TSTP Solution File: LDA002-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : LDA002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n022.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 20:28:27 EDT 2024

% Result   : Unsatisfiable 2.10s 0.66s
% Output   : CNFRefutation 2.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  105 ( 105 unt;   0 def)
%            Number of atoms       :  105 ( 104 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;  11 con; 0-2 aty)
%            Number of variables   :   22 (  22   !;   0   ?)

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

fof(f2,axiom,
    n2 = f(n1,n1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    n3 = f(n2,n1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    u = f(n2,n2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    u1 = f(u,n1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    u2 = f(u,n2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    u3 = f(u,n3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    uu = f(u,u),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    a = f(f(n3,n2),u2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    b = f(u1,u3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    v = f(uu,uu),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    f(a,v) != f(b,v),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,plain,
    ! [X0,X1,X2] : f(X0,f(X1,X2)) = f(f(X0,X1),f(X0,X2)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f14,plain,
    n2 = f(n1,n1),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f15,plain,
    n3 = f(n2,n1),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f16,plain,
    u = f(n2,n2),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f17,plain,
    u1 = f(u,n1),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f18,plain,
    u2 = f(u,n2),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f19,plain,
    u3 = f(u,n3),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f20,plain,
    uu = f(u,u),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f21,plain,
    a = f(f(n3,n2),u2),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f22,plain,
    b = f(u1,u3),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f23,plain,
    v = f(uu,uu),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f24,plain,
    f(a,v) != f(b,v),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f25,plain,
    ! [X0] : f(f(n3,n2),f(u2,X0)) = f(a,f(f(n3,n2),X0)),
    inference(paramodulation,[status(thm)],[f21,f13]) ).

fof(f28,plain,
    ! [X0] : f(u1,f(u3,X0)) = f(b,f(u1,X0)),
    inference(paramodulation,[status(thm)],[f22,f13]) ).

fof(f339,plain,
    ! [X0] : f(n1,f(X0,n1)) = f(f(n1,X0),n2),
    inference(paramodulation,[status(thm)],[f14,f13]) ).

fof(f340,plain,
    ! [X0] : f(n1,f(n1,X0)) = f(n2,f(n1,X0)),
    inference(paramodulation,[status(thm)],[f14,f13]) ).

fof(f349,plain,
    ! [X0] : f(n2,f(X0,n1)) = f(f(n2,X0),n3),
    inference(paramodulation,[status(thm)],[f15,f13]) ).

fof(f350,plain,
    ! [X0] : f(n2,f(n1,X0)) = f(n3,f(n2,X0)),
    inference(paramodulation,[status(thm)],[f15,f13]) ).

fof(f363,plain,
    ! [X0] : f(n2,f(n2,X0)) = f(u,f(n2,X0)),
    inference(paramodulation,[status(thm)],[f16,f13]) ).

fof(f370,plain,
    ! [X0] : f(u,f(X0,n1)) = f(f(u,X0),u1),
    inference(paramodulation,[status(thm)],[f17,f13]) ).

fof(f382,plain,
    ! [X0] : f(u,f(n2,X0)) = f(u2,f(u,X0)),
    inference(paramodulation,[status(thm)],[f18,f13]) ).

fof(f383,plain,
    ! [X0] : f(n2,f(n2,X0)) = f(u2,f(u,X0)),
    inference(forward_demodulation,[status(thm)],[f363,f382]) ).

fof(f398,plain,
    ! [X0] : f(u,f(X0,u)) = f(f(u,X0),uu),
    inference(paramodulation,[status(thm)],[f20,f13]) ).

fof(f400,plain,
    f(n2,f(n2,n1)) = f(u,n3),
    inference(paramodulation,[status(thm)],[f16,f349]) ).

fof(f401,plain,
    f(n2,n3) = f(u,n3),
    inference(forward_demodulation,[status(thm)],[f15,f400]) ).

fof(f402,plain,
    f(n2,n3) = u3,
    inference(forward_demodulation,[status(thm)],[f19,f401]) ).

fof(f468,plain,
    f(n2,f(n1,n2)) = f(n3,u),
    inference(paramodulation,[status(thm)],[f16,f350]) ).

fof(f502,plain,
    f(n2,f(n1,f(n1,n2))) = f(n3,f(n3,u)),
    inference(paramodulation,[status(thm)],[f468,f350]) ).

fof(f503,plain,
    f(n2,f(n2,f(n1,n2))) = f(n3,f(n3,u)),
    inference(forward_demodulation,[status(thm)],[f340,f502]) ).

fof(f504,plain,
    f(n2,f(n3,u)) = f(n3,f(n3,u)),
    inference(forward_demodulation,[status(thm)],[f468,f503]) ).

fof(f532,plain,
    f(n2,f(n2,n2)) = f(u,u),
    inference(paramodulation,[status(thm)],[f16,f363]) ).

fof(f533,plain,
    f(n2,u) = f(u,u),
    inference(forward_demodulation,[status(thm)],[f16,f532]) ).

