TSTP Solution File: REL010+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : REL010+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 : Wed May 31 12:32:17 EDT 2023

% Result   : Theorem 4.89s 1.00s
% Output   : CNFRefutation 4.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   94 (  90 unt;   0 def)
%            Number of atoms       :   98 (  97 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    8 (   4   ~;   0   |;   2   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    6 (   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   :  114 (; 111   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X0] : composition(X0,one) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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') ).

fof(f8,axiom,
    ! [X0] : converse(converse(X0)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X0] : top = join(X0,complement(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X0] : zero = meet(X0,complement(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,conjecture,
    ! [X0,X1,X2] :
      ( meet(composition(X0,X1),X2) = zero
     => meet(X1,composition(converse(X0),X2)) = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( meet(composition(X0,X1),X2) = zero
       => meet(X1,composition(converse(X0),X2)) = zero ),
    inference(negated_conjecture,[status(cth)],[f17]) ).

fof(f19,plain,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f20,plain,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f21,plain,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f22,plain,
    ! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f24,plain,
    ! [X0] : composition(X0,one) = X0,
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f25,plain,
    ! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f26,plain,
    ! [X0] : converse(converse(X0)) = X0,
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f27,plain,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f28,plain,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f29,plain,
    ! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f30,plain,
    ! [X0] : top = join(X0,complement(X0)),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f31,plain,
    ! [X0] : zero = meet(X0,complement(X0)),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f32,plain,
    ! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f35,plain,
    ? [X0,X1,X2] :
      ( meet(composition(X0,X1),X2) = zero
      & meet(X1,composition(converse(X0),X2)) != zero ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f36,plain,
    ( meet(composition(sk0_0,sk0_1),sk0_2) = zero
    & meet(sk0_1,composition(converse(sk0_0),sk0_2)) != zero ),
    inference(skolemization,[status(esa)],[f35]) ).

fof(f37,plain,
    meet(composition(sk0_0,sk0_1),sk0_2) = zero,
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    meet(sk0_1,composition(converse(sk0_0),sk0_2)) != zero,
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f39,plain,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
    inference(forward_demodulation,[status(thm)],[f19,f21]) ).

fof(f40,plain,
    ! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
    inference(forward_demodulation,[status(thm)],[f19,f29]) ).

fof(f41,plain,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
    inference(backward_demodulation,[status(thm)],[f22,f39]) ).

fof(f42,plain,
    ! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
    inference(forward_demodulation,[status(thm)],[f19,f41]) ).

fof(f46,plain,
    ! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
    inference(paramodulation,[status(thm)],[f26,f27]) ).

fof(f49,plain,
    ! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
    inference(paramodulation,[status(thm)],[f26,f28]) ).

fof(f472,plain,
    ! [X0,X1,X2] : join(meet(composition(converse(X0),X1),X2),composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2)))) = composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(converse(converse(X0)),X2))),
    inference(paramodulation,[status(thm)],[f26,f32]) ).

fof(f473,plain,
    ! [X0,X1,X2] : join(meet(composition(converse(X0),X1),X2),composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2)))) = composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2))),
    inference(forward_demodulation,[status(thm)],[f26,f472]) ).

fof(f535,plain,
    ! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
    inference(paramodulation,[status(thm)],[f30,f46]) ).

fof(f548,plain,
    ! [X0] : converse(converse(X0)) = composition(converse(one),X0),
    inference(paramodulation,[status(thm)],[f24,f49]) ).

fof(f549,plain,
    ! [X0] : X0 = composition(converse(one),X0),
    inference(forward_demodulation,[status(thm)],[f26,f548]) ).

fof(f618,plain,
    one = converse(one),
    inference(paramodulation,[status(thm)],[f24,f549]) ).

fof(f663,plain,
    ! [X0] : X0 = composition(one,X0),
    inference(backward_demodulation,[status(thm)],[f618,f549]) ).

fof(f753,plain,
    ! [X0] : meet(X0,complement(X0)) = complement(top),
    inference(paramodulation,[status(thm)],[f30,f22]) ).

fof(f754,plain,
    zero = complement(top),
    inference(forward_demodulation,[status(thm)],[f31,f753]) ).

