain,
    ! [X0] : join(complement(X0),composition(one,complement(X0))) = complement(X0),
    inference(forward_demodulation,[status(thm)],[f212,f246]) ).

fof(f248,plain,
    ! [X0] : join(complement(X0),complement(X0)) = complement(X0),
    inference(forward_demodulation,[status(thm)],[f224,f247]) ).

fof(f250,plain,
    zero = meet(sk2,converse(sk1)),
    inference(paramodulation,[status(thm)],[f29,f177]) ).

fof(f258,plain,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
    inference(paramodulation,[status(thm)],[f16,f17]) ).

fof(f275,plain,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
    inference(forward_demodulation,[status(thm)],[f16,f18]) ).

fof(f276,plain,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f19,f275]) ).

fof(f277,plain,
    ! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
    inference(forward_demodulation,[status(thm)],[f16,f276]) ).

fof(f290,plain,
    ! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
    inference(paramodulation,[status(thm)],[f19,f277]) ).

fof(f291,plain,
    ! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
    inference(forward_demodulation,[status(thm)],[f16,f290]) ).

fof(f292,plain,
    ! [X0] : X0 = join(meet(X0,complement(complement(X0))),complement(top)),
    inference(paramodulation,[status(thm)],[f27,f277]) ).

fof(f293,plain,
    ! [X0] : X0 = join(complement(top),meet(X0,complement(complement(X0)))),
    inference(forward_demodulation,[status(thm)],[f16,f292]) ).

fof(f294,plain,
    ! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
    inference(forward_demodulation,[status(thm)],[f199,f293]) ).

fof(f301,plain,
    ! [X0,X1,X2] : join(meet(X0,X1),join(complement(join(complement(X0),X1)),X2)) = join(X0,X2),
    inference(paramodulation,[status(thm)],[f277,f17]) ).

fof(f313,plain,
    sk2 = join(zero,complement(join(complement(sk2),converse(sk1)))),
    inference(paramodulation,[status(thm)],[f250,f277]) ).

fof(f339,plain,
    ! [X0] : X0 = join(meet(X0,complement(X0)),complement(complement(X0))),
    inference(paramodulation,[status(thm)],[f248,f277]) ).

fof(f340,plain,
    ! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
    inference(forward_demodulation,[status(thm)],[f16,f339]) ).

fof(f341,plain,
    ! [X0] : X0 = join(complement(complement(X0)),zero),
    inference(forward_demodulation,[status(thm)],[f28,f340]) ).

fof(f342,plain,
    ! [X0] : X0 = join(zero,complement(complement(X0))),
    inference(forward_demodulation,[status(thm)],[f16,f341]) ).

fof(f517,plain,
    ! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
    inference(paramodulation,[status(thm)],[f177,f291]) ).

fof(f529,plain,
    ! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
    inference(paramodulation,[status(thm)],[f177,f291]) ).

fof(f596,plain,
    ! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
    inference(paramodulation,[status(thm)],[f28,f529]) ).

fof(f597,plain,
    ! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
    inference(forward_demodulation,[status(thm)],[f16,f596]) ).

fof(f598,plain,
    ! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
    inference(forward_demodulation,[status(thm)],[f177,f597]) ).

fof(f599,plain,
    ! [X0] : complement(complement(X0)) = X0,
    inference(forward_demodulation,[status(thm)],[f294,f598]) ).

fof(f613,plain,
    ! [X0] : X0 = join(zero,X0),
    inference(backward_demodulation,[status(thm)],[f599,f342]) ).

fof(f627,plain,
    ! [X0] : join(complement(complement(X0)),X0) = complement(complement(X0)),
    inference(paramodulation,[status(thm)],[f599,f248]) ).

fof(f628,plain,
    ! [X0] : join(X0,complement(complement(X0))) = complement(complement(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f627]) ).

fof(f629,plain,
    ! [X0] : join(X0,X0) = complement(complement(X0)),
    inference(forward_demodulation,[status(thm)],[f599,f628]) ).

fof(f630,plain,
    ! [X0] : join(X0,X0) = X0,
    inference(forward_demodulation,[status(thm)],[f599,f629]) ).

fof(f853,plain,
    ! [X0,X1] : join(X0,join(X0,X1)) = join(X0,X1),
    inference(paramodulation,[status(thm)],[f630,f17]) ).

