%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET122-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 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 12:34:04 EDT 2023

% Result   : Unsatisfiable 54.94s 7.30s
% Output   : CNFRefutation 54.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   49 (  10 unt;   0 def)
%            Number of atoms       :   95 (  36 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   81 (  35   ~;  42   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   66 (;  66   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f15,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,cross_product(X,Y))
      | ordered_pair(first(Z),second(Z)) = Z ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f95,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f145,axiom,
    ! [X,Y] : member(ordered_pair(X,Y),universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f152,axiom,
    ! [W,X,Y,Z] :
      ( ordered_pair(W,X) != ordered_pair(Y,Z)
      | ~ member(X,universal_class)
      | X = Z ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f155,axiom,
    ! [X] :
      ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
      | second(X) = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f157,axiom,
    ! [X] :
      ( ordered_pair(first(X),second(X)) = X
      | second(X) = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f168,negated_conjecture,
    ~ member(y,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f169,negated_conjecture,
    second(ordered_pair(x,y)) != ordered_pair(x,y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f189,plain,
    ! [V,Y] :
      ( ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,Y) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f190,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f189]) ).

fof(f192,plain,
    ! [Z] :
      ( ! [X,Y] : ~ member(Z,cross_product(X,Y))
      | ordered_pair(first(Z),second(Z)) = Z ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f193,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,cross_product(X1,X2))
      | ordered_pair(first(X0),second(X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f281,plain,
    ! [V] :
      ( ! [U,X,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,universal_class) ),
    inference(miniscoping,[status(esa)],[f95]) ).

fof(f282,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X1,universal_class) ),
    inference(cnf_transformation,[status(esa)],[f281]) ).

fof(f342,plain,
    ! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
    inference(cnf_transformation,[status(esa)],[f145]) ).

fof(f353,plain,
    ! [X,Z] :
      ( ! [W,Y] : ordered_pair(W,X) != ordered_pair(Y,Z)
      | ~ member(X,universal_class)
      | X = Z ),
    inference(miniscoping,[status(esa)],[f152]) ).

fof(f354,plain,
    ! [X0,X1,X2,X3] :
      ( ordered_pair(X0,X1) != ordered_pair(X2,X3)
      | ~ member(X1,universal_class)
      | X1 = X3 ),
    inference(cnf_transformation,[status(esa)],[f353]) ).

fof(f357,plain,
    ! [X0] :
      ( member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class))
      | second(X0) = X0 ),
    inference(cnf_transformation,[status(esa)],[f155]) ).

fof(f359,plain,
    ! [X0] :
      ( ordered_pair(first(X0),second(X0)) = X0
      | second(X0) = X0 ),
    inference(cnf_transformation,[status(esa)],[f157]) ).

fof(f372,plain,
    ~ member(y,universal_class),
    inference(cnf_transformation,[status(esa)],[f168]) ).

fof(f373,plain,
    second(ordered_pair(x,y)) != ordered_pair(x,y),
    inference(cnf_transformation,[status(esa)],[f169]) ).

fof(f378,plain,
    ( spl0_0
  <=> ordered_pair(x,y) = ordered_pair(x,y) ),
    introduced(split_symbol_definition) ).

fof(f380,plain,
    ( ordered_pair(x,y) != ordered_pair(x,y)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f378]) ).

fof(f386,plain,
    ( $false
    | spl0_0 ),
    inference(trivial_equality_resolution,[status(esa)],[f380]) ).

fof(f387,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f386]) ).

fof(f1698,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ member(X1,universal_class)
      | X1 = second(ordered_pair(X0,X1)) ),
    inference(resolution,[status(thm)],[f193,f354]) ).

fof(f6099,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | X1 = second(ordered_pair(X0,X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[f1698,f282]) ).

fof(f12254,plain,
    ! [X0] :
      ( member(X0,cross_product(universal_class,universal_class))
      | second(X0) = X0
      | second(X0) = X0 ),
    inference(paramodulation,[status(thm)],[f359,f357]) ).

