TSTP Solution File: SYN349+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SYN349+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 : Tue Apr 30 20:51:58 EDT 2024

% Result   : Theorem 0.11s 0.34s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   37 (   6 unt;   0 def)
%            Number of atoms       :  140 (   0 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  149 (  46   ~;  66   |;  18   &)
%                                         (  15 <=>;   2  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :   77 (  67   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ? [X1] :
    ! [X2] :
    ? [X3] :
    ! [X4] :
      ( ( big_f(X1,X4)
      <=> big_f(X2,X4) )
     => ( ( ( big_f(X1,X4)
          <=> big_f(X4,X3) )
        <=> big_f(X3,X4) )
      <=> big_f(X4,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ~ ? [X1] :
      ! [X2] :
      ? [X3] :
      ! [X4] :
        ( ( big_f(X1,X4)
        <=> big_f(X2,X4) )
       => ( ( ( big_f(X1,X4)
            <=> big_f(X4,X3) )
          <=> big_f(X3,X4) )
        <=> big_f(X4,X2) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f3,plain,
    ! [X1] :
    ? [X2] :
    ! [X3] :
    ? [X4] :
      ( ( big_f(X1,X4)
      <=> big_f(X2,X4) )
      & ( ( ( big_f(X1,X4)
          <=> big_f(X4,X3) )
        <=> big_f(X3,X4) )
      <~> big_f(X4,X2) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f4,plain,
    ! [X1,X3,X4] :
      ( pd0_0(X4,X3,X1)
    <=> ( big_f(X1,X4)
      <=> big_f(X4,X3) ) ),
    introduced(predicate_definition,[f3]) ).

fof(f5,plain,
    ! [X1] :
    ? [X2] :
    ! [X3] :
    ? [X4] :
      ( ( big_f(X1,X4)
      <=> big_f(X2,X4) )
      & ( ( pd0_0(X4,X3,X1)
        <=> big_f(X3,X4) )
      <~> big_f(X4,X2) ) ),
    inference(formula_renaming,[status(thm)],[f3,f4]) ).

fof(f6,plain,
    ! [X1] :
    ? [X2] :
    ! [X3] :
    ? [X4] :
      ( ( ~ big_f(X1,X4)
        | big_f(X2,X4) )
      & ( big_f(X1,X4)
        | ~ big_f(X2,X4) )
      & ( ( ( ~ pd0_0(X4,X3,X1)
            | big_f(X3,X4) )
          & ( pd0_0(X4,X3,X1)
            | ~ big_f(X3,X4) ) )
        | big_f(X4,X2) )
      & ( ( ( ~ pd0_0(X4,X3,X1)
            | ~ big_f(X3,X4) )
          & ( pd0_0(X4,X3,X1)
            | big_f(X3,X4) ) )
        | ~ big_f(X4,X2) ) ),
    inference(NNF_transformation,[status(esa)],[f5]) ).

fof(f7,plain,
    ! [X1,X3] :
      ( ( ~ big_f(X1,sk0_1(X3,X1))
        | big_f(sk0_0(X1),sk0_1(X3,X1)) )
      & ( big_f(X1,sk0_1(X3,X1))
        | ~ big_f(sk0_0(X1),sk0_1(X3,X1)) )
      & ( ( ( ~ pd0_0(sk0_1(X3,X1),X3,X1)
            | big_f(X3,sk0_1(X3,X1)) )
          & ( pd0_0(sk0_1(X3,X1),X3,X1)
            | ~ big_f(X3,sk0_1(X3,X1)) ) )
        | big_f(sk0_1(X3,X1),sk0_0(X1)) )
      & ( ( ( ~ pd0_0(sk0_1(X3,X1),X3,X1)
            | ~ big_f(X3,sk0_1(X3,X1)) )
          & ( pd0_0(sk0_1(X3,X1),X3,X1)
            | big_f(X3,sk0_1(X3,X1)) ) )
        | ~ big_f(sk0_1(X3,X1),sk0_0(X1)) ) ),
    inference(skolemization,[status(esa)],[f6]) ).

