TSTP Solution File: RNG001-1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : RNG001-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.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 : Wed May 31 12:32:32 EDT 2023

% Result   : Unsatisfiable 0.19s 0.47s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   50 (  24 unt;   0 def)
%            Number of atoms       :  103 (  14 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  108 (  55   ~;  53   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  148 (; 148   !;   0   ?)

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

fof(f2,axiom,
    ! [X] : sum(X,additive_identity,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y] : sum(X,Y,add(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X] : sum(additive_inverse(X),X,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y,U,Z,V,W] :
      ( ~ sum(X,Y,U)
      | ~ sum(Y,Z,V)
      | ~ sum(U,Z,W)
      | sum(X,V,W) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y,Z] :
      ( ~ sum(X,Y,Z)
      | sum(Y,X,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X,Y,V1,Z,V2,V3,V4] :
      ( ~ product(X,Y,V1)
      | ~ product(X,Z,V2)
      | ~ sum(Y,Z,V3)
      | ~ sum(V1,V2,V4)
      | product(X,V3,V4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X,Y,U,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X,Y,U,V] :
      ( ~ product(X,Y,U)
      | ~ product(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    ~ product(a,additive_identity,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,plain,
    ! [X0] : sum(additive_identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f20,plain,
    ! [X0] : sum(X0,additive_identity,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f21,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f22,plain,
    ! [X0,X1] : sum(X0,X1,add(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f23,plain,
    ! [X0] : sum(additive_inverse(X0),X0,additive_identity),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f25,plain,
    ! [X,V,W] :
      ( ! [U,Z] :
          ( ! [Y] :
              ( ~ sum(X,Y,U)
              | ~ sum(Y,Z,V) )
          | ~ sum(U,Z,W) )
      | sum(X,V,W) ),
    inference(miniscoping,[status(esa)],[f7]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X1,X3,X4)
      | ~ sum(X2,X3,X5)
      | sum(X0,X4,X5) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | sum(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f36,plain,
    ! [X,V3,V4] :
      ( ! [V1,V2] :
          ( ! [Y,Z] :
              ( ~ product(X,Y,V1)
              | ~ product(X,Z,V2)
              | ~ sum(Y,Z,V3) )
          | ~ sum(V1,V2,V4) )
      | product(X,V3,V4) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X3,X4)
      | ~ sum(X1,X3,X5)
      | ~ sum(X2,X4,X6)
      | product(X0,X5,X6) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f42,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ sum(X,Y,U)
          | ~ sum(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f43,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f44,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ product(X,Y,U)
          | ~ product(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f45,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f46,plain,
    ~ product(a,additive_identity,additive_identity),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f49,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ sum(X3,X1,X4)
      | ~ sum(multiply(X0,X3),X2,X5)
      | product(X0,X4,X5) ),
    inference(resolution,[status(thm)],[f21,f37]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | multiply(X0,X1) = X2 ),
    inference(resolution,[status(thm)],[f21,f45]) ).

fof(f84,plain,
    ! [X0,X1] : sum(X0,X1,add(X1,X0)),
    inference(resolution,[status(thm)],[f29,f22]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ~ sum(additive_inverse(X0),X0,X1)
      | additive_identity = X1 ),
    inference(resolution,[status(thm)],[f43,f23]) ).

fof(f106,plain,
    ! [X0] : additive_identity = add(additive_inverse(X0),X0),
    inference(resolution,[status(thm)],[f86,f22]) ).

fof(f122,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(additive_identity,X1,X3)
      | sum(additive_inverse(X0),X2,X3) ),
    inference(resolution,[status(thm)],[f26,f23]) ).

fof(f123,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | sum(additive_identity,X2,X3) ),
    inference(resolution,[status(thm)],[f26,f19]) ).

fof(f125,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(additive_identity,X0,X1)
      | ~ sum(X2,X0,X3)
      | sum(X2,X1,X3) ),
    inference(resolution,[status(thm)],[f26,f20]) ).

fof(f136,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(multiply(X3,X0),multiply(X3,X1),X4)
      | product(X3,X2,X4) ),
    inference(resolution,[status(thm)],[f49,f21]) ).

fof(f143,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | sum(additive_identity,add(X1,X0),X2) ),
    inference(resolution,[status(thm)],[f123,f84]) ).

fof(f168,plain,
    ! [X0,X1] : sum(additive_identity,add(X0,X1),add(X1,X0)),
    inference(resolution,[status(thm)],[f143,f22]) ).

fof(f288,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,add(X1,X2),X3)
      | sum(X0,add(X2,X1),X3) ),
    inference(resolution,[status(thm)],[f125,f168]) ).

fof(f343,plain,
    ! [X0,X1,X2] : sum(X0,add(X1,X2),add(X0,add(X2,X1))),
    inference(resolution,[status(thm)],[f288,f22]) ).

fof(f455,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,add(X1,X2),X3)
      | add(X0,add(X2,X1)) = X3 ),
    inference(resolution,[status(thm)],[f343,f43]) ).

fof(f753,plain,
    ! [X0,X1,X2] :
      ( ~ sum(multiply(X0,additive_identity),multiply(X0,X1),X2)
      | product(X0,X1,X2) ),
    inference(resolution,[status(thm)],[f136,f19]) ).

fof(f1306,plain,
    ! [X0,X1,X2] :
      ( ~ sum(additive_identity,X0,X1)
      | sum(additive_inverse(X2),add(X0,X2),X1) ),
    inference(resolution,[status(thm)],[f122,f84]) ).

fof(f1754,plain,
    ! [X0,X1] : product(X0,X1,add(multiply(X0,X1),multiply(X0,additive_identity))),
    inference(resolution,[status(thm)],[f753,f84]) ).

fof(f1776,plain,
    ! [X0,X1] : multiply(X0,X1) = add(multiply(X0,X1),multiply(X0,additive_identity)),
    inference(resolution,[status(thm)],[f1754,f53]) ).

fof(f2305,plain,
    ! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
    inference(resolution,[status(thm)],[f1306,f19]) ).

fof(f2321,plain,
    ! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
    inference(resolution,[status(thm)],[f2305,f455]) ).

fof(f2431,plain,
    ! [X0,X1] : add(additive_inverse(multiply(X0,X1)),multiply(X0,X1)) = multiply(X0,additive_identity),
    inference(paramodulation,[status(thm)],[f1776,f2321]) ).

fof(f2432,plain,
    ! [X0] : additive_identity = multiply(X0,additive_identity),
    inference(forward_demodulation,[status(thm)],[f106,f2431]) ).

fof(f2662,plain,
    ! [X0] : product(X0,additive_identity,additive_identity),
    inference(paramodulation,[status(thm)],[f2432,f21]) ).

fof(f2710,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f46,f2662]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : RNG001-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 10:33:01 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 0.19/0.47  % Refutation found
% 0.19/0.47  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.47  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.49  % Elapsed time: 0.152400 seconds
% 0.19/0.49  % CPU time: 0.762937 seconds
% 0.19/0.49  % Memory used: 21.416 MB
%------------------------------------------------------------------------------