TSTP Solution File: SEU133+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU133+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 12:35:55 EDT 2023

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   22 (   7 unt;   0 def)
%            Number of atoms       :   90 (   8 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  108 (  40   ~;  41   |;  22   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   71 (;  65   !;   6   ?)

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

fof(f3,axiom,
    ! [A,B,C] :
      ( C = set_difference(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & ~ in(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,conjecture,
    ! [A,B] : subset(set_difference(A,B),A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,negated_conjecture,
    ~ ! [A,B] : subset(set_difference(A,B),A),
    inference(negated_conjecture,[status(cth)],[f10]) ).

fof(f19,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f20,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
      & ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f19]) ).

fof(f21,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(miniscoping,[status(esa)],[f20]) ).

fof(f22,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_0(B,A),A)
          & ~ in(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f21]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f26,plain,
    ! [A,B,C] :
      ( ( C != set_difference(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | ( in(D,A)
                & ~ in(D,B) ) )
            & ( in(D,C)
              | ~ in(D,A)
              | in(D,B) ) ) )
      & ( C = set_difference(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ~ in(D,A)
              | in(D,B) )
            & ( in(D,C)
              | ( in(D,A)
                & ~ in(D,B) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f27,plain,
    ( ! [A,B,C] :
        ( C != set_difference(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ( in(D,A)
                & ~ in(D,B) ) )
          & ! [D] :
              ( in(D,C)
              | ~ in(D,A)
              | in(D,B) ) ) )
    & ! [A,B,C] :
        ( C = set_difference(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ~ in(D,A)
              | in(D,B) )
            & ( in(D,C)
              | ( in(D,A)
                & ~ in(D,B) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f26]) ).

fof(f28,plain,
    ( ! [A,B,C] :
        ( C != set_difference(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ( in(D,A)
                & ~ in(D,B) ) )
          & ! [D] :
              ( in(D,C)
              | ~ in(D,A)
              | in(D,B) ) ) )
    & ! [A,B,C] :
        ( C = set_difference(A,B)
        | ( ( ~ in(sk0_1(C,B,A),C)
            | ~ in(sk0_1(C,B,A),A)
            | in(sk0_1(C,B,A),B) )
          & ( in(sk0_1(C,B,A),C)
            | ( in(sk0_1(C,B,A),A)
              & ~ in(sk0_1(C,B,A),B) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f27]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_difference(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f42,plain,
    ? [A,B] : ~ subset(set_difference(A,B),A),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f43,plain,
    ~ subset(set_difference(sk0_4,sk0_5),sk0_4),
    inference(skolemization,[status(esa)],[f42]) ).

fof(f44,plain,
    ~ subset(set_difference(sk0_4,sk0_5),sk0_4),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_difference(X1,X2))
      | in(X0,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f29]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( subset(set_difference(X0,X1),X2)
      | in(sk0_0(X2,set_difference(X0,X1)),X0) ),
    inference(resolution,[status(thm)],[f24,f55]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( subset(set_difference(X0,X1),X0)
      | subset(set_difference(X0,X1),X0) ),
    inference(resolution,[status(thm)],[f64,f25]) ).

fof(f88,plain,
    ! [X0,X1] : subset(set_difference(X0,X1),X0),
    inference(duplicate_literals_removal,[status(esa)],[f87]) ).

fof(f105,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f44,f88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU133+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n006.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 09:09:02 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
% 0.13/0.38  % Elapsed time: 0.025658 seconds
% 0.13/0.38  % CPU time: 0.035569 seconds
% 0.13/0.38  % Memory used: 14.359 MB
%------------------------------------------------------------------------------