fof(f8,plain,
    ! [X0,X1] :
      ( ~ big_f(X0,sk0_1(X1,X0))
      | big_f(sk0_0(X0),sk0_1(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f9,plain,
    ! [X0,X1] :
      ( big_f(X0,sk0_1(X1,X0))
      | ~ big_f(sk0_0(X0),sk0_1(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ~ pd0_0(sk0_1(X0,X1),X0,X1)
      | big_f(X0,sk0_1(X0,X1))
      | big_f(sk0_1(X0,X1),sk0_0(X1)) ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( pd0_0(sk0_1(X0,X1),X0,X1)
      | ~ big_f(X0,sk0_1(X0,X1))
      | big_f(sk0_1(X0,X1),sk0_0(X1)) ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ~ pd0_0(sk0_1(X0,X1),X0,X1)
      | ~ big_f(X0,sk0_1(X0,X1))
      | ~ big_f(sk0_1(X0,X1),sk0_0(X1)) ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( pd0_0(sk0_1(X0,X1),X0,X1)
      | big_f(X0,sk0_1(X0,X1))
      | ~ big_f(sk0_1(X0,X1),sk0_0(X1)) ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f14,plain,
    ! [X1,X3,X4] :
      ( ( ~ pd0_0(X4,X3,X1)
        | ( ( ~ big_f(X1,X4)
            | big_f(X4,X3) )
          & ( big_f(X1,X4)
            | ~ big_f(X4,X3) ) ) )
      & ( pd0_0(X4,X3,X1)
        | ( ( ~ big_f(X1,X4)
            | ~ big_f(X4,X3) )
          & ( big_f(X1,X4)
            | big_f(X4,X3) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f15,plain,
    ( ! [X1,X3,X4] :
        ( ~ pd0_0(X4,X3,X1)
        | ( ( ~ big_f(X1,X4)
            | big_f(X4,X3) )
          & ( big_f(X1,X4)
            | ~ big_f(X4,X3) ) ) )
    & ! [X1,X3,X4] :
        ( pd0_0(X4,X3,X1)
        | ( ( ~ big_f(X1,X4)
            | ~ big_f(X4,X3) )
          & ( big_f(X1,X4)
            | big_f(X4,X3) ) ) ) ),
    inference(miniscoping,[status(esa)],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | ~ big_f(X2,X0)
      | big_f(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | big_f(X2,X0)
      | ~ big_f(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( pd0_0(X0,X1,X2)
      | ~ big_f(X2,X0)
      | ~ big_f(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( pd0_0(X0,X1,X2)
      | big_f(X2,X0)
      | big_f(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( big_f(X0,sk0_1(X0,X1))
      | big_f(sk0_1(X0,X1),sk0_0(X1))
      | big_f(X1,sk0_1(X0,X1))
      | big_f(sk0_1(X0,X1),X0) ),
    inference(resolution,[status(thm)],[f10,f19]) ).

fof(f22,plain,
    ! [X0] :
      ( big_f(sk0_1(sk0_0(X0),X0),sk0_0(X0))
      | big_f(X0,sk0_1(sk0_0(X0),X0))
      | big_f(sk0_1(sk0_0(X0),X0),sk0_0(X0))
      | big_f(X0,sk0_1(sk0_0(X0),X0)) ),
    inference(resolution,[status(thm)],[f20,f9]) ).

fof(f23,plain,
    ! [X0] :
      ( big_f(sk0_1(sk0_0(X0),X0),sk0_0(X0))
      | big_f(X0,sk0_1(sk0_0(X0),X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f22]) ).

