TSTP Solution File: REL031+2 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : REL031+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n001.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 12:32:25 EDT 2023

% Result   : Theorem 8.15s 1.47s
% Output   : CNFRefutation 8.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   51 (  47 unt;   0 def)
%            Number of atoms       :   59 (  58 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   13 (   5   ~;   0   |;   6   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   68 (;  66   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X0] : composition(X0,one) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X0] : converse(converse(X0)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,conjecture,
    ! [X0,X1] :
      ( ( join(composition(converse(X0),X0),one) = one
        & join(composition(converse(X1),X1),one) = one )
     => join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( join(composition(converse(X0),X0),one) = one
          & join(composition(converse(X1),X1),one) = one )
       => join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) = one ),
    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(f23,plain,
    ! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f5]) ).

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(f35,plain,
    ? [X0,X1] :
      ( join(composition(converse(X0),X0),one) = one
      & join(composition(converse(X1),X1),one) = one
      & join(composition(converse(composition(X0,X1)),composition(X0,X1)),one) != one ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

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

fof(f37,plain,
    join(composition(converse(sk0_0),sk0_0),one) = one,
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    join(composition(converse(sk0_1),sk0_1),one) = one,
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f39,plain,
    join(composition(converse(composition(sk0_0,sk0_1)),composition(sk0_0,sk0_1)),one) != one,
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f40,plain,
    one = join(one,composition(converse(sk0_1),sk0_1)),
    inference(paramodulation,[status(thm)],[f38,f19]) ).

fof(f41,plain,
    one = join(one,composition(converse(sk0_0),sk0_0)),
    inference(paramodulation,[status(thm)],[f37,f19]) ).

fof(f44,plain,
    join(one,composition(converse(composition(sk0_0,sk0_1)),composition(sk0_0,sk0_1))) != one,
    inference(paramodulation,[status(thm)],[f19,f39]) ).

fof(f54,plain,
    ! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
    inference(paramodulation,[status(thm)],[f24,f23]) ).

fof(f63,plain,
    ! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
    inference(paramodulation,[status(thm)],[f26,f28]) ).

fof(f64,plain,
    ! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
    inference(paramodulation,[status(thm)],[f26,f28]) ).

fof(f65,plain,
    ! [X0,X1,X2] : composition(converse(X0),composition(converse(X1),X2)) = composition(converse(composition(X1,X0)),X2),
    inference(paramodulation,[status(thm)],[f28,f23]) ).

fof(f72,plain,
    ! [X0] : join(one,join(composition(converse(sk0_1),sk0_1),X0)) = join(one,X0),
    inference(paramodulation,[status(thm)],[f40,f20]) ).

fof(f122,plain,
    ! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
    inference(paramodulation,[status(thm)],[f26,f27]) ).

fof(f133,plain,
    ! [X0] : converse(converse(X0)) = composition(converse(one),X0),
    inference(paramodulation,[status(thm)],[f24,f64]) ).

fof(f134,plain,
    ! [X0] : X0 = composition(converse(one),X0),
    inference(forward_demodulation,[status(thm)],[f26,f133]) ).

fof(f148,plain,
    ! [X0] : composition(one,X0) = composition(converse(one),X0),
    inference(paramodulation,[status(thm)],[f54,f134]) ).

fof(f149,plain,
    ! [X0] : composition(one,X0) = X0,
    inference(forward_demodulation,[status(thm)],[f134,f148]) ).

fof(f162,plain,
    ! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
    inference(paramodulation,[status(thm)],[f149,f25]) ).

fof(f380,plain,
    ! [X0] : join(one,composition(join(converse(sk0_1),X0),sk0_1)) = join(one,composition(X0,sk0_1)),
    inference(paramodulation,[status(thm)],[f25,f72]) ).

fof(f517,plain,
    ! [X0] : composition(one,X0) = join(X0,composition(composition(converse(sk0_0),sk0_0),X0)),
    inference(paramodulation,[status(thm)],[f41,f162]) ).

fof(f518,plain,
    ! [X0] : X0 = join(X0,composition(composition(converse(sk0_0),sk0_0),X0)),
    inference(forward_demodulation,[status(thm)],[f149,f517]) ).

fof(f519,plain,
    ! [X0] : X0 = join(X0,composition(converse(sk0_0),composition(sk0_0,X0))),
    inference(forward_demodulation,[status(thm)],[f23,f518]) ).

fof(f576,plain,
    ! [X0] : converse(converse(X0)) = join(X0,converse(composition(converse(sk0_0),composition(sk0_0,converse(X0))))),
    inference(paramodulation,[status(thm)],[f519,f122]) ).

fof(f577,plain,
    ! [X0] : X0 = join(X0,converse(composition(converse(sk0_0),composition(sk0_0,converse(X0))))),
    inference(forward_demodulation,[status(thm)],[f26,f576]) ).

fof(f578,plain,
    ! [X0] : X0 = join(X0,composition(converse(composition(sk0_0,converse(X0))),sk0_0)),
    inference(forward_demodulation,[status(thm)],[f64,f577]) ).

fof(f579,plain,
    ! [X0] : X0 = join(X0,composition(composition(X0,converse(sk0_0)),sk0_0)),
    inference(forward_demodulation,[status(thm)],[f63,f578]) ).

fof(f580,plain,
    ! [X0] : X0 = join(X0,composition(X0,composition(converse(sk0_0),sk0_0))),
    inference(forward_demodulation,[status(thm)],[f23,f579]) ).

fof(f1078,plain,
    ! [X0] : converse(X0) = join(converse(X0),composition(converse(composition(sk0_0,X0)),sk0_0)),
    inference(paramodulation,[status(thm)],[f65,f580]) ).

fof(f2956,plain,
    join(one,composition(converse(sk0_1),sk0_1)) = join(one,composition(composition(converse(composition(sk0_0,sk0_1)),sk0_0),sk0_1)),
    inference(paramodulation,[status(thm)],[f1078,f380]) ).

fof(f2957,plain,
    one = join(one,composition(composition(converse(composition(sk0_0,sk0_1)),sk0_0),sk0_1)),
    inference(forward_demodulation,[status(thm)],[f40,f2956]) ).

fof(f2958,plain,
    one = join(one,composition(converse(composition(sk0_0,sk0_1)),composition(sk0_0,sk0_1))),
    inference(forward_demodulation,[status(thm)],[f23,f2957]) ).

fof(f2959,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f2958,f44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : REL031+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n001.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Tue May 30 10:33:00 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  % Drodi V3.5.1
% 8.15/1.47  % Refutation found
% 8.15/1.47  % SZS status Theorem for theBenchmark: Theorem is valid
% 8.15/1.47  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.15/1.53  % Elapsed time: 1.202639 seconds
% 8.15/1.53  % CPU time: 8.660884 seconds
% 8.15/1.53  % Memory used: 112.584 MB
%------------------------------------------------------------------------------