TSTP Solution File: SET012-3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET012-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n013.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 12:33:30 EDT 2023

% Result   : Unsatisfiable 6.52s 1.26s
% Output   : CNFRefutation 6.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   66 (  15 unt;   0 def)
%            Number of atoms       :  128 (  12 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  112 (  50   ~;  56   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   7 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   42 (;  42   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] :
      ( ~ member(X,Y)
      | little_set(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] :
      ( little_set(f1(X,Y))
      | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y] :
      ( member(f1(X,Y),X)
      | member(f1(X,Y),Y)
      | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y] :
      ( ~ member(f1(X,Y),X)
      | ~ member(f1(X,Y),Y)
      | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f31,axiom,
    ! [Z,X] :
      ( ~ member(Z,complement(X))
      | ~ member(Z,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f32,axiom,
    ! [Z,X] :
      ( member(Z,complement(X))
      | ~ little_set(Z)
      | member(Z,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f86,axiom,
    ! [Xf] :
      ( ~ function(Xf)
      | relation(Xf) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f87,axiom,
    ! [Xf] :
      ( ~ function(Xf)
      | single_valued_set(Xf) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f88,axiom,
    ! [Xf] :
      ( function(Xf)
      | ~ relation(Xf)
      | ~ single_valued_set(Xf) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f100,axiom,
    function(f25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f142,hypothesis,
    complement(as) = bs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f143,hypothesis,
    complement(bs) = cs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f144,negated_conjecture,
    as != cs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f145,plain,
    ! [X] :
      ( ! [Y] : ~ member(X,Y)
      | little_set(X) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | little_set(X0) ),
    inference(cnf_transformation,[status(esa)],[f145]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( little_set(f1(X0,X1))
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( member(f1(X0,X1),X0)
      | member(f1(X0,X1),X1)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f149,plain,
    ! [X0,X1] :
      ( ~ member(f1(X0,X1),X0)
      | ~ member(f1(X0,X1),X1)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ~ member(X0,complement(X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f185,plain,
    ! [X0,X1] :
      ( member(X0,complement(X1))
      | ~ little_set(X0)
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f251,plain,
    ! [X0] :
      ( ~ function(X0)
      | relation(X0) ),
    inference(cnf_transformation,[status(esa)],[f86]) ).

fof(f252,plain,
    ! [X0] :
      ( ~ function(X0)
      | single_valued_set(X0) ),
    inference(cnf_transformation,[status(esa)],[f87]) ).

fof(f253,plain,
    ! [X0] :
      ( function(X0)
      | ~ relation(X0)
      | ~ single_valued_set(X0) ),
    inference(cnf_transformation,[status(esa)],[f88]) ).

fof(f267,plain,
    function(f25),
    inference(cnf_transformation,[status(esa)],[f100]) ).

fof(f322,plain,
    complement(as) = bs,
    inference(cnf_transformation,[status(esa)],[f142]) ).

fof(f323,plain,
    complement(bs) = cs,
    inference(cnf_transformation,[status(esa)],[f143]) ).

fof(f324,plain,
    as != cs,
    inference(cnf_transformation,[status(esa)],[f144]) ).

fof(f328,plain,
    relation(f25),
    inference(resolution,[status(thm)],[f251,f267]) ).

fof(f329,plain,
    single_valued_set(f25),
    inference(resolution,[status(thm)],[f252,f267]) ).

fof(f336,plain,
    little_set(f1(as,cs)),
    inference(resolution,[status(thm)],[f147,f324]) ).

fof(f354,plain,
    ( spl0_0
  <=> function(f25) ),
    introduced(split_symbol_definition) ).

fof(f357,plain,
    ( spl0_1
  <=> single_valued_set(f25) ),
    introduced(split_symbol_definition) ).

fof(f359,plain,
    ( ~ single_valued_set(f25)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f357]) ).

fof(f366,plain,
    ( spl0_2
  <=> relation(f25) ),
    introduced(split_symbol_definition) ).

fof(f368,plain,
    ( ~ relation(f25)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f366]) ).

fof(f369,plain,
    ( function(f25)
    | ~ relation(f25) ),
    inference(resolution,[status(thm)],[f253,f329]) ).