fof(f534,plain,
    f(n2,u) = uu,
    inference(forward_demodulation,[status(thm)],[f20,f533]) ).

fof(f575,plain,
    f(n1,n2) = f(n2,f(n1,n1)),
    inference(paramodulation,[status(thm)],[f14,f340]) ).

fof(f576,plain,
    f(n1,n2) = f(n2,n2),
    inference(forward_demodulation,[status(thm)],[f14,f575]) ).

fof(f577,plain,
    f(n1,n2) = u,
    inference(forward_demodulation,[status(thm)],[f16,f576]) ).

fof(f593,plain,
    f(n2,u) = f(n3,u),
    inference(backward_demodulation,[status(thm)],[f577,f468]) ).

fof(f594,plain,
    uu = f(n3,u),
    inference(forward_demodulation,[status(thm)],[f534,f593]) ).

fof(f612,plain,
    f(n2,f(n3,u)) = f(n3,uu),
    inference(backward_demodulation,[status(thm)],[f594,f504]) ).

fof(f613,plain,
    f(n2,uu) = f(n3,uu),
    inference(forward_demodulation,[status(thm)],[f594,f612]) ).

fof(f647,plain,
    f(n2,f(n2,u)) = f(u,uu),
    inference(paramodulation,[status(thm)],[f534,f363]) ).

fof(f648,plain,
    f(n2,uu) = f(u,uu),
    inference(forward_demodulation,[status(thm)],[f534,f647]) ).

fof(f659,plain,
    ! [X0] : f(n2,f(X0,u)) = f(f(n2,X0),uu),
    inference(paramodulation,[status(thm)],[f534,f13]) ).

fof(f661,plain,
    f(n1,u) = f(n2,f(n1,n2)),
    inference(paramodulation,[status(thm)],[f577,f340]) ).

fof(f662,plain,
    f(n1,u) = f(n2,u),
    inference(forward_demodulation,[status(thm)],[f577,f661]) ).

fof(f663,plain,
    f(n1,u) = uu,
    inference(forward_demodulation,[status(thm)],[f534,f662]) ).

fof(f664,plain,
    f(n1,f(n2,n1)) = f(u,n2),
    inference(paramodulation,[status(thm)],[f577,f339]) ).

fof(f665,plain,
    f(n1,n3) = f(u,n2),
    inference(forward_demodulation,[status(thm)],[f15,f664]) ).

fof(f666,plain,
    f(n1,n3) = u2,
    inference(forward_demodulation,[status(thm)],[f18,f665]) ).

fof(f674,plain,
    ! [X0] : f(n1,f(n2,X0)) = f(u,f(n1,X0)),
    inference(paramodulation,[status(thm)],[f577,f13]) ).

fof(f707,plain,
    ! [X0] : f(n3,f(X0,u)) = f(f(n3,X0),uu),
    inference(paramodulation,[status(thm)],[f594,f13]) ).

fof(f709,plain,
    f(n1,uu) = f(n2,f(n1,u)),
    inference(paramodulation,[status(thm)],[f663,f340]) ).

fof(f710,plain,
    f(n1,uu) = f(n2,uu),
    inference(forward_demodulation,[status(thm)],[f663,f709]) ).

fof(f742,plain,
    f(u,f(n1,n1)) = f(u1,u1),
    inference(paramodulation,[status(thm)],[f17,f370]) ).

fof(f743,plain,
    f(n1,f(n2,n1)) = f(u1,u1),
    inference(forward_demodulation,[status(thm)],[f674,f742]) ).

fof(f744,plain,
    f(n1,n3) = f(u1,u1),
    inference(forward_demodulation,[status(thm)],[f15,f743]) ).

fof(f745,plain,
    u2 = f(u1,u1),
    inference(forward_demodulation,[status(thm)],[f666,f744]) ).

fof(f784,plain,
    ! [X0] : f(u1,f(u1,X0)) = f(u2,f(u1,X0)),
    inference(paramodulation,[status(thm)],[f745,f13]) ).

fof(f826,plain,
    ! [X0] : f(n3,f(X0,uu)) = f(f(n3,X0),f(n2,uu)),
    inference(paramodulation,[status(thm)],[f613,f13]) ).

fof(f932,plain,
    f(n2,f(n2,uu)) = f(u2,f(n2,uu)),
    inference(paramodulation,[status(thm)],[f648,f383]) ).

fof(f935,plain,
    f(n2,f(n2,u)) = f(u2,uu),
    inference(paramodulation,[status(thm)],[f20,f383]) ).

fof(f936,plain,
    f(n2,uu) = f(u2,uu),
    inference(forward_demodulation,[status(thm)],[f534,f935]) ).

fof(f1028,plain,
    f(f(n3,n2),f(n2,uu)) = f(a,f(f(n3,n2),uu)),
    inference(paramodulation,[status(thm)],[f936,f25]) ).

fof(f1029,plain,
    f(n3,f(n2,uu)) = f(a,f(f(n3,n2),uu)),
    inference(forward_demodulation,[status(thm)],[f826,f1028]) ).

