TSTP Solution File: COL002-2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : COL002-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 20:13:28 EDT 2024

% Result   : Unsatisfiable 2.82s 0.70s
% Output   : CNFRefutation 2.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   18 (  16 unt;   0 def)
%            Number of atoms       :   20 (  15 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    9 (   7   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   28 (  28   !;   0   ?)

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

fof(f2,axiom,
    ! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f5,axiom,
    ! [Weak_sage] :
      ( Weak_sage != apply(fixed_pt,Weak_sage)
      | fixed_point(Weak_sage) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,negated_conjecture,
    ! [X] : ~ fixed_point(apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,plain,
    ! [X0,X1,X2] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f8,plain,
    ! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f10,plain,
    ! [X0] : apply(i,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f11,plain,
    ! [X0] :
      ( X0 != apply(fixed_pt,X0)
      | fixed_point(X0) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f12,plain,
    ! [X0] : ~ fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f18,plain,
    ! [X0,X1] : apply(apply(apply(s,i),X0),X1) = apply(X1,apply(X0,X1)),
    inference(paramodulation,[status(thm)],[f10,f7]) ).

fof(f22,plain,
    ! [X0,X1] : apply(apply(apply(s,X0),i),X1) = apply(apply(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f10,f7]) ).

fof(f32,plain,
    ! [X0] : apply(apply(apply(s,i),i),X0) = apply(X0,X0),
    inference(paramodulation,[status(thm)],[f10,f18]) ).

fof(f113,plain,
    ! [X0,X1] : apply(apply(apply(s,apply(b,X0)),i),X1) = apply(X0,apply(X1,X1)),
    inference(paramodulation,[status(thm)],[f8,f22]) ).

fof(f811,plain,
    ! [X0] : apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i)) != apply(fixed_pt,apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))),
    inference(resolution,[status(thm)],[f11,f12]) ).

fof(f812,plain,
    ! [X0] : apply(apply(apply(s,i),i),apply(apply(s,apply(b,X0)),i)) != apply(fixed_pt,apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))),
    inference(forward_demodulation,[status(thm)],[f32,f811]) ).

fof(f813,plain,
    ! [X0] : apply(apply(apply(s,i),i),apply(apply(s,apply(b,X0)),i)) != apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,X0)),i)),
    inference(forward_demodulation,[status(thm)],[f113,f812]) ).

fof(f3469,plain,
    $false,
    inference(resolution,[status(thm)],[f813,f32]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : COL002-2 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n028.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon Apr 29 22:50:44 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  % Drodi V3.6.0
% 2.82/0.70  % Refutation found
% 2.82/0.70  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.82/0.70  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.82/0.72  % Elapsed time: 0.381015 seconds
% 2.82/0.72  % CPU time: 2.905097 seconds
% 2.82/0.72  % Total memory used: 99.314 MB
% 2.82/0.72  % Net memory used: 98.915 MB
%------------------------------------------------------------------------------