TSTP Solution File: FLD071-2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : FLD071-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n001.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 12:07:10 EDT 2023

% Result   : Unsatisfiable 4.67s 0.98s
% Output   : CNFRefutation 4.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   84 (  17 unt;   0 def)
%            Number of atoms       :  204 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  223 ( 103   ~; 112   |;   0   &)
%                                         (   8 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   9 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   78 (;  78   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f11,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

fof(f18,axiom,
    ! [X,Y] :
      ( less_or_equal(X,Y)
      | less_or_equal(Y,X)
      | ~ defined(X)
      | ~ defined(Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [Y,Z] :
      ( less_or_equal(additive_identity,multiply(Y,Z))
      | ~ less_or_equal(additive_identity,Y)
      | ~ less_or_equal(additive_identity,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [X] :
      ( equalish(X,X)
      | ~ defined(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [X,Y] :
      ( equalish(X,Y)
      | ~ equalish(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ! [X,Z,Y] :
      ( equalish(X,Z)
      | ~ equalish(X,Y)
      | ~ equalish(Y,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f26,axiom,
    ! [Y,Z,X] :
      ( less_or_equal(Y,Z)
      | ~ less_or_equal(X,Z)
      | ~ equalish(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,hypothesis,
    defined(u),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f31,negated_conjecture,
    less_or_equal(additive_identity,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f32,negated_conjecture,
    less_or_equal(additive_identity,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f33,negated_conjecture,
    equalish(multiply(a,b),u),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f34,negated_conjecture,
    ~ less_or_equal(additive_identity,u),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f51,plain,
    defined(additive_identity),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( equalish(X0,X1)
      | ~ less_or_equal(X0,X1)
      | ~ less_or_equal(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f58,plain,
    ! [Z,Y] :
      ( ! [X] :
          ( less_or_equal(X,Z)
          | ~ less_or_equal(X,Y) )
      | ~ less_or_equal(Y,Z) ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ less_or_equal(X0,X2)
      | ~ less_or_equal(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f60,plain,
    ! [Y] :
      ( ! [X] :
          ( less_or_equal(X,Y)
          | less_or_equal(Y,X)
          | ~ defined(X) )
      | ~ defined(Y) ),
    inference(miniscoping,[status(esa)],[f18]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( less_or_equal(X0,X1)
      | less_or_equal(X1,X0)
      | ~ defined(X0)
      | ~ defined(X1) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f64,plain,
    ! [Z] :
      ( ! [Y] :
          ( less_or_equal(additive_identity,multiply(Y,Z))
          | ~ less_or_equal(additive_identity,Y) )
      | ~ less_or_equal(additive_identity,Z) ),
    inference(miniscoping,[status(esa)],[f20]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( less_or_equal(additive_identity,multiply(X0,X1))
      | ~ less_or_equal(additive_identity,X0)
      | ~ less_or_equal(additive_identity,X1) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f66,plain,
    ! [X0] :
      ( equalish(X0,X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( equalish(X0,X1)
      | ~ equalish(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f68,plain,
    ! [Z,Y] :
      ( ! [X] :
          ( equalish(X,Z)
          | ~ equalish(X,Y) )
      | ~ equalish(Y,Z) ),
    inference(miniscoping,[status(esa)],[f23]) ).

fof(f69,plain,
    ! [X0,X1,X2] :
      ( equalish(X0,X1)
      | ~ equalish(X0,X2)
      | ~ equalish(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f74,plain,
    ! [Y,X] :
      ( ! [Z] :
          ( less_or_equal(Y,Z)
          | ~ less_or_equal(X,Z) )
      | ~ equalish(X,Y) ),
    inference(miniscoping,[status(esa)],[f26]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ less_or_equal(X2,X1)
      | ~ equalish(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f74]) ).

fof(f79,plain,
    defined(u),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f80,plain,
    less_or_equal(additive_identity,a),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f81,plain,
    less_or_equal(additive_identity,b),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f82,plain,
    equalish(multiply(a,b),u),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f83,plain,
    ~ less_or_equal(additive_identity,u),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f85,plain,
    equalish(u,multiply(a,b)),
    inference(resolution,[status(thm)],[f67,f82]) ).

fof(f106,plain,
    ! [X0] :
      ( equalish(X0,multiply(a,b))
      | ~ equalish(X0,u) ),
    inference(resolution,[status(thm)],[f69,f85]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ~ equalish(X0,u)
      | equalish(X1,multiply(a,b))
      | ~ equalish(X1,X0) ),
    inference(resolution,[status(thm)],[f106,f69]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ~ equalish(X0,u)
      | ~ equalish(X1,X0)
      | equalish(multiply(a,b),X1) ),
    inference(resolution,[status(thm)],[f109,f67]) ).

