%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : COL077-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n026.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 56.22s 7.39s
% Output   : CNFRefutation 56.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   19 (  16 unt;   0 def)
%            Number of atoms       :   22 (  21 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   7   ~;   3   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    6 (   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   :   31 (  31   !;   0   ?)

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

fof(f9,axiom,
    ! [X,Y] :
      ( X = Y
      | apply(X,n(X,Y)) != apply(Y,n(X,Y)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X] : apply(identity,X) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
    file('/export/starexec/sandbox2/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(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f41,plain,
    ! [X0] :
      ( X0 = identity
      | apply(X0,n(X0,identity)) != n(X0,identity) ),
    inference(paramodulation,[status(thm)],[f23,f21]) ).

fof(f345,plain,
    ! [X0,X1,X2] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
    inference(paramodulation,[status(thm)],[f13,f18]) ).

fof(f14873,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,f345]) ).

fof(f15633,plain,
    apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction) != identity,
    inference(forward_demodulation,[status(thm)],[f14873,f24]) ).

fof(f31255,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,f14873]) ).

fof(f31256,plain,
    ! [X0,X1,X2] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),X2) = X2,
    inference(forward_demodulation,[status(thm)],[f13,f31255]) ).

fof(f31519,plain,
    ! [X0,X1] : apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1) = identity,
    inference(resolution,[status(thm)],[f31256,f41]) ).

fof(f31672,plain,
    identity != identity,
    inference(backward_demodulation,[status(thm)],[f31519,f15633]) ).

fof(f31673,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f31672]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : COL077-1 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.29  % Computer : n026.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 300
% 0.10/0.29  % DateTime : Mon Apr 29 22:47:19 EDT 2024
% 0.10/0.29  % CPUTime  : 
% 0.10/0.30  % Drodi V3.6.0
% 56.22/7.39  % Refutation found
% 56.22/7.39  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 56.22/7.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 56.60/7.45  % Elapsed time: 7.135417 seconds
% 56.60/7.45  % CPU time: 56.209216 seconds
% 56.60/7.45  % Total memory used: 983.494 MB
% 56.60/7.45  % Net memory used: 961.070 MB
%------------------------------------------------------------------------------