fof(f1030,plain,
    f(n2,f(n1,uu)) = f(a,f(f(n3,n2),uu)),
    inference(forward_demodulation,[status(thm)],[f350,f1029]) ).

fof(f1031,plain,
    f(n2,f(n2,uu)) = f(a,f(f(n3,n2),uu)),
    inference(forward_demodulation,[status(thm)],[f710,f1030]) ).

fof(f1032,plain,
    f(n2,f(n2,uu)) = f(a,f(n3,f(n2,u))),
    inference(forward_demodulation,[status(thm)],[f707,f1031]) ).

fof(f1033,plain,
    f(n2,f(n2,uu)) = f(a,f(n2,f(n1,u))),
    inference(forward_demodulation,[status(thm)],[f350,f1032]) ).

fof(f1034,plain,
    f(n2,f(n2,uu)) = f(a,f(n2,uu)),
    inference(forward_demodulation,[status(thm)],[f663,f1033]) ).

fof(f1284,plain,
    f(u,f(u,u)) = f(uu,uu),
    inference(paramodulation,[status(thm)],[f20,f398]) ).

fof(f1285,plain,
    f(u,uu) = f(uu,uu),
    inference(forward_demodulation,[status(thm)],[f20,f1284]) ).

fof(f1286,plain,
    f(n2,uu) = f(uu,uu),
    inference(forward_demodulation,[status(thm)],[f648,f1285]) ).

fof(f1287,plain,
    f(n2,uu) = v,
    inference(forward_demodulation,[status(thm)],[f23,f1286]) ).

fof(f1299,plain,
    f(u,f(n1,u)) = f(u1,uu),
    inference(paramodulation,[status(thm)],[f17,f398]) ).

fof(f1300,plain,
    f(n1,f(n2,u)) = f(u1,uu),
    inference(forward_demodulation,[status(thm)],[f674,f1299]) ).

fof(f1301,plain,
    f(n1,uu) = f(u1,uu),
    inference(forward_demodulation,[status(thm)],[f534,f1300]) ).

fof(f1302,plain,
    f(n2,uu) = f(u1,uu),
    inference(forward_demodulation,[status(thm)],[f710,f1301]) ).

fof(f1303,plain,
    v = f(u1,uu),
    inference(forward_demodulation,[status(thm)],[f1287,f1302]) ).

fof(f1342,plain,
    f(n2,f(n2,uu)) = f(a,v),
    inference(backward_demodulation,[status(thm)],[f1287,f1034]) ).

fof(f1343,plain,
    f(n2,v) = f(a,v),
    inference(forward_demodulation,[status(thm)],[f1287,f1342]) ).

fof(f1350,plain,
    f(n2,f(n2,uu)) = f(u2,v),
    inference(backward_demodulation,[status(thm)],[f1287,f932]) ).

fof(f1351,plain,
    f(n2,v) = f(u2,v),
    inference(forward_demodulation,[status(thm)],[f1287,f1350]) ).

fof(f1389,plain,
    f(n2,v) != f(b,v),
    inference(backward_demodulation,[status(thm)],[f1343,f24]) ).

fof(f1427,plain,
    f(u1,f(u3,uu)) = f(b,v),
    inference(paramodulation,[status(thm)],[f1303,f28]) ).

fof(f1595,plain,
    f(n2,f(n3,u)) = f(u3,uu),
    inference(paramodulation,[status(thm)],[f402,f659]) ).

fof(f1596,plain,
    f(n2,uu) = f(u3,uu),
    inference(forward_demodulation,[status(thm)],[f594,f1595]) ).

fof(f1597,plain,
    v = f(u3,uu),
    inference(forward_demodulation,[status(thm)],[f1287,f1596]) ).

fof(f1626,plain,
    f(u1,v) = f(b,v),
    inference(backward_demodulation,[status(thm)],[f1597,f1427]) ).

fof(f1627,plain,
    f(n2,v) != f(u1,v),
    inference(backward_demodulation,[status(thm)],[f1626,f1389]) ).

fof(f2038,plain,
    f(u1,f(u1,uu)) = f(u2,v),
    inference(paramodulation,[status(thm)],[f1303,f784]) ).

fof(f2039,plain,
    f(u1,v) = f(u2,v),
    inference(forward_demodulation,[status(thm)],[f1303,f2038]) ).

fof(f2040,plain,
    f(u1,v) = f(n2,v),
    inference(forward_demodulation,[status(thm)],[f1351,f2039]) ).

fof(f2041,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f2040,f1627]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LDA002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Apr 29 22:12:28 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 2.10/0.66  % Refutation found
% 2.10/0.66  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.10/0.66  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.56/0.70  % Elapsed time: 0.344216 seconds
% 2.56/0.70  % CPU time: 2.595148 seconds
% 2.56/0.70  % Total memory used: 74.347 MB
% 2.56/0.70  % Net memory used: 73.678 MB
%------------------------------------------------------------------------------