TSTP Solution File: COL044-6 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : COL044-6 : TPTP v8.1.2. Released v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 20:13:38 EDT 2024

% Result   : Unsatisfiable 5.34s 1.12s
% Output   : CNFRefutation 5.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   24 (  24 unt;   0 def)
%            Number of atoms       :   24 (  23 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :   12 (   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   :   44 (  44   !;   0   ?)

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

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

fof(f3,axiom,
    strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),
    file('/export/starexec/sandbox/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/sandbox/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,X2] : apply(apply(apply(n,X0),X1),X2) = apply(apply(apply(X0,X2),X1),X2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f7,plain,
    strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),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(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b),apply(b,X0)) = apply(strong_fixed_point,X0),
    inference(paramodulation,[status(thm)],[f7,f5]) ).

fof(f10,plain,
    ! [X0] : apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,X0))) = apply(strong_fixed_point,X0),
    inference(forward_demodulation,[status(thm)],[f5,f9]) ).

fof(f13,plain,
    ! [X0,X1,X2] : apply(apply(apply(n,apply(n,X0)),X1),X2) = apply(apply(apply(apply(X0,X1),X2),X1),X2),
    inference(paramodulation,[status(thm)],[f6,f6]) ).

fof(f14,plain,
    ! [X0,X1,X2] : apply(apply(apply(n,apply(b,X0)),X1),X2) = apply(apply(X0,apply(X2,X1)),X2),
    inference(paramodulation,[status(thm)],[f5,f6]) ).

fof(f19,plain,
    ! [X0,X1,X2,X3] : apply(apply(apply(n,apply(apply(b,X0),X1)),X2),X3) = apply(apply(apply(X0,apply(X1,X3)),X2),X3),
    inference(paramodulation,[status(thm)],[f5,f6]) ).

fof(f120,plain,
    ! [X0,X1,X2] : apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X2,X1),X2)),
    inference(paramodulation,[status(thm)],[f5,f14]) ).

fof(f172,plain,
    ! [X0,X1,X2] : apply(apply(X0,X1),apply(X0,X2)) = apply(apply(apply(apply(n,apply(b,b)),X1),X0),X2),
    inference(paramodulation,[status(thm)],[f14,f5]) ).

fof(f259,plain,
    ! [X0,X1,X2] : apply(apply(apply(n,apply(n,X0)),X1),X2) = apply(apply(apply(n,apply(X0,X1)),X1),X2),
    inference(forward_demodulation,[status(thm)],[f6,f13]) ).

fof(f636,plain,
    ! [X0,X1] : apply(apply(X0,X1),apply(X0,X1)) = apply(apply(apply(n,apply(n,apply(b,b))),X0),X1),
    inference(paramodulation,[status(thm)],[f6,f172]) ).

fof(f845,plain,
    ! [X0,X1,X2] : apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
    inference(paramodulation,[status(thm)],[f5,f19]) ).

fof(f1694,plain,
    ! [X0] : apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))) = apply(strong_fixed_point,X0),
    inference(paramodulation,[status(thm)],[f10,f845]) ).

fof(f3970,plain,
    ! [X0] : apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))) = apply(strong_fixed_point,X0),
    inference(forward_demodulation,[status(thm)],[f259,f1694]) ).

fof(f3972,plain,
    ! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),apply(n,apply(b,apply(b,X0)))),
    inference(paramodulation,[status(thm)],[f636,f3970]) ).

fof(f4086,plain,
    ! [X0,X1] : apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X1)))),apply(n,apply(b,apply(b,X1)))) = apply(X0,apply(strong_fixed_point,X1)),
    inference(paramodulation,[status(thm)],[f3972,f120]) ).

fof(f4155,plain,
    ! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
    inference(backward_demodulation,[status(thm)],[f4086,f3972]) ).

fof(f4200,plain,
    $false,
    inference(resolution,[status(thm)],[f4155,f8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : COL044-6 : TPTP v8.1.2. Released v2.1.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n025.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 22:41:26 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 5.34/1.12  % Refutation found
% 5.34/1.12  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.34/1.12  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.18/1.17  % Elapsed time: 0.803821 seconds
% 6.18/1.17  % CPU time: 6.202750 seconds
% 6.18/1.17  % Total memory used: 155.908 MB
% 6.18/1.17  % Net memory used: 155.159 MB
%------------------------------------------------------------------------------