TSTP Solution File: COL003-20 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : COL003-20 : TPTP v8.1.2. Released v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 20:13:30 EDT 2024

% Result   : Unsatisfiable 218.36s 27.83s
% Output   : CNFRefutation 218.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   23 (  23 unt;   0 def)
%            Number of atoms       :   23 (  22 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   32 (  32   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] : apply(apply(w,X),Y) = apply(apply(X,Y),Y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,negated_conjecture,
    apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,plain,
    ! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

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

fof(f7,plain,
    strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f8,plain,
    apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f9,plain,
    ! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
    inference(paramodulation,[status(thm)],[f6,f6]) ).

fof(f28,plain,
    ! [X0,X1] : apply(apply(w,w),apply(apply(b,X0),X1)) = apply(apply(X0,apply(X1,apply(apply(b,X0),X1))),apply(apply(b,X0),X1)),
    inference(paramodulation,[status(thm)],[f5,f9]) ).

fof(f29,plain,
    ! [X0,X1,X2] : apply(apply(w,apply(apply(b,X0),X1)),X2) = apply(apply(X0,apply(X1,X2)),X2),
    inference(paramodulation,[status(thm)],[f5,f6]) ).

fof(f50,plain,
    ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X0)),
    inference(paramodulation,[status(thm)],[f7,f5]) ).

fof(f51,plain,
    ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(b,w),apply(apply(apply(b,b),b),X0))),
    inference(forward_demodulation,[status(thm)],[f5,f50]) ).

fof(f52,plain,
    ! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0)))),
    inference(forward_demodulation,[status(thm)],[f5,f51]) ).

fof(f200,plain,
    ! [X0,X1,X2] : apply(apply(w,apply(apply(b,apply(b,X0)),X1)),X2) = apply(X0,apply(apply(X1,X2),X2)),
    inference(paramodulation,[status(thm)],[f5,f29]) ).

fof(f15901,plain,
    ! [X0,X1,X2] : apply(apply(w,apply(apply(b,apply(b,X0)),X1)),X2) = apply(X0,apply(apply(w,X1),X2)),
    inference(paramodulation,[status(thm)],[f6,f200]) ).

fof(f16665,plain,
    ! [X0,X1,X2] : apply(X0,apply(apply(w,X1),X2)) = apply(X0,apply(apply(X1,X2),X2)),
    inference(backward_demodulation,[status(thm)],[f15901,f200]) ).

fof(f35137,plain,
    ! [X0] : apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0)))) = apply(X0,apply(apply(w,apply(apply(b,w),apply(b,apply(b,X0)))),apply(apply(b,w),apply(b,apply(b,X0))))),
    inference(paramodulation,[status(thm)],[f28,f15901]) ).

fof(f35138,plain,
    ! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(apply(w,apply(apply(b,w),apply(b,apply(b,X0)))),apply(apply(b,w),apply(b,apply(b,X0))))),
    inference(forward_demodulation,[status(thm)],[f52,f35137]) ).

fof(f35139,plain,
    ! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,X0))))),
    inference(forward_demodulation,[status(thm)],[f16665,f35138]) ).

fof(f35140,plain,
    ! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
    inference(forward_demodulation,[status(thm)],[f52,f35139]) ).

fof(f35631,plain,
    apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt),
    inference(backward_demodulation,[status(thm)],[f35140,f8]) ).

fof(f35632,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f35631]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : COL003-20 : TPTP v8.1.2. Released v2.1.0.
% 0.12/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n027.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 22:54:02 EDT 2024
% 0.13/0.36  % CPUTime  : 
% 0.13/0.37  % Drodi V3.6.0
% 218.36/27.83  % Refutation found
% 218.36/27.83  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 218.36/27.83  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 221.21/29.03  % Elapsed time: 28.428369 seconds
% 221.21/29.03  % CPU time: 203.933787 seconds
% 221.21/29.03  % Total memory used: 1.980 GB
% 221.21/29.03  % Net memory used: 1.961 GB
%------------------------------------------------------------------------------