fof(f857,plain,
    sk2 = complement(join(complement(sk2),converse(sk1))),
    inference(backward_demodulation,[status(thm)],[f613,f313]) ).

fof(f1063,plain,
    complement(sk2) = join(complement(sk2),converse(sk1)),
    inference(paramodulation,[status(thm)],[f857,f599]) ).

fof(f1096,plain,
    converse(complement(sk2)) = join(converse(complement(sk2)),sk1),
    inference(paramodulation,[status(thm)],[f1063,f35]) ).

fof(f1097,plain,
    converse(complement(sk2)) = join(sk1,converse(complement(sk2))),
    inference(forward_demodulation,[status(thm)],[f16,f1096]) ).

fof(f1324,plain,
    ! [X0,X1] : join(meet(X0,X1),X1) = join(meet(X0,X1),meet(X1,complement(X0))),
    inference(paramodulation,[status(thm)],[f517,f853]) ).

fof(f1325,plain,
    ! [X0,X1] : join(X0,meet(X1,X0)) = join(meet(X1,X0),meet(X0,complement(X1))),
    inference(forward_demodulation,[status(thm)],[f16,f1324]) ).

fof(f1326,plain,
    ! [X0,X1] : join(X0,meet(X1,X0)) = X0,
    inference(forward_demodulation,[status(thm)],[f517,f1325]) ).

fof(f1348,plain,
    ! [X0] : join(X0,top) = join(X0,complement(X0)),
    inference(paramodulation,[status(thm)],[f27,f853]) ).

fof(f1349,plain,
    ! [X0] : join(X0,top) = top,
    inference(forward_demodulation,[status(thm)],[f27,f1348]) ).

fof(f1365,plain,
    ! [X0] : join(top,X0) = top,
    inference(paramodulation,[status(thm)],[f16,f1349]) ).

fof(f1369,plain,
    ! [X0] : converse(top) = join(X0,converse(top)),
    inference(paramodulation,[status(thm)],[f1349,f34]) ).

fof(f1673,plain,
    ! [X0,X1] : join(X0,top) = join(complement(X1),join(X0,X1)),
    inference(paramodulation,[status(thm)],[f27,f258]) ).

fof(f1674,plain,
    ! [X0,X1] : top = join(complement(X0),join(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f1349,f1673]) ).

fof(f1675,plain,
    ! [X0,X1] : top = join(X0,join(complement(X0),X1)),
    inference(forward_demodulation,[status(thm)],[f258,f1674]) ).

fof(f1932,plain,
    ! [X0,X1] : converse(converse(X0)) = join(X0,converse(meet(X1,converse(X0)))),
    inference(paramodulation,[status(thm)],[f1326,f34]) ).

fof(f1933,plain,
    ! [X0,X1] : X0 = join(X0,converse(meet(X1,converse(X0)))),
    inference(forward_demodulation,[status(thm)],[f23,f1932]) ).

fof(f2260,plain,
    converse(top) = top,
    inference(paramodulation,[status(thm)],[f1365,f1369]) ).

fof(f2372,plain,
    ! [X0,X1] : top = join(X0,join(X1,complement(X0))),
    inference(paramodulation,[status(thm)],[f16,f1675]) ).

fof(f2393,plain,
    ! [X0,X1] : X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(top)),
    inference(paramodulation,[status(thm)],[f1675,f277]) ).

fof(f2394,plain,
    ! [X0,X1] : X0 = join(complement(top),meet(X0,join(complement(complement(X0)),X1))),
    inference(forward_demodulation,[status(thm)],[f16,f2393]) ).

fof(f2395,plain,
    ! [X0,X1] : X0 = join(zero,meet(X0,join(complement(complement(X0)),X1))),
    inference(forward_demodulation,[status(thm)],[f199,f2394]) ).

fof(f2396,plain,
    ! [X0,X1] : X0 = meet(X0,join(complement(complement(X0)),X1)),
    inference(forward_demodulation,[status(thm)],[f613,f2395]) ).

fof(f2397,plain,
    ! [X0,X1] : X0 = meet(X0,join(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f599,f2396]) ).

fof(f2438,plain,
    ! [X0,X1] : meet(X0,X1) = meet(meet(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f517,f2397]) ).

fof(f2439,plain,
    ! [X0,X1] : meet(X0,X1) = meet(X1,meet(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f177,f2438]) ).