fof(f29,plain,
    ! [X0] :
      ( big_f(sk0_0(X0),sk0_1(sk0_0(X0),X0))
      | big_f(X0,sk0_1(sk0_0(X0),X0))
      | pd0_0(sk0_1(sk0_0(X0),X0),sk0_0(X0),X0)
      | big_f(sk0_0(X0),sk0_1(sk0_0(X0),X0)) ),
    inference(resolution,[status(thm)],[f20,f13]) ).

fof(f30,plain,
    ! [X0] :
      ( big_f(sk0_0(X0),sk0_1(sk0_0(X0),X0))
      | big_f(X0,sk0_1(sk0_0(X0),X0))
      | pd0_0(sk0_1(sk0_0(X0),X0),sk0_0(X0),X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f29]) ).

fof(f31,plain,
    ! [X0] :
      ( big_f(X0,sk0_1(sk0_0(X0),X0))
      | pd0_0(sk0_1(sk0_0(X0),X0),sk0_0(X0),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f30,f9]) ).

fof(f47,plain,
    ! [X0] :
      ( big_f(X0,sk0_1(sk0_0(X0),X0))
      | big_f(X0,sk0_1(sk0_0(X0),X0))
      | ~ big_f(sk0_1(sk0_0(X0),X0),sk0_0(X0)) ),
    inference(resolution,[status(thm)],[f31,f17]) ).

fof(f48,plain,
    ! [X0] :
      ( big_f(X0,sk0_1(sk0_0(X0),X0))
      | ~ big_f(sk0_1(sk0_0(X0),X0),sk0_0(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f47]) ).

fof(f49,plain,
    ! [X0] : big_f(X0,sk0_1(sk0_0(X0),X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f48,f23]) ).

fof(f50,plain,
    ! [X0] : big_f(sk0_0(X0),sk0_1(sk0_0(X0),X0)),
    inference(resolution,[status(thm)],[f49,f8]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( pd0_0(sk0_1(sk0_0(X0),X0),X1,X0)
      | ~ big_f(sk0_1(sk0_0(X0),X0),X1) ),
    inference(resolution,[status(thm)],[f49,f18]) ).

fof(f53,plain,
    ! [X0] :
      ( pd0_0(sk0_1(sk0_0(X0),X0),sk0_0(X0),X0)
      | big_f(sk0_1(sk0_0(X0),X0),sk0_0(X0)) ),
    inference(resolution,[status(thm)],[f50,f11]) ).

fof(f69,plain,
    ! [X0] : pd0_0(sk0_1(sk0_0(X0),X0),sk0_0(X0),X0),
    inference(forward_subsumption_resolution,[status(thm)],[f53,f51]) ).

fof(f70,plain,
    ! [X0] :
      ( ~ big_f(sk0_0(X0),sk0_1(sk0_0(X0),X0))
      | ~ big_f(sk0_1(sk0_0(X0),X0),sk0_0(X0)) ),
    inference(resolution,[status(thm)],[f69,f12]) ).

fof(f71,plain,
    ! [X0] : ~ big_f(sk0_1(sk0_0(X0),X0),sk0_0(X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f70,f50]) ).

fof(f74,plain,
    ! [X0] :
      ( ~ big_f(X0,sk0_1(sk0_0(X0),X0))
      | big_f(sk0_1(sk0_0(X0),X0),sk0_0(X0)) ),
    inference(resolution,[status(thm)],[f69,f16]) ).

fof(f75,plain,
    ! [X0] : big_f(sk0_1(sk0_0(X0),X0),sk0_0(X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f74,f49]) ).

fof(f83,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f71,f75]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : SYN349+1 : TPTP v8.1.2. Released v2.0.0.
% 0.05/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n019.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon Apr 29 21:57:59 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  % Drodi V3.6.0
% 0.11/0.34  % Refutation found
% 0.11/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.35  % Elapsed time: 0.019340 seconds
% 0.11/0.35  % CPU time: 0.038653 seconds
% 0.11/0.35  % Total memory used: 2.506 MB
% 0.11/0.35  % Net memory used: 2.478 MB
%------------------------------------------------------------------------------