TSTP Solution File: SEU230+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU230+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 12:36:22 EDT 2023

% Result   : Theorem 0.20s 0.39s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   25 (  14 unt;   0 def)
%            Number of atoms       :  101 (  34 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  121 (  45   ~;  48   |;  24   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-3 aty)
%            Number of variables   :   71 (;  66   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [A,B] : set_union2(A,B) = set_union2(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A] : succ(A) = set_union2(A,singleton(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B] :
      ( B = singleton(A)
    <=> ! [C] :
          ( in(C,B)
        <=> C = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B,C] :
      ( C = set_union2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            | in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f32,conjecture,
    ! [A] : in(A,succ(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f33,negated_conjecture,
    ~ ! [A] : in(A,succ(A)),
    inference(negated_conjecture,[status(cth)],[f32]) ).

fof(f50,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f51,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f52,plain,
    ! [A,B] :
      ( ( B != singleton(A)
        | ! [C] :
            ( ( ~ in(C,B)
              | C = A )
            & ( in(C,B)
              | C != A ) ) )
      & ( B = singleton(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | C != A )
            & ( in(C,B)
              | C = A ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f53,plain,
    ( ! [A,B] :
        ( B != singleton(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | C = A )
          & ! [C] :
              ( in(C,B)
              | C != A ) ) )
    & ! [A,B] :
        ( B = singleton(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | C != A )
            & ( in(