TSTP Solution File: FLD032-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : FLD032-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n024.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 20:16:25 EDT 2024

% Result   : Unsatisfiable 14.03s 2.13s
% Output   : CNFRefutation 14.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   52 (  13 unt;   0 def)
%            Number of atoms       :  129 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  140 (  63   ~;  74   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   51 (  51   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X] :
      ( equalish(multiply(multiplicative_identity,X),X)
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X] :
      ( equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
      | ~ defined(X)
      | equalish(X,additive_identity) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X,Y] :
      ( equalish(multiply(X,Y),multiply(Y,X))
      | ~ defined(X)
      | ~ defined(Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [X] :
      ( defined(multiplicative_inverse(X))
      | ~ defined(X)
      | equalish(X,additive_identity) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [X,Y] :
      ( equalish(X,Y)
      | ~ equalish(Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ! [X,Z,Y] :
      ( equalish(X,Z)
      | ~ equalish(X,Y)
      | ~ equalish(Y,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    ! [X,Z,Y] :
      ( equalish(multiply(X,Z),multiply(Y,Z))
      | ~ defined(Z)
      | ~ equalish(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,hypothesis,
    defined(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f29,negated_conjecture,
    ~ equalish(a,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,negated_conjecture,
    equalish(multiplicative_inverse(a),multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,negated_conjecture,
    ~ equalish(a,multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f40,plain,
    ! [X0] :
      ( equalish(multiply(multiplicative_identity,X0),X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f41,plain,
    ! [X0] :
      ( equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity)
      | ~ defined(X0)
      | equalish(X0,additive_identity) ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f42,plain,
    ! [Y] :
      ( ! [X] :
          ( equalish(multiply(X,Y),multiply(Y,X))
          | ~ defined(X) )
      | ~ defined(Y) ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( equalish(multiply(X0,X1),multiply(X1,X0))
      | ~ defined(X0)
      | ~ defined(X1) ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f53,plain,
    ! [X0] :
      ( defined(multiplicative_inverse(X0))
      | ~ defined(X0)
      | equalish(X0,additive_identity) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( equalish(X0,X1)
      | ~ equalish(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f65,plain,
    ! [Z,Y] :
      ( ! [X] :
          ( equalish(X,Z)
          | ~ equalish(X,Y) )
      | ~ equalish(Y,Z) ),
    inference(miniscoping,[status(esa)],[f23]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( equalish(X0,X1)
      | ~ equalish(X0,X2)
      | ~ equalish(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f69,plain,
    ! [X,Y] :
      ( ! [Z] :
          ( equalish(multiply(X,Z),multiply(Y,Z))
          | ~ defined(Z) )
      | ~ equalish(X,Y) ),
    inference(miniscoping,[status(esa)],[f25]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( equalish(multiply(X0,X1),multiply(X2,X1))
      | ~ defined(X1)
      | ~ equalish(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f74,plain,
    defined(a),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f75,plain,
    ~ equalish(a,additive_identity),
    inference(cnf_transformation,[status(esa)],[f29]) ).

fof(f76,plain,
    equalish(multiplicative_inverse(a),multiplicative_identity),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f77,plain,
    ~ equalish(a,multiplicative_identity),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f79,plain,
    equalish(multiplicative_identity,multiplicative_inverse(a)),
    inference(resolution,[status(thm)],[f64,f76]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ~ defined(X0)
      | equalish(X0,additive_identity)
      | equalish(X1,multiplicative_identity)
      | ~ equalish(X1,multiply(X0,multiplicative_inverse(X0))) ),
    inference(resolution,[status(thm)],[f41,f66]) ).

fof(f108,plain,
    ! [X0] :
      ( ~ defined(X0)
      | equalish(X0,multiply(multiplicative_identity,X0)) ),
    inference(resolution,[status(thm)],[f40,f64]) ).

fof(f230,plain,
    ( spl0_16
  <=> defined(a) ),
    introduced(split_symbol_definition) ).

fof(f232,plain,
    ( ~ defined(a)
    | spl0_16 ),
    inference(component_clause,[status(thm)],[f230]) ).

fof(f233,plain,
    ( spl0_17
  <=> equalish(a,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f234,plain,
    ( equalish(a,additive_identity)
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f233]) ).

fof(f238,plain,
    ( $false
    | spl0_16 ),
    inference(forward_subsumption_resolution,[status(thm)],[f232,f74]) ).

fof(f239,plain,
    spl0_16,
    inference(contradiction_clause,[status(thm)],[f238]) ).

fof(f292,plain,
    ( $false
    | ~ spl0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f234,f75]) ).

