%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : COL078-1 : TPTP v8.1.2. Released v1.2.0.
% 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 20:13:46 EDT 2024

% Result   : Unsatisfiable 7.47s 1.35s
% Output   : CNFRefutation 7.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   21 (  16 unt;   0 def)
%            Number of atoms       :   26 (  25 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   12 (   7   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   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;   2 con; 0-2 aty)
%            Number of variables   :   37 (  37   !;   0   ?)

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

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

fof(f9,axiom,
    ! [X,Y] :
      ( X = Y
      | apply(X,n(X,Y)) != apply(Y,n(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X] : apply(identity,X) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,plain,
    ! [X0,X1] : apply(k(X0),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f18,plain,
    ! [X0,X1,X2] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( X0 = X1
      | apply(X0,n(X0,X1)) != apply(X1,n(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f23,plain,
    ! [X0] : apply(identity,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f24,plain,
    apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f26,plain,
    ! [X0,X1,X2] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
    inference(paramodulation,[status(thm)],[f13,f18]) ).

fof(f39,plain,
    ! [X0,X1,X2] : apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2) = apply(X1,apply(apply(X0,X1),X2)),
    inference(paramodulation,[status(thm)],[f18,f26]) ).

fof(f296,plain,
    ! [X0,X1,X2] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2) = apply(k(X2),apply(apply(X0,k(X2)),apply(X1,X2))),
    inference(paramodulation,[status(thm)],[f18,f39]) ).

fof(f297,plain,
    ! [X0,X1,X2] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2) = X2,
    inference(forward_demodulation,[status(thm)],[f13,f296]) ).

fof(f881,plain,
    ! [X0,X1] :
      ( k(X0) = X1
      | X0 != apply(X1,n(k(X0),X1)) ),
    inference(paramodulation,[status(thm)],[f13,f21]) ).

fof(f882,plain,
    ! [X0] :
      ( identity = X0
      | n(identity,X0) != apply(X0,n(identity,X0)) ),
    inference(paramodulation,[status(thm)],[f23,f21]) ).

fof(f993,plain,
    ! [X0,X1,X2] :
      ( k(X0) = apply(apply(apply(abstraction,abstraction),X1),X2)
      | X0 != apply(X2,apply(apply(X1,X2),n(k(X0),apply(apply(apply(abstraction,abstraction),X1),X2)))) ),
    inference(paramodulation,[status(thm)],[f39,f881]) ).

fof(f2977,plain,
    ! [X0,X1] : identity = apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),
    inference(resolution,[status(thm)],[f882,f297]) ).

fof(f3824,plain,
    ! [X0] : k(identity) = apply(abstraction,apply(apply(abstraction,abstraction),X0)),
    inference(resolution,[status(thm)],[f2977,f881]) ).

fof(f4001,plain,
    k(k(identity)) = apply(apply(apply(abstraction,abstraction),abstraction),abstraction),
    inference(resolution,[status(thm)],[f3824,f993]) ).

fof(f4002,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f4001,f24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : COL078-1 : TPTP v8.1.2. Released v1.2.0.
% 0.08/0.14  % 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 22:52:32 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 7.47/1.35  % Refutation found
% 7.47/1.35  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.47/1.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.79/1.43  % Elapsed time: 1.063028 seconds
% 7.79/1.43  % CPU time: 7.842575 seconds
% 7.79/1.43  % Total memory used: 208.512 MB
% 7.79/1.43  % Net memory used: 205.837 MB
%------------------------------------------------------------------------------