fof(f755,plain,
    ! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
    inference(paramodulation,[status(thm)],[f19,f22]) ).

fof(f756,plain,
    ! [X0,X1] : meet(X0,X1) = meet(X1,X0),
    inference(forward_demodulation,[status(thm)],[f22,f755]) ).

fof(f772,plain,
    zero = meet(sk0_2,composition(sk0_0,sk0_1)),
    inference(paramodulation,[status(thm)],[f37,f756]) ).

fof(f834,plain,
    ! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
    inference(paramodulation,[status(thm)],[f30,f20]) ).

fof(f847,plain,
    ! [X0] : join(X0,top) = join(top,complement(complement(X0))),
    inference(paramodulation,[status(thm)],[f30,f834]) ).

fof(f868,plain,
    ! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
    inference(paramodulation,[status(thm)],[f663,f25]) ).

fof(f900,plain,
    ! [X0] : join(complement(X0),composition(one,complement(composition(one,X0)))) = complement(X0),
    inference(paramodulation,[status(thm)],[f618,f40]) ).

fof(f901,plain,
    ! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
    inference(forward_demodulation,[status(thm)],[f663,f900]) ).

fof(f902,plain,
    ! [X0] : join(complement(X0),complement(X0)) = complement(X0),
    inference(forward_demodulation,[status(thm)],[f663,f901]) ).

fof(f1079,plain,
    join(zero,complement(top)) = complement(top),
    inference(paramodulation,[status(thm)],[f754,f902]) ).

fof(f1080,plain,
    join(zero,zero) = complement(top),
    inference(forward_demodulation,[status(thm)],[f754,f1079]) ).

fof(f1081,plain,
    join(zero,zero) = zero,
    inference(forward_demodulation,[status(thm)],[f754,f1080]) ).

fof(f1107,plain,
    ! [X0] : meet(X0,X0) = complement(complement(X0)),
    inference(paramodulation,[status(thm)],[f902,f22]) ).

fof(f1108,plain,
    ! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
    inference(paramodulation,[status(thm)],[f902,f834]) ).

fof(f1109,plain,
    ! [X0] : top = join(top,complement(X0)),
    inference(forward_demodulation,[status(thm)],[f30,f1108]) ).

fof(f1132,plain,
    ! [X0] : join(X0,top) = top,
    inference(backward_demodulation,[status(thm)],[f1109,f847]) ).

fof(f1135,plain,
    ! [X0] : join(top,X0) = top,
    inference(paramodulation,[status(thm)],[f19,f1132]) ).

fof(f1176,plain,
    ! [X0] : join(zero,join(zero,X0)) = join(zero,X0),
    inference(paramodulation,[status(thm)],[f1081,f20]) ).

fof(f1247,plain,
    ! [X0] : join(zero,join(X0,zero)) = join(zero,X0),
    inference(paramodulation,[status(thm)],[f19,f1176]) ).

fof(f1252,plain,
    converse(top) = top,
    inference(paramodulation,[status(thm)],[f1135,f535]) ).

fof(f2255,plain,
    ! [X0] : composition(top,X0) = join(X0,composition(top,X0)),
    inference(paramodulation,[status(thm)],[f1132,f868]) ).

fof(f2327,plain,
    composition(top,top) = top,
    inference(paramodulation,[status(thm)],[f1135,f2255]) ).

fof(f2417,plain,
    join(complement(top),composition(converse(top),complement(top))) = complement(top),
    inference(paramodulation,[status(thm)],[f2327,f40]) ).

fof(f2418,plain,
    composition(join(one,converse(top)),complement(top)) = complement(top),
    inference(forward_demodulation,[status(thm)],[f868,f2417]) ).

fof(f2419,plain,
    composition(join(one,top),complement(top)) = complement(top),
    inference(forward_demodulation,[status(thm)],[f1252,f2418]) ).

fof(f2420,plain,
    composition(top,complement(top)) = complement(top),
    inference(forward_demodulation,[status(thm)],[f1132,f2419]) ).

fof(f2421,plain,
    composition(top,zero) = complement(top),
    inference(forward_demodulation,[status(thm)],[f754,f2420]) ).

