TSTP Solution File: GRP175-2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP175-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n031.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 20:19:38 EDT 2024

% Result   : Unsatisfiable 0.19s 0.45s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   31 (  31 unt;   0 def)
%            Number of atoms       :   31 (  30 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   41 (  41   !;   0   ?)

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

fof(f2,axiom,
    ! [X] : multiply(inverse(X),X) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y] : greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X,Y,Z] : multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [Y,Z,X] : multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,hypothesis,
    greatest_lower_bound(identity,b) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,negated_conjecture,
    greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,plain,
    ! [X0] : multiply(identity,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f19,plain,
    ! [X0] : multiply(inverse(X0),X0) = identity,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f21,plain,
    ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f22,plain,
    ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f27,plain,
    ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f28,plain,
    ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f30,plain,
    ! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f31,plain,
    ! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f33,plain,
    greatest_lower_bound(identity,b) = identity,
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f34,plain,
    greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f90,plain,
    ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
    inference(paramodulation,[status(thm)],[f19,f30]) ).

fof(f112,plain,
    ! [X0,X1] : X0 = least_upper_bound(X0,greatest_lower_bound(X1,X0)),
    inference(paramodulation,[status(thm)],[f21,f27]) ).

fof(f126,plain,
    b = least_upper_bound(b,identity),
    inference(paramodulation,[status(thm)],[f33,f112]) ).

fof(f187,plain,
    ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
    inference(paramodulation,[status(thm)],[f18,f31]) ).

fof(f201,plain,
    b = least_upper_bound(identity,b),
    inference(forward_demodulation,[status(thm)],[f22,f126]) ).

fof(f574,plain,
    identity != multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))),
    inference(paramodulation,[status(thm)],[f90,f34]) ).

fof(f1714,plain,
    ! [X0,X1] : X0 = greatest_lower_bound(X0,multiply(least_upper_bound(identity,X1),X0)),
    inference(paramodulation,[status(thm)],[f187,f28]) ).

fof(f2143,plain,
    ! [X0] : X0 = greatest_lower_bound(X0,multiply(b,X0)),
    inference(paramodulation,[status(thm)],[f201,f1714]) ).

fof(f2331,plain,
    identity != multiply(inverse(a),a),
    inference(backward_demodulation,[status(thm)],[f2143,f574]) ).

fof(f2358,plain,
    identity != identity,
    inference(forward_demodulation,[status(thm)],[f19,f2331]) ).

fof(f2359,plain,
    $false,
    inference(equality_resolution,[status(esa)],[f2358]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP175-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n031.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Apr 30 00:55:13 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Drodi V3.6.0
% 0.19/0.45  % Refutation found
% 0.19/0.45  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.45  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.47  % Elapsed time: 0.126144 seconds
% 0.19/0.47  % CPU time: 0.932854 seconds
% 0.19/0.47  % Total memory used: 27.100 MB
% 0.19/0.47  % Net memory used: 26.764 MB
%------------------------------------------------------------------------------