fof(f293,plain,
    ~ spl0_17,
    inference(contradiction_clause,[status(thm)],[f292]) ).

fof(f1174,plain,
    ! [X0] :
      ( ~ defined(multiplicative_inverse(X0))
      | ~ defined(X0)
      | ~ defined(X0)
      | equalish(X0,additive_identity)
      | equalish(multiply(multiplicative_inverse(X0),X0),multiplicative_identity) ),
    inference(resolution,[status(thm)],[f43,f100]) ).

fof(f1175,plain,
    ! [X0] :
      ( ~ defined(multiplicative_inverse(X0))
      | ~ defined(X0)
      | equalish(X0,additive_identity)
      | equalish(multiply(multiplicative_inverse(X0),X0),multiplicative_identity) ),
    inference(duplicate_literals_removal,[status(esa)],[f1174]) ).

fof(f1176,plain,
    ! [X0] :
      ( ~ defined(X0)
      | equalish(X0,additive_identity)
      | equalish(multiply(multiplicative_inverse(X0),X0),multiplicative_identity) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1175,f53]) ).

fof(f2081,plain,
    ! [X0,X1] :
      ( ~ defined(X0)
      | equalish(X0,additive_identity)
      | equalish(X1,multiplicative_identity)
      | ~ equalish(X1,multiply(multiplicative_inverse(X0),X0)) ),
    inference(resolution,[status(thm)],[f1176,f66]) ).

fof(f2693,plain,
    ! [X0,X1] :
      ( ~ defined(X0)
      | ~ equalish(X1,multiplicative_inverse(X0))
      | ~ defined(X0)
      | equalish(X0,additive_identity)
      | equalish(multiply(X1,X0),multiplicative_identity) ),
    inference(resolution,[status(thm)],[f70,f2081]) ).

fof(f2694,plain,
    ! [X0,X1] :
      ( ~ defined(X0)
      | ~ equalish(X1,multiplicative_inverse(X0))
      | equalish(X0,additive_identity)
      | equalish(multiply(X1,X0),multiplicative_identity) ),
    inference(duplicate_literals_removal,[status(esa)],[f2693]) ).

fof(f4383,plain,
    ! [X0,X1,X2] :
      ( ~ defined(X0)
      | ~ equalish(X1,multiplicative_inverse(X0))
      | equalish(X0,additive_identity)
      | equalish(X2,multiplicative_identity)
      | ~ equalish(X2,multiply(X1,X0)) ),
    inference(resolution,[status(thm)],[f2694,f66]) ).

fof(f4816,plain,
    ! [X0] :
      ( ~ defined(X0)
      | ~ equalish(multiplicative_identity,multiplicative_inverse(X0))
      | equalish(X0,additive_identity)
      | equalish(X0,multiplicative_identity)
      | ~ defined(X0) ),
    inference(resolution,[status(thm)],[f4383,f108]) ).

fof(f4817,plain,
    ! [X0] :
      ( ~ defined(X0)
      | ~ equalish(multiplicative_identity,multiplicative_inverse(X0))
      | equalish(X0,additive_identity)
      | equalish(X0,multiplicative_identity) ),
    inference(duplicate_literals_removal,[status(esa)],[f4816]) ).

fof(f4821,plain,
    ( spl0_429
  <=> equalish(a,multiplicative_identity) ),
    introduced(split_symbol_definition) ).

fof(f4822,plain,
    ( equalish(a,multiplicative_identity)
    | ~ spl0_429 ),
    inference(component_clause,[status(thm)],[f4821]) ).

fof(f4824,plain,
    ( ~ defined(a)
    | equalish(a,additive_identity)
    | equalish(a,multiplicative_identity) ),
    inference(resolution,[status(thm)],[f4817,f79]) ).

fof(f4825,plain,
    ( ~ spl0_16
    | spl0_17
    | spl0_429 ),
    inference(split_clause,[status(thm)],[f4824,f230,f233,f4821]) ).

fof(f4834,plain,
    ( $false
    | ~ spl0_429 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4822,f77]) ).

fof(f4835,plain,
    ~ spl0_429,
    inference(contradiction_clause,[status(thm)],[f4834]) ).

fof(f4836,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f239,f293,f4825,f4835]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : FLD032-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Apr 29 23:20:06 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 14.03/2.13  % Refutation found
% 14.03/2.13  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 14.03/2.13  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.03/2.16  % Elapsed time: 1.809371 seconds
% 14.03/2.16  % CPU time: 14.250688 seconds
% 14.03/2.16  % Total memory used: 120.286 MB
% 14.03/2.16  % Net memory used: 109.276 MB
%------------------------------------------------------------------------------