fof(f12255,plain,
    ! [X0] :
      ( member(X0,cross_product(universal_class,universal_class))
      | second(X0) = X0 ),
    inference(duplicate_literals_removal,[status(esa)],[f12254]) ).

fof(f14500,plain,
    ! [X0,X1] :
      ( second(ordered_pair(X0,X1)) = ordered_pair(X0,X1)
      | X1 = second(ordered_pair(X0,X1)) ),
    inference(resolution,[status(thm)],[f12255,f6099]) ).

fof(f14731,plain,
    ! [X0] :
      ( member(second(X0),universal_class)
      | second(X0) = X0 ),
    inference(resolution,[status(thm)],[f190,f357]) ).

fof(f15832,plain,
    ( spl0_1065
  <=> member(y,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f15833,plain,
    ( member(y,universal_class)
    | ~ spl0_1065 ),
    inference(component_clause,[status(thm)],[f15832]) ).

fof(f15846,plain,
    ( $false
    | ~ spl0_1065 ),
    inference(forward_subsumption_resolution,[status(thm)],[f15833,f372]) ).

fof(f15847,plain,
    ~ spl0_1065,
    inference(contradiction_clause,[status(thm)],[f15846]) ).

fof(f15849,plain,
    y = second(ordered_pair(x,y)),
    inference(resolution,[status(thm)],[f14500,f373]) ).

fof(f15865,plain,
    ( spl0_1067
  <=> y = second(ordered_pair(x,y)) ),
    introduced(split_symbol_definition) ).

fof(f15866,plain,
    ( y = second(ordered_pair(x,y))
    | ~ spl0_1067 ),
    inference(component_clause,[status(thm)],[f15865]) ).

fof(f15868,plain,
    ( ordered_pair(x,y) != ordered_pair(x,y)
    | y = second(ordered_pair(x,y)) ),
    inference(paramodulation,[status(thm)],[f14500,f373]) ).

fof(f15869,plain,
    ( ~ spl0_0
    | spl0_1067 ),
    inference(split_clause,[status(thm)],[f15868,f378,f15865]) ).

fof(f15903,plain,
    ( spl0_1070
  <=> second(ordered_pair(x,y)) = ordered_pair(x,y) ),
    introduced(split_symbol_definition) ).

fof(f15904,plain,
    ( second(ordered_pair(x,y)) = ordered_pair(x,y)
    | ~ spl0_1070 ),
    inference(component_clause,[status(thm)],[f15903]) ).

fof(f15920,plain,
    ( y = ordered_pair(x,y)
    | ~ spl0_1070 ),
    inference(forward_demodulation,[status(thm)],[f15849,f15904]) ).

fof(f15976,plain,
    ( member(y,universal_class)
    | ~ spl0_1070 ),
    inference(paramodulation,[status(thm)],[f15920,f342]) ).

fof(f15977,plain,
    ( spl0_1065
    | ~ spl0_1070 ),
    inference(split_clause,[status(thm)],[f15976,f15832,f15903]) ).

fof(f16326,plain,
    ( member(y,universal_class)
    | second(ordered_pair(x,y)) = ordered_pair(x,y)
    | ~ spl0_1067 ),
    inference(paramodulation,[status(thm)],[f15866,f14731]) ).

fof(f16327,plain,
    ( spl0_1065
    | spl0_1070
    | ~ spl0_1067 ),
    inference(split_clause,[status(thm)],[f16326,f15832,f15903,f15865]) ).

fof(f16332,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f387,f15847,f15869,f15977,f16327]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET122-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n013.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 10:07:20 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  % Drodi V3.5.1
% 54.94/7.30  % Refutation found
% 54.94/7.30  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 54.94/7.30  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 55.69/7.38  % Elapsed time: 7.013549 seconds
% 55.69/7.38  % CPU time: 55.565317 seconds
% 55.69/7.38  % Memory used: 374.142 MB
%------------------------------------------------------------------------------