TSTP Solution File: GRP191-2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP191-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 20:19:42 EDT 2024

% Result   : Unsatisfiable 13.87s 2.14s
% Output   : CNFRefutation 14.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   68 (  68 unt;   0 def)
%            Number of atoms       :   68 (  67 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    5 (   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   :  119 ( 119   !;   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(f3,axiom,
    ! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
    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(f7,axiom,
    ! [X,Y,Z] : least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X] : least_upper_bound(X,X) = 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(f12,axiom,
    ! [X,Y,Z] : multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
    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(a,b) = b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,negated_conjecture,
    least_upper_bound(inverse(a),inverse(b)) != inverse(b),
    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(f20,plain,
    ! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f3]) ).

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(f24,plain,
    ! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f25,plain,
    ! [X0] : least_upper_bound(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f8]) ).

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(f29,plain,
    ! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
    inference(cnf_transformation,[status(esa)],[f12]) ).

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(a,b) = b,
    inference(cnf_transformation,[status(esa)],[f16]) ).

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

fof(f35,plain,
    least_upper_bound(a,b) = a,
    inference(paramodulation,[status(thm)],[f33,f27]) ).

fof(f38,plain,
    ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
    inference(paramodulation,[status(thm)],[f22,f28]) ).

fof(f98,plain,
    ! [X0,X1] : least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
    inference(paramodulation,[status(thm)],[f25,f24]) ).

fof(f115,plain,
    ! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
    inference(paramodulation,[status(thm)],[f22,f98]) ).

fof(f209,plain,
    ! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X1,X2),multiply(X0,X2)),
    inference(paramodulation,[status(thm)],[f22,f31]) ).

fof(f210,plain,
    ! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = multiply(least_upper_bound(X1,X0),X2),
    inference(forward_demodulation,[status(thm)],[f31,f209]) ).

fof(f344,plain,
    ! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
    inference(paramodulation,[status(thm)],[f115,f38]) ).

fof(f351,plain,
    ! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
    inference(paramodulation,[status(thm)],[f19,f20]) ).

fof(f352,plain,
    ! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f18,f351]) ).

fof(f365,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
    inference(paramodulation,[status(thm)],[f352,f352]) ).

fof(f366,plain,
    ! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
    inference(paramodulation,[status(thm)],[f19,f352]) ).

fof(f367,plain,
    ! [X0] : X0 = multiply(X0,identity),
    inference(forward_demodulation,[status(thm)],[f365,f366]) ).

fof(f374,plain,
    ! [X0,X1,X2] : multiply(inverse(X0),least_upper_bound(X1,multiply(X0,X2))) = least_upper_bound(multiply(inverse(X0),X1),X2),
    inference(paramodulation,[status(thm)],[f352,f29]) ).

fof(f395,plain,
    ! [X0] : multiply(X0,inverse(X0)) = identity,
    inference(paramodulation,[status(thm)],[f19,f365]) ).

fof(f396,plain,
    ! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
    inference(paramodulation,[status(thm)],[f367,f365]) ).

fof(f397,plain,
    ! [X0] : X0 = inverse(inverse(X0)),
    inference(forward_demodulation,[status(thm)],[f367,f396]) ).

fof(f422,plain,
    ! [X0,X1] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
    inference(paramodulation,[status(thm)],[f20,f395]) ).

fof(f431,plain,
    ! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(X1)) = least_upper_bound(multiply(X0,inverse(X1)),identity),
    inference(paramodulation,[status(thm)],[f395,f31]) ).

fof(f432,plain,
    ! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(X1)) = least_upper_bound(identity,multiply(X0,inverse(X1))),
    inference(forward_demodulation,[status(thm)],[f22,f431]) ).

fof(f513,plain,
    ! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X2),multiply(X0,X1)),
    inference(paramodulation,[status(thm)],[f21,f30]) ).

fof(f514,plain,
    ! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = multiply(X0,greatest_lower_bound(X2,X1)),
    inference(forward_demodulation,[status(thm)],[f30,f513]) ).

