TSTP Solution File: COL076-2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : COL076-2 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 20:13:46 EDT 2024

% Result   : Unsatisfiable 211.95s 27.08s
% Output   : CNFRefutation 211.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   26 (  21 unt;   0 def)
%            Number of atoms       :   31 (  30 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   15 (  10   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   54 (  54   !;   0   ?)

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

fof(f3,axiom,
    ! [X,Y] : apply(projection2,pair(X,Y)) = Y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X,Y,Z] : apply(pair(X,Y),Z) = pair(apply(X,Z),apply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y] :
      ( X = Y
      | apply(X,n(X,Y)) != apply(Y,n(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X,Y] : apply(apply(f,X),Y) = apply(X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    ! [Y] : Y != apply(eq,pair(apply(k,Y),apply(k,projection2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,plain,
    ! [X0,X1] : apply(apply(k,X0),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f12,plain,
    ! [X0,X1] : apply(projection2,pair(X0,X1)) = X1,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f14,plain,
    ! [X0,X1,X2] : apply(pair(X0,X1),X2) = pair(apply(X0,X2),apply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f15,plain,
    ! [X0,X1,X2] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( X0 = X1
      | apply(X0,n(X0,X1)) != apply(X1,n(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f17,plain,
    ! [X0,X1] : apply(apply(f,X0),X1) = apply(X0,X0),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f18,plain,
    ! [X0] : X0 != apply(eq,pair(apply(k,X0),apply(k,projection2))),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f20,plain,
    ! [X0,X1,X2] : apply(pair(apply(k,X0),X1),X2) = pair(X0,apply(X1,X2)),
    inference(paramodulation,[status(thm)],[f10,f14]) ).

fof(f21,plain,
    ! [X0,X1,X2] : apply(pair(X0,projection2),pair(X1,X2)) = pair(apply(X0,pair(X1,X2)),X2),
    inference(paramodulation,[status(thm)],[f12,f14]) ).

fof(f330,plain,
    ! [X0,X1] :
      ( apply(k,X0) = X1
      | X0 != apply(X1,n(apply(k,X0),X1)) ),
    inference(paramodulation,[status(thm)],[f10,f16]) ).

fof(f530,plain,
    ! [X0,X1,X2] : apply(apply(apply(abstraction,apply(k,X0)),X1),X2) = apply(X0,apply(X1,X2)),
    inference(paramodulation,[status(thm)],[f10,f15]) ).

fof(f1647,plain,
    ! [X0] : apply(k,apply(X0,X0)) = apply(f,X0),
    inference(resolution,[status(thm)],[f330,f17]) ).

fof(f1650,plain,
    ! [X0,X1,X2] :
      ( apply(k,X0) = pair(apply(k,X1),X2)
      | X0 != pair(X1,apply(X2,n(apply(k,X0),pair(apply(k,X1),X2)))) ),
    inference(paramodulation,[status(thm)],[f20,f330]) ).

fof(f250772,plain,
    ! [X0,X1,X2] :
      ( apply(k,X0) = pair(apply(k,X1),apply(k,X2))
      | X0 != pair(X1,X2) ),
    inference(paramodulation,[status(thm)],[f10,f1650]) ).

fof(f250773,plain,
    ! [X0,X1] : apply(k,pair(X0,X1)) = pair(apply(k,X0),apply(k,X1)),
    inference(destructive_equality_resolution,[status(esa)],[f250772]) ).

fof(f251555,plain,
    ! [X0] : X0 != apply(eq,apply(k,pair(X0,projection2))),
    inference(backward_demodulation,[status(thm)],[f250773,f18]) ).

fof(f252466,plain,
    ! [X0,X1] : apply(X0,pair(X1,projection2)) != apply(eq,apply(k,apply(pair(X0,projection2),pair(X1,projection2)))),
    inference(paramodulation,[status(thm)],[f21,f251555]) ).

fof(f262343,plain,
    ! [X0] : apply(X0,pair(X0,projection2)) != apply(eq,apply(f,pair(X0,projection2))),
    inference(paramodulation,[status(thm)],[f1647,f252466]) ).

fof(f262463,plain,
    $false,
    inference(resolution,[status(thm)],[f262343,f530]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem  : COL076-2 : TPTP v8.1.2. Released v1.2.0.
% 0.10/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34  % Computer : n005.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit : 300
% 0.11/0.34  % WCLimit  : 300
% 0.11/0.34  % DateTime : Mon Apr 29 22:22:56 EDT 2024
% 0.11/0.34  % CPUTime  : 
% 0.18/0.35  % Drodi V3.6.0
% 211.95/27.08  % Refutation found
% 211.95/27.08  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 211.95/27.08  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 214.80/28.00  % Elapsed time: 27.414967 seconds
% 214.80/28.00  % CPU time: 194.661856 seconds
% 214.80/28.00  % Total memory used: 2.415 GB
% 214.80/28.00  % Net memory used: 2.397 GB
%------------------------------------------------------------------------------