TSTP Solution File: SET903+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET903+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n017.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 12:35:30 EDT 2023

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   47 (   7 unt;   0 def)
%            Number of atoms       :  123 (  69 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  129 (  53   ~;  40   |;  29   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   51 (;  45   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ! [A,B,C] :
      ~ ( singleton(A) = set_union2(B,C)
        & ~ ( B = singleton(A)
            & C = singleton(A) )
        & ~ ( B = empty_set
            & C = singleton(A) )
        & ~ ( B = singleton(A)
            & C = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,conjecture,
    ! [A,B,C] :
      ~ ( singleton(A) = set_union2(B,C)
        & B != C
        & B != empty_set
        & C != empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ~ ! [A,B,C] :
        ~ ( singleton(A) = set_union2(B,C)
          & B != C
          & B != empty_set
          & C != empty_set ),
    inference(negated_conjecture,[status(cth)],[f9]) ).

fof(f25,plain,
    ! [A,B,C] :
      ( singleton(A) != set_union2(B,C)
      | ( B = singleton(A)
        & C = singleton(A) )
      | ( B = empty_set
        & C = singleton(A) )
      | ( B = singleton(A)
        & C = empty_set ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f26,plain,
    ! [A,B,C] :
      ( pd0_0(C,B,A)
     => ( B = singleton(A)
        & C = singleton(A) ) ),
    introduced(predicate_definition,[f25]) ).

fof(f27,plain,
    ! [A,B,C] :
      ( pd0_1(C,B,A)
     => ( B = empty_set
        & C = singleton(A) ) ),
    introduced(predicate_definition,[f25]) ).

fof(f28,plain,
    ! [A,B,C] :
      ( singleton(A) != set_union2(B,C)
      | pd0_0(C,B,A)
      | pd0_1(C,B,A)
      | ( B = singleton(A)
        & C = empty_set ) ),
    inference(formula_renaming,[status(thm)],[f25,f27,f26]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( singleton(X0) != set_union2(X1,X2)
      | pd0_0(X2,X1,X0)
      | pd0_1(X2,X1,X0)
      | X1 = singleton(X0) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( singleton(X0) != set_union2(X1,X2)
      | pd0_0(X2,X1,X0)
      | pd0_1(X2,X1,X0)
      | X2 = empty_set ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f31,plain,
    ? [A,B,C] :
      ( singleton(A) = set_union2(B,C)
      & B != C
      & B != empty_set
      & C != empty_set ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f32,plain,
    ? [C] :
      ( ? [B] :
          ( ? [A] : singleton(A) = set_union2(B,C)
          & B != C
          & B != empty_set )
      & C != empty_set ),
    inference(miniscoping,[status(esa)],[f31]) ).

fof(f33,plain,
    ( singleton(sk0_4) = set_union2(sk0_3,sk0_2)
    & sk0_3 != sk0_2
    & sk0_3 != empty_set
    & sk0_2 != empty_set ),
    inference(skolemization,[status(esa)],[f32]) ).

fof(f34,plain,
    singleton(sk0_4) = set_union2(sk0_3,sk0_2),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f35,plain,
    sk0_3 != sk0_2,
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f36,plain,
    sk0_3 != empty_set,
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f37,plain,
    sk0_2 != empty_set,
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f38,plain,
    ! [A,B,C] :
      ( ~ pd0_0(C,B,A)
      | ( B = singleton(A)
        & C = singleton(A) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f26]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | X1 = singleton(X2) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | X0 = singleton(X2) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f41,plain,
    ! [A,B,C] :
      ( ~ pd0_1(C,B,A)
      | ( B = empty_set
        & C = singleton(A) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f27]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_1(X0,X1,X2)
      | X1 = empty_set ),
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f75,plain,
    ( spl0_5
  <=> sk0_3 = empty_set ),
    introduced(split_symbol_definition) ).

fof(f76,plain,
    ( sk0_3 = empty_set
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f75]) ).

fof(f80,plain,
    ( spl0_6
  <=> pd0_0(sk0_2,sk0_3,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f81,plain,
    ( pd0_0(sk0_2,sk0_3,sk0_4)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f80]) ).

fof(f83,plain,
    ( spl0_7
  <=> pd0_1(sk0_2,sk0_3,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f84,plain,
    ( pd0_1(sk0_2,sk0_3,sk0_4)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f83]) ).

fof(f86,plain,
    ( spl0_8
  <=> sk0_2 = empty_set ),
    introduced(split_symbol_definition) ).

fof(f87,plain,
    ( sk0_2 = empty_set
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f86]) ).

fof(f89,plain,
    ( pd0_0(sk0_2,sk0_3,sk0_4)
    | pd0_1(sk0_2,sk0_3,sk0_4)
    | sk0_2 = empty_set ),
    inference(resolution,[status(thm)],[f30,f34]) ).

fof(f90,plain,
    ( spl0_6
    | spl0_7
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f89,f80,f83,f86]) ).

fof(f108,plain,
    ( $false
    | ~ spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f87,f37]) ).

fof(f109,plain,
    ~ spl0_8,
    inference(contradiction_clause,[status(thm)],[f108]) ).

fof(f110,plain,
    ( $false
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f76,f36]) ).

fof(f111,plain,
    ~ spl0_5,
    inference(contradiction_clause,[status(thm)],[f110]) ).

fof(f125,plain,
    ! [X0,X1,X2] :
      ( singleton(X0) != set_union2(X1,X2)
      | pd0_1(X2,X1,X0)
      | X1 = singleton(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f29,f39]) ).

fof(f131,plain,
    ( spl0_12
  <=> sk0_3 = singleton(sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f132,plain,
    ( sk0_3 = singleton(sk0_4)
    | ~ spl0_12 ),
    inference(component_clause,[status(thm)],[f131]) ).

fof(f134,plain,
    ( pd0_1(sk0_2,sk0_3,sk0_4)
    | sk0_3 = singleton(sk0_4) ),
    inference(resolution,[status(thm)],[f125,f34]) ).

fof(f135,plain,
    ( spl0_7
    | spl0_12 ),
    inference(split_clause,[status(thm)],[f134,f83,f131]) ).

fof(f155,plain,
    ( sk0_3 = empty_set
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f84,f42]) ).

fof(f156,plain,
    ( spl0_5
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f155,f75,f83]) ).

fof(f157,plain,
    ( sk0_2 = singleton(sk0_4)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f81,f40]) ).

fof(f184,plain,
    ( sk0_2 = sk0_3
    | ~ spl0_12
    | ~ spl0_6 ),
    inference(forward_demodulation,[status(thm)],[f132,f157]) ).

fof(f185,plain,
    ( $false
    | ~ spl0_12
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f184,f35]) ).

fof(f186,plain,
    ( ~ spl0_12
    | ~ spl0_6 ),
    inference(contradiction_clause,[status(thm)],[f185]) ).

fof(f187,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f90,f109,f111,f135,f156,f186]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET903+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n017.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 09:39:25 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.13/0.36  % Refutation found
% 0.13/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.58  % Elapsed time: 0.017792 seconds
% 0.22/0.58  % CPU time: 0.019143 seconds
% 0.22/0.58  % Memory used: 3.638 MB
%------------------------------------------------------------------------------