fof(f2304,plain,
    ! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
    inference(paramodulation,[status(thm)],[f422,f352]) ).

fof(f2305,plain,
    ! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
    inference(forward_demodulation,[status(thm)],[f367,f2304]) ).

fof(f2344,plain,
    ! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
    inference(paramodulation,[status(thm)],[f2305,f2305]) ).

fof(f2345,plain,
    ! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
    inference(forward_demodulation,[status(thm)],[f397,f2344]) ).

fof(f2682,plain,
    ! [X0,X1,X2] : multiply(inverse(multiply(X0,greatest_lower_bound(X1,X2))),X0) = inverse(greatest_lower_bound(X2,X1)),
    inference(paramodulation,[status(thm)],[f514,f2345]) ).

fof(f2683,plain,
    ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = inverse(greatest_lower_bound(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f2345,f2682]) ).

fof(f2736,plain,
    ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = inverse(greatest_lower_bound(least_upper_bound(X1,X0),least_upper_bound(X0,X1))),
    inference(paramodulation,[status(thm)],[f344,f2683]) ).

fof(f2737,plain,
    ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = inverse(least_upper_bound(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f344,f2736]) ).

fof(f2791,plain,
    ! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(least_upper_bound(X1,X0))) = identity,
    inference(paramodulation,[status(thm)],[f2737,f395]) ).

fof(f4393,plain,
    ! [X0,X1] : multiply(least_upper_bound(least_upper_bound(X0,X1),X0),inverse(least_upper_bound(X0,X1))) = identity,
    inference(paramodulation,[status(thm)],[f98,f2791]) ).

fof(f4394,plain,
    ! [X0,X1] : multiply(least_upper_bound(X0,least_upper_bound(X0,X1)),inverse(least_upper_bound(X0,X1))) = identity,
    inference(forward_demodulation,[status(thm)],[f210,f4393]) ).

fof(f4395,plain,
    ! [X0,X1] : least_upper_bound(identity,multiply(X0,inverse(least_upper_bound(X0,X1)))) = identity,
    inference(forward_demodulation,[status(thm)],[f432,f4394]) ).

fof(f5382,plain,
    ! [X0,X1] : least_upper_bound(identity,multiply(X0,inverse(least_upper_bound(X1,X0)))) = identity,
    inference(paramodulation,[status(thm)],[f2737,f4395]) ).

fof(f9351,plain,
    least_upper_bound(identity,multiply(b,inverse(a))) = identity,
    inference(paramodulation,[status(thm)],[f35,f5382]) ).

fof(f21544,plain,
    multiply(inverse(b),identity) = least_upper_bound(multiply(inverse(b),identity),inverse(a)),
    inference(paramodulation,[status(thm)],[f9351,f374]) ).

fof(f21545,plain,
    inverse(b) = least_upper_bound(multiply(inverse(b),identity),inverse(a)),
    inference(forward_demodulation,[status(thm)],[f367,f21544]) ).

fof(f21546,plain,
    inverse(b) = least_upper_bound(inverse(a),multiply(inverse(b),identity)),
    inference(forward_demodulation,[status(thm)],[f22,f21545]) ).

fof(f21547,plain,
    inverse(b) = least_upper_bound(inverse(a),inverse(b)),
    inference(forward_demodulation,[status(thm)],[f367,f21546]) ).

fof(f21548,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f21547,f34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP191-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33  % Computer : n019.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Tue Apr 30 00:27:44 EDT 2024
% 0.19/0.34  % CPUTime  : 
% 0.19/0.34  % Drodi V3.6.0
% 13.87/2.14  % Refutation found
% 13.87/2.14  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.87/2.14  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.31/2.20  % Elapsed time: 1.844101 seconds
% 14.31/2.20  % CPU time: 14.460496 seconds
% 14.31/2.20  % Total memory used: 217.479 MB
% 14.31/2.20  % Net memory used: 215.196 MB
%------------------------------------------------------------------------------