TSTP Solution File: COL006-3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : COL006-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 20:13:31 EDT 2024

% Result   : Unsatisfiable 6.96s 1.26s
% Output   : CNFRefutation 7.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   29 (  27 unt;   0 def)
%            Number of atoms       :   31 (  26 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   20 (  18   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   37 (  37   !;   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] : apply(apply(k,X),Y) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [Strong_fixed_point] :
      ( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt))
      | fixed_point(Strong_fixed_point) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,negated_conjecture,
    ~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,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(f6,plain,
    ! [X0,X1] : apply(apply(k,X0),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f7,plain,
    ! [X0] :
      ( apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt))
      | fixed_point(X0) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f8,plain,
    ~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))))),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f9,plain,
    apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt) != apply(fixed_pt,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt)),
    inference(resolution,[status(thm)],[f7,f8]) ).

fof(f13,plain,
    ! [X0,X1] : apply(apply(apply(s,k),X0),X1) = X1,
    inference(paramodulation,[status(thm)],[f6,f5]) ).

fof(f15,plain,
    ! [X0,X1,X2] : apply(apply(apply(s,apply(k,X0)),X1),X2) = apply(X0,apply(X1,X2)),
    inference(paramodulation,[status(thm)],[f6,f5]) ).

fof(f18,plain,
    ! [X0,X1,X2] : apply(apply(apply(s,X0),apply(k,X1)),X2) = apply(apply(X0,X2),X1),
    inference(paramodulation,[status(thm)],[f6,f5]) ).

fof(f35,plain,
    ! [X0,X1,X2] : apply(apply(apply(s,X0),apply(apply(s,k),X1)),X2) = apply(apply(X0,X2),X2),
    inference(paramodulation,[status(thm)],[f13,f5]) ).

fof(f36,plain,
    ! [X0,X1,X2] : apply(apply(apply(s,apply(apply(s,k),X0)),X1),X2) = apply(X2,apply(X1,X2)),
    inference(paramodulation,[status(thm)],[f13,f5]) ).

fof(f71,plain,
    apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),fixed_pt) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))),
    inference(backward_demodulation,[status(thm)],[f15,f9]) ).

fof(f72,plain,
    apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))),
    inference(forward_demodulation,[status(thm)],[f15,f71]) ).

fof(f73,plain,
    apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(apply(s,apply(k,s)),k),fixed_pt),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))),
    inference(forward_demodulation,[status(thm)],[f18,f72]) ).

fof(f74,plain,
    apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt))),
    inference(forward_demodulation,[status(thm)],[f15,f73]) ).

fof(f75,plain,
    apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(apply(s,apply(k,s)),k),fixed_pt),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
    inference(forward_demodulation,[status(thm)],[f18,f74]) ).

fof(f76,plain,
    apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
    inference(forward_demodulation,[status(thm)],[f15,f75]) ).

fof(f462,plain,
    ! [X0,X1,X2,X3] : apply(apply(apply(s,X0),apply(apply(s,k),X1)),X2) = apply(apply(apply(s,X0),apply(apply(s,k),X3)),X2),
    inference(paramodulation,[status(thm)],[f35,f35]) ).

fof(f1892,plain,
    ! [X0] : apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),X0)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
    inference(paramodulation,[status(thm)],[f462,f76]) ).

fof(f2688,plain,
    ! [X0] : apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),X0)),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
    inference(paramodulation,[status(thm)],[f36,f1892]) ).

fof(f4973,plain,
    ! [X0,X1] : apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),X0)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),X1)),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
    inference(paramodulation,[status(thm)],[f462,f2688]) ).

fof(f4995,plain,
    ! [X0] : apply(apply(apply(apply(s,k),k),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),X0)),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
    inference(paramodulation,[status(thm)],[f35,f4973]) ).

fof(f4996,plain,
    ! [X0] : apply(apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),X0)),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
    inference(forward_demodulation,[status(thm)],[f13,f4995]) ).

fof(f4997,plain,
    ! [X0] : apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),X0)),apply(s,apply(k,fixed_pt))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),
    inference(forward_demodulation,[status(thm)],[f15,f4996]) ).

fof(f5115,plain,
    apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(s,apply(k,fixed_pt)),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
    inference(paramodulation,[status(thm)],[f36,f4997]) ).

fof(f5116,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f5115]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : COL006-3 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Apr 29 22:47:34 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 6.96/1.26  % Refutation found
% 6.96/1.26  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.96/1.26  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.21/1.30  % Elapsed time: 0.950880 seconds
% 7.21/1.30  % CPU time: 7.382957 seconds
% 7.21/1.30  % Total memory used: 221.938 MB
% 7.21/1.30  % Net memory used: 220.895 MB
%------------------------------------------------------------------------------