fof(f152,plain,
    ( spl0_10
  <=> defined(u) ),
    introduced(split_symbol_definition) ).

fof(f154,plain,
    ( ~ defined(u)
    | spl0_10 ),
    inference(component_clause,[status(thm)],[f152]) ).

fof(f182,plain,
    ! [X0,X1,X2] :
      ( ~ equalish(X0,u)
      | ~ equalish(X1,X0)
      | equalish(X2,X1)
      | ~ equalish(X2,multiply(a,b)) ),
    inference(resolution,[status(thm)],[f132,f69]) ).

fof(f296,plain,
    ! [X0,X1] :
      ( ~ equalish(X0,u)
      | ~ equalish(X1,X0)
      | equalish(u,X1) ),
    inference(resolution,[status(thm)],[f182,f85]) ).

fof(f307,plain,
    ! [X0] :
      ( ~ equalish(X0,multiply(a,b))
      | equalish(u,X0) ),
    inference(resolution,[status(thm)],[f296,f82]) ).

fof(f415,plain,
    ! [X0] :
      ( less_or_equal(X0,b)
      | ~ equalish(additive_identity,X0) ),
    inference(resolution,[status(thm)],[f75,f81]) ).

fof(f416,plain,
    ! [X0] :
      ( less_or_equal(X0,a)
      | ~ equalish(additive_identity,X0) ),
    inference(resolution,[status(thm)],[f75,f80]) ).

fof(f417,plain,
    ( $false
    | spl0_10 ),
    inference(forward_subsumption_resolution,[status(thm)],[f79,f154]) ).

fof(f418,plain,
    spl0_10,
    inference(contradiction_clause,[status(thm)],[f417]) ).

fof(f442,plain,
    ( spl0_42
  <=> less_or_equal(additive_identity,b) ),
    introduced(split_symbol_definition) ).

fof(f445,plain,
    ( spl0_43
  <=> defined(additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f447,plain,
    ( ~ defined(additive_identity)
    | spl0_43 ),
    inference(component_clause,[status(thm)],[f445]) ).

fof(f448,plain,
    ( less_or_equal(additive_identity,b)
    | ~ defined(additive_identity) ),
    inference(resolution,[status(thm)],[f415,f66]) ).

fof(f449,plain,
    ( spl0_42
    | ~ spl0_43 ),
    inference(split_clause,[status(thm)],[f448,f442,f445]) ).

fof(f450,plain,
    ( $false
    | spl0_43 ),
    inference(forward_subsumption_resolution,[status(thm)],[f447,f51]) ).

fof(f451,plain,
    spl0_43,
    inference(contradiction_clause,[status(thm)],[f450]) ).

fof(f463,plain,
    ( spl0_45
  <=> less_or_equal(additive_identity,a) ),
    introduced(split_symbol_definition) ).

fof(f466,plain,
    ( less_or_equal(additive_identity,a)
    | ~ defined(additive_identity) ),
    inference(resolution,[status(thm)],[f416,f66]) ).

fof(f467,plain,
    ( spl0_45
    | ~ spl0_43 ),
    inference(split_clause,[status(thm)],[f466,f463,f445]) ).

fof(f547,plain,
    ( spl0_59
  <=> less_or_equal(u,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f548,plain,
    ( less_or_equal(u,additive_identity)
    | ~ spl0_59 ),
    inference(component_clause,[status(thm)],[f547]) ).

fof(f550,plain,
    ( less_or_equal(u,additive_identity)
    | ~ defined(u)
    | ~ defined(additive_identity) ),
    inference(resolution,[status(thm)],[f61,f83]) ).

fof(f551,plain,
    ( spl0_59
    | ~ spl0_10
    | ~ spl0_43 ),
    inference(split_clause,[status(thm)],[f550,f547,f152,f445]) ).

fof(f563,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ defined(X0)
      | ~ defined(X1)
      | less_or_equal(X2,X0)
      | ~ less_or_equal(X2,X1) ),
    inference(resolution,[status(thm)],[f61,f59]) ).

fof(f566,plain,
    ! [X0] :
      ( less_or_equal(X0,additive_identity)
      | ~ equalish(u,X0)
      | ~ spl0_59 ),
    inference(resolution,[status(thm)],[f548,f75]) ).

fof(f568,plain,
    ( spl0_62
  <=> less_or_equal(additive_identity,u) ),
    introduced(split_symbol_definition) ).