fof(f2422,plain,
    composition(top,zero) = zero,
    inference(forward_demodulation,[status(thm)],[f754,f2421]) ).

fof(f2450,plain,
    ! [X0] : X0 = join(zero,complement(join(complement(X0),complement(X0)))),
    inference(paramodulation,[status(thm)],[f31,f42]) ).

fof(f2451,plain,
    ! [X0] : X0 = join(zero,meet(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f22,f2450]) ).

fof(f2452,plain,
    ! [X0] : X0 = join(zero,complement(complement(X0))),
    inference(forward_demodulation,[status(thm)],[f1107,f2451]) ).

fof(f3125,plain,
    ! [X0] : composition(join(X0,top),zero) = join(composition(X0,zero),zero),
    inference(paramodulation,[status(thm)],[f2422,f25]) ).

fof(f3126,plain,
    ! [X0] : composition(top,zero) = join(composition(X0,zero),zero),
    inference(forward_demodulation,[status(thm)],[f1132,f3125]) ).

fof(f3127,plain,
    ! [X0] : zero = join(composition(X0,zero),zero),
    inference(forward_demodulation,[status(thm)],[f2422,f3126]) ).

fof(f3128,plain,
    ! [X0] : zero = join(zero,composition(X0,zero)),
    inference(forward_demodulation,[status(thm)],[f19,f3127]) ).

fof(f3157,plain,
    ! [X0] : join(zero,X0) = join(zero,complement(complement(X0))),
    inference(paramodulation,[status(thm)],[f2452,f1176]) ).

fof(f3158,plain,
    ! [X0] : join(zero,X0) = X0,
    inference(forward_demodulation,[status(thm)],[f2452,f3157]) ).

fof(f3171,plain,
    ! [X0] : join(X0,zero) = join(zero,X0),
    inference(backward_demodulation,[status(thm)],[f3158,f1247]) ).

fof(f3172,plain,
    ! [X0] : join(X0,zero) = X0,
    inference(forward_demodulation,[status(thm)],[f3158,f3171]) ).

fof(f3239,plain,
    ! [X0] : zero = composition(X0,zero),
    inference(backward_demodulation,[status(thm)],[f3158,f3128]) ).

fof(f5611,plain,
    join(meet(composition(converse(sk0_0),sk0_2),sk0_1),composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),zero)) = composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),meet(sk0_2,composition(sk0_0,sk0_1))),
    inference(paramodulation,[status(thm)],[f772,f473]) ).

fof(f5612,plain,
    join(meet(sk0_1,composition(converse(sk0_0),sk0_2)),composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),zero)) = composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),meet(sk0_2,composition(sk0_0,sk0_1))),
    inference(forward_demodulation,[status(thm)],[f756,f5611]) ).

fof(f5613,plain,
    join(meet(sk0_1,composition(converse(sk0_0),sk0_2)),zero) = composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),meet(sk0_2,composition(sk0_0,sk0_1))),
    inference(forward_demodulation,[status(thm)],[f3239,f5612]) ).

fof(f5614,plain,
    meet(sk0_1,composition(converse(sk0_0),sk0_2)) = composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),meet(sk0_2,composition(sk0_0,sk0_1))),
    inference(forward_demodulation,[status(thm)],[f3172,f5613]) ).

fof(f5615,plain,
    meet(sk0_1,composition(converse(sk0_0),sk0_2)) = composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),zero),
    inference(forward_demodulation,[status(thm)],[f772,f5614]) ).

fof(f5616,plain,
    meet(sk0_1,composition(converse(sk0_0),sk0_2)) = zero,
    inference(forward_demodulation,[status(thm)],[f3239,f5615]) ).

fof(f5617,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f5616,f38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : REL010+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n015.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue May 30 10:19:04 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  % Drodi V3.5.1
% 4.89/1.00  % Refutation found
% 4.89/1.00  % SZS status Theorem for theBenchmark: Theorem is valid
% 4.89/1.00  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.89/1.05  % Elapsed time: 0.692300 seconds
% 4.89/1.05  % CPU time: 5.312364 seconds
% 4.89/1.05  % Memory used: 84.362 MB
%------------------------------------------------------------------------------