%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP657+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n032.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 20:21:18 EDT 2024

% Result   : Theorem 7.17s 1.28s
% Output   : CNFRefutation 7.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   23 (  17 unt;   0 def)
%            Number of atoms       :   29 (  28 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   17 (  11   ~;   4   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   0 con; 1-2 aty)
%            Number of variables   :   45 (  40   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [B,A] : ld(A,mult(A,B)) = B,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [B,A] : mult(rd(A,B),B) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [B,A] : rd(mult(A,B),B) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [C,B,A] : mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,conjecture,
    ? [X0] :
    ! [X1] :
      ( mult(X1,X0) = X1
      & mult(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,negated_conjecture,
    ~ ? [X0] :
      ! [X1] :
        ( mult(X1,X0) = X1
        & mult(X0,X1) = X1 ),
    inference(negated_conjecture,[status(cth)],[f6]) ).

fof(f9,plain,
    ! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f10,plain,
    ! [X0,X1] : mult(rd(X0,X1),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f11,plain,
    ! [X0,X1] : rd(mult(X0,X1),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f12,plain,
    ! [X0,X1,X2] : mult(mult(X0,X1),mult(X2,X0)) = mult(X0,mult(mult(X1,X2),X0)),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f13,plain,
    ! [X0] :
    ? [X1] :
      ( mult(X1,X0) != X1
      | mult(X0,X1) != X1 ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f14,plain,
    ! [X0] :
      ( ? [X1] : mult(X1,X0) != X1
      | ? [X1] : mult(X0,X1) != X1 ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f15,plain,
    ! [X0] :
      ( mult(sk0_0(X0),X0) != sk0_0(X0)
      | mult(X0,sk0_1(X0)) != sk0_1(X0) ),
    inference(skolemization,[status(esa)],[f14]) ).

fof(f16,plain,
    ! [X0] :
      ( mult(sk0_0(X0),X0) != sk0_0(X0)
      | mult(X0,sk0_1(X0)) != sk0_1(X0) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f1361,plain,
    ! [X0,X1,X2] : rd(mult(X0,mult(mult(X1,X2),X0)),mult(X2,X0)) = mult(X0,X1),
    inference(paramodulation,[status(thm)],[f12,f11]) ).

fof(f1438,plain,
    ! [X0,X1,X2] : rd(mult(X0,mult(X1,X0)),mult(X2,X0)) = mult(X0,rd(X1,X2)),
    inference(paramodulation,[status(thm)],[f10,f1361]) ).

fof(f1512,plain,
    ! [X0,X1] : X0 = mult(X0,rd(X1,X1)),
    inference(paramodulation,[status(thm)],[f11,f1438]) ).

fof(f1793,plain,
    ! [X0,X1] : ld(X0,X0) = rd(X1,X1),
    inference(paramodulation,[status(thm)],[f1512,f9]) ).

fof(f2161,plain,
    ! [X0,X1] : X0 = mult(X0,ld(X1,X1)),
    inference(paramodulation,[status(thm)],[f1793,f1512]) ).

fof(f2162,plain,
    ! [X0,X1] : mult(ld(X0,X0),X1) = X1,
    inference(paramodulation,[status(thm)],[f1793,f10]) ).

fof(f2688,plain,
    ! [X0] : mult(sk0_0(ld(X0,X0)),ld(X0,X0)) != sk0_0(ld(X0,X0)),
    inference(resolution,[status(thm)],[f2162,f16]) ).

fof(f2689,plain,
    ! [X0] : sk0_0(ld(X0,X0)) != sk0_0(ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f2161,f2688]) ).

fof(f2690,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f2689]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : GRP657+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.32  % Computer : n032.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Tue Apr 30 00:29:35 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 0.12/0.33  % Drodi V3.6.0
% 7.17/1.28  % Refutation found
% 7.17/1.28  % SZS status Theorem for theBenchmark: Theorem is valid
% 7.17/1.28  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.17/1.32  % Elapsed time: 0.982849 seconds
% 7.17/1.32  % CPU time: 7.494262 seconds
% 7.17/1.32  % Total memory used: 261.564 MB
% 7.17/1.32  % Net memory used: 260.721 MB
%------------------------------------------------------------------------------