fof(f2462,plain,
    ! [X0,X1] : X0 = meet(X0,join(X1,X0)),
    inference(paramodulation,[status(thm)],[f16,f2397]) ).

fof(f4158,plain,
    ! [X0,X1] : top = join(X0,complement(meet(X0,X1))),
    inference(paramodulation,[status(thm)],[f2372,f301]) ).

fof(f4407,plain,
    ! [X0,X1] : top = join(X0,complement(meet(X1,X0))),
    inference(paramodulation,[status(thm)],[f2439,f4158]) ).

fof(f4561,plain,
    ! [X0,X1] : meet(X0,meet(X1,complement(X0))) = complement(top),
    inference(paramodulation,[status(thm)],[f4407,f19]) ).

fof(f4562,plain,
    ! [X0,X1] : meet(X0,meet(X1,complement(X0))) = zero,
    inference(forward_demodulation,[status(thm)],[f199,f4561]) ).

fof(f4710,plain,
    ! [X0,X1] : meet(complement(X0),meet(X1,X0)) = zero,
    inference(paramodulation,[status(thm)],[f599,f4562]) ).

fof(f5388,plain,
    ! [X0,X1] : meet(complement(join(X0,X1)),X1) = zero,
    inference(paramodulation,[status(thm)],[f2462,f4710]) ).

fof(f5389,plain,
    ! [X0,X1] : meet(X0,complement(join(X1,X0))) = zero,
    inference(forward_demodulation,[status(thm)],[f177,f5388]) ).

fof(f7019,plain,
    sk1 = meet(sk1,converse(complement(sk2))),
    inference(paramodulation,[status(thm)],[f1097,f2397]) ).

fof(f7035,plain,
    top = join(converse(complement(sk2)),complement(sk1)),
    inference(paramodulation,[status(thm)],[f7019,f4407]) ).

fof(f7036,plain,
    top = join(complement(sk1),converse(complement(sk2))),
    inference(forward_demodulation,[status(thm)],[f16,f7035]) ).

fof(f8156,plain,
    converse(top) = join(converse(complement(sk1)),complement(sk2)),
    inference(paramodulation,[status(thm)],[f7036,f35]) ).

fof(f8157,plain,
    top = join(converse(complement(sk1)),complement(sk2)),
    inference(forward_demodulation,[status(thm)],[f2260,f8156]) ).

fof(f8158,plain,
    top = join(complement(sk2),converse(complement(sk1))),
    inference(forward_demodulation,[status(thm)],[f16,f8157]) ).

fof(f10072,plain,
    sk2 = join(meet(sk2,converse(complement(sk1))),complement(top)),
    inference(paramodulation,[status(thm)],[f8158,f277]) ).

fof(f10073,plain,
    sk2 = join(complement(top),meet(sk2,converse(complement(sk1)))),
    inference(forward_demodulation,[status(thm)],[f16,f10072]) ).

fof(f10074,plain,
    sk2 = join(zero,meet(sk2,converse(complement(sk1)))),
    inference(forward_demodulation,[status(thm)],[f199,f10073]) ).

fof(f10075,plain,
    sk2 = meet(sk2,converse(complement(sk1))),
    inference(forward_demodulation,[status(thm)],[f613,f10074]) ).

fof(f10111,plain,
    complement(sk1) = join(complement(sk1),converse(sk2)),
    inference(paramodulation,[status(thm)],[f10075,f1933]) ).

fof(f10167,plain,
    meet(converse(sk2),complement(complement(sk1))) = zero,
    inference(paramodulation,[status(thm)],[f10111,f5389]) ).

fof(f10168,plain,
    meet(converse(sk2),sk1) = zero,
    inference(forward_demodulation,[status(thm)],[f599,f10167]) ).

fof(f10169,plain,
    meet(sk1,converse(sk2)) = zero,
    inference(forward_demodulation,[status(thm)],[f177,f10168]) ).

fof(f10170,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f10169,f30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : REL006-1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 21:22:39 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 2.85/0.76  % Refutation found
% 2.85/0.76  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.85/0.76  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.29/0.79  % Elapsed time: 0.428905 seconds
% 3.29/0.79  % CPU time: 3.296014 seconds
% 3.29/0.79  % Total memory used: 78.110 MB
% 3.29/0.79  % Net memory used: 75.179 MB
%------------------------------------------------------------------------------