fof(f370,plain,
    ( spl0_0
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f369,f354,f366]) ).

fof(f373,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f368,f328]) ).

fof(f374,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f373]) ).

fof(f382,plain,
    ! [X0] :
      ( ~ member(X0,bs)
      | ~ member(X0,as) ),
    inference(paramodulation,[status(thm)],[f322,f184]) ).

fof(f437,plain,
    ( spl0_3
  <=> member(f1(as,cs),as) ),
    introduced(split_symbol_definition) ).

fof(f440,plain,
    ( spl0_4
  <=> member(f1(as,cs),cs) ),
    introduced(split_symbol_definition) ).

fof(f441,plain,
    ( member(f1(as,cs),cs)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f440]) ).

fof(f442,plain,
    ( ~ member(f1(as,cs),cs)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f440]) ).

fof(f443,plain,
    ( member(f1(as,cs),as)
    | member(f1(as,cs),cs) ),
    inference(resolution,[status(thm)],[f148,f324]) ).

fof(f444,plain,
    ( spl0_3
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f443,f437,f440]) ).

fof(f463,plain,
    ( ~ member(f1(as,cs),as)
    | ~ member(f1(as,cs),cs) ),
    inference(resolution,[status(thm)],[f149,f324]) ).

fof(f464,plain,
    ( ~ spl0_3
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f463,f437,f440]) ).

fof(f1432,plain,
    ! [X0,X1] :
      ( ~ little_set(X0)
      | member(X0,X1)
      | ~ member(X0,complement(complement(X1))) ),
    inference(resolution,[status(thm)],[f185,f184]) ).

fof(f1433,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(X0,complement(complement(X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1432,f146]) ).

fof(f1499,plain,
    ( spl0_67
  <=> little_set(f1(as,cs)) ),
    introduced(split_symbol_definition) ).

fof(f1501,plain,
    ( ~ little_set(f1(as,cs))
    | spl0_67 ),
    inference(component_clause,[status(thm)],[f1499]) ).

fof(f1529,plain,
    ! [X0] :
      ( member(X0,complement(bs))
      | ~ little_set(X0)
      | ~ member(X0,as) ),
    inference(resolution,[status(thm)],[f185,f382]) ).

fof(f1530,plain,
    ! [X0] :
      ( member(X0,cs)
      | ~ little_set(X0)
      | ~ member(X0,as) ),
    inference(forward_demodulation,[status(thm)],[f323,f1529]) ).

fof(f1531,plain,
    ! [X0] :
      ( member(X0,cs)
      | ~ member(X0,as) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1530,f146]) ).

fof(f1558,plain,
    ( $false
    | spl0_67 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1501,f336]) ).

fof(f1559,plain,
    spl0_67,
    inference(contradiction_clause,[status(thm)],[f1558]) ).

fof(f1567,plain,
    ( ~ member(f1(as,cs),as)
    | spl0_4 ),
    inference(resolution,[status(thm)],[f1531,f442]) ).

fof(f1568,plain,
    ( ~ spl0_3
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f1567,f437,f440]) ).

fof(f1688,plain,
    ! [X0] :
      ( member(X0,as)
      | ~ member(X0,complement(bs)) ),
    inference(paramodulation,[status(thm)],[f322,f1433]) ).

fof(f1689,plain,
    ! [X0] :
      ( member(X0,as)
      | ~ member(X0,cs) ),
    inference(forward_demodulation,[status(thm)],[f323,f1688]) ).

fof(f2974,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f359,f329]) ).

fof(f2975,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f2974]) ).

fof(f3114,plain,
    ( member(f1(as,cs),as)
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f1689,f441]) ).

fof(f3115,plain,
    ( spl0_3
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f3114,f437,f440]) ).

fof(f3142,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f370,f374,f444,f464,f1559,f1568,f2975,f3115]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET012-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n013.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Tue May 30 10:12:50 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.10/0.33  % Drodi V3.5.1
% 6.52/1.26  % Refutation found
% 6.52/1.26  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.52/1.26  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.52/1.29  % Elapsed time: 0.954165 seconds
% 6.52/1.29  % CPU time: 6.668384 seconds
% 6.52/1.29  % Memory used: 139.059 MB
%------------------------------------------------------------------------------