fof(f569,plain,
    ( less_or_equal(additive_identity,u)
    | ~ spl0_62 ),
    inference(component_clause,[status(thm)],[f568]) ).

fof(f660,plain,
    ( less_or_equal(multiply(a,b),additive_identity)
    | ~ spl0_59 ),
    inference(resolution,[status(thm)],[f566,f85]) ).

fof(f879,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ defined(X0)
      | ~ defined(X1)
      | less_or_equal(X2,X0)
      | less_or_equal(X1,X2)
      | ~ defined(X1)
      | ~ defined(X2) ),
    inference(resolution,[status(thm)],[f563,f61]) ).

fof(f880,plain,
    ! [X0,X1,X2] :
      ( less_or_equal(X0,X1)
      | ~ defined(X0)
      | ~ defined(X1)
      | less_or_equal(X2,X0)
      | less_or_equal(X1,X2)
      | ~ defined(X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f879]) ).

fof(f1383,plain,
    ( spl0_138
  <=> equalish(additive_identity,multiply(a,b)) ),
    introduced(split_symbol_definition) ).

fof(f1384,plain,
    ( equalish(additive_identity,multiply(a,b))
    | ~ spl0_138 ),
    inference(component_clause,[status(thm)],[f1383]) ).

fof(f1386,plain,
    ( spl0_139
  <=> less_or_equal(additive_identity,multiply(a,b)) ),
    introduced(split_symbol_definition) ).

fof(f1388,plain,
    ( ~ less_or_equal(additive_identity,multiply(a,b))
    | spl0_139 ),
    inference(component_clause,[status(thm)],[f1386]) ).

fof(f1389,plain,
    ( equalish(additive_identity,multiply(a,b))
    | ~ less_or_equal(additive_identity,multiply(a,b))
    | ~ spl0_59 ),
    inference(resolution,[status(thm)],[f660,f57]) ).

fof(f1390,plain,
    ( spl0_138
    | ~ spl0_139
    | ~ spl0_59 ),
    inference(split_clause,[status(thm)],[f1389,f1383,f1386,f547]) ).

fof(f1685,plain,
    ( ~ less_or_equal(additive_identity,a)
    | ~ less_or_equal(additive_identity,b)
    | spl0_139 ),
    inference(resolution,[status(thm)],[f1388,f65]) ).

fof(f1686,plain,
    ( ~ spl0_45
    | ~ spl0_42
    | spl0_139 ),
    inference(split_clause,[status(thm)],[f1685,f463,f442,f1386]) ).

fof(f2159,plain,
    ( equalish(u,additive_identity)
    | ~ spl0_138 ),
    inference(resolution,[status(thm)],[f1384,f307]) ).

fof(f4026,plain,
    ! [X0,X1] :
      ( less_or_equal(X0,X0)
      | ~ defined(X0)
      | ~ defined(X0)
      | ~ defined(X0)
      | less_or_equal(X1,X0)
      | ~ equalish(X0,X1) ),
    inference(resolution,[status(thm)],[f880,f75]) ).

fof(f4027,plain,
    ! [X0,X1] :
      ( less_or_equal(X0,X0)
      | ~ defined(X0)
      | less_or_equal(X1,X0)
      | ~ equalish(X0,X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f4026]) ).

fof(f4028,plain,
    ! [X0,X1] :
      ( ~ defined(X0)
      | less_or_equal(X1,X0)
      | ~ equalish(X0,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f4027,f75]) ).

fof(f4708,plain,
    ( ~ defined(u)
    | less_or_equal(additive_identity,u)
    | ~ spl0_138 ),
    inference(resolution,[status(thm)],[f4028,f2159]) ).

fof(f4709,plain,
    ( ~ spl0_10
    | spl0_62
    | ~ spl0_138 ),
    inference(split_clause,[status(thm)],[f4708,f152,f568,f1383]) ).

fof(f4771,plain,
    ( $false
    | ~ spl0_62 ),
    inference(forward_subsumption_resolution,[status(thm)],[f569,f83]) ).

fof(f4772,plain,
    ~ spl0_62,
    inference(contradiction_clause,[status(thm)],[f4771]) ).

fof(f4773,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f418,f449,f451,f467,f551,f1390,f1686,f4709,f4772]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : FLD071-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n001.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 : Tue May 30 11:32:30 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 4.67/0.98  % Refutation found
% 4.67/0.98  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.67/0.98  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.67/1.00  % Elapsed time: 0.652464 seconds
% 4.67/1.00  % CPU time: 5.101396 seconds
% 4.67/1.00  % Memory used: 41.011 MB
%------------------------------------------------------------------------------