TSTP Solution File: SET929+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.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 12:35:33 EDT 2023

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   40 (   3 unt;   0 def)
%            Number of atoms       :  107 (  22 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  110 (  43   ~;  45   |;  14   &)
%                                         (   7 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   49 (;  43   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B] :
      ( set_difference(A,B) = empty_set
    <=> subset(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B,C] :
      ( subset(unordered_pair(A,B),C)
    <=> ( in(A,C)
        & in(B,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,conjecture,
    ! [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) = empty_set
    <=> ( in(A,C)
        & in(B,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ~ ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) = empty_set
      <=> ( in(A,C)
          & in(B,C) ) ),
    inference(negated_conjecture,[status(cth)],[f9]) ).

fof(f13,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f21,plain,
    ! [A,B] :
      ( ( set_difference(A,B) != empty_set
        | subset(A,B) )
      & ( set_difference(A,B) = empty_set
        | ~ subset(A,B) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f22,plain,
    ( ! [A,B] :
        ( set_difference(A,B) != empty_set
        | subset(A,B) )
    & ! [A,B] :
        ( set_difference(A,B) = empty_set
        | ~ subset(A,B) ) ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( set_difference(X0,X1) != empty_set
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( set_difference(X0,X1) = empty_set
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f25,plain,
    ! [A,B,C] :
      ( ( ~ subset(unordered_pair(A,B),C)
        | ( in(A,C)
          & in(B,C) ) )
      & ( subset(unordered_pair(A,B),C)
        | ~ in(A,C)
        | ~ in(B,C) ) ),
    inference(NNF_transformation,[status(esa)],[f8]) ).

fof(f26,plain,
    ( ! [A,B,C] :
        ( ~ subset(unordered_pair(A,B),C)
        | ( in(A,C)
          & in(B,C) ) )
    & ! [A,B,C] :
        ( subset(unordered_pair(A,B),C)
        | ~ in(A,C)
        | ~ in(B,C) ) ),
    inference(miniscoping,[status(esa)],[f25]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ~ subset(unordered_pair(X0,X1),X2)
      | in(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( subset(unordered_pair(X0,X1),X2)
      | ~ in(X0,X2)
      | ~ in(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f30,plain,
    ? [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) = empty_set
    <~> ( in(A,C)
        & in(B,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f31,plain,
    ? [A,B,C] :
      ( ( set_difference(unordered_pair(A,B),C) = empty_set
        | ( in(A,C)
          & in(B,C) ) )
      & ( set_difference(unordered_pair(A,B),C) != empty_set
        | ~ in(A,C)
        | ~ in(B,C) ) ),
    inference(NNF_transformation,[status(esa)],[f30]) ).

fof(f32,plain,
    ( ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = empty_set
      | ( in(sk0_2,sk0_4)
        & in(sk0_3,sk0_4) ) )
    & ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != empty_set
      | ~ in(sk0_2,sk0_4)
      | ~ in(sk0_3,sk0_4) ) ),
    inference(skolemization,[status(esa)],[f31]) ).

fof(f33,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = empty_set
    | in(sk0_2,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f34,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = empty_set
    | in(sk0_3,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f35,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != empty_set
    | ~ in(sk0_2,sk0_4)
    | ~ in(sk0_3,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f36,plain,
    ( spl0_0
  <=> set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = empty_set ),
    introduced(split_symbol_definition) ).

fof(f37,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = empty_set
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f36]) ).

fof(f38,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != empty_set
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f36]) ).

fof(f39,plain,
    ( spl0_1
  <=> in(sk0_2,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f41,plain,
    ( ~ in(sk0_2,sk0_4)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f39]) ).

fof(f42,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f33,f36,f39]) ).

fof(f43,plain,
    ( spl0_2
  <=> in(sk0_3,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f46,plain,
    ( spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f34,f36,f43]) ).

fof(f47,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f35,f36,f39,f43]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ~ subset(unordered_pair(X0,X1),X2)
      | in(X1,X2) ),
    inference(paramodulation,[status(thm)],[f13,f27]) ).

fof(f66,plain,
    ( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f37,f23]) ).

fof(f77,plain,
    ( in(sk0_3,sk0_4)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f66,f49]) ).

fof(f78,plain,
    ( in(sk0_2,sk0_4)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f66,f27]) ).

fof(f79,plain,
    ( $false
    | spl0_1
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f78,f41]) ).

fof(f80,plain,
    ( spl0_1
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f79]) ).

fof(f83,plain,
    ( ~ subset(unordered_pair(sk0_2,sk0_3),sk0_4)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f38,f24]) ).

fof(f84,plain,
    ( ~ in(sk0_2,sk0_4)
    | ~ in(sk0_3,sk0_4)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f83,f29]) ).

fof(f85,plain,
    ( ~ spl0_1
    | ~ spl0_2
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f84,f39,f43,f36]) ).

fof(f86,plain,
    ( spl0_2
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f77,f43,f36]) ).

fof(f87,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f42,f46,f47,f80,f85,f86]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n007.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 10:00:17 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.36  % Elapsed time: 0.023454 seconds
% 0.18/0.36  % CPU time: 0.032330 seconds
% 0.18/0.36  % Memory used: 14.280 MB
%------------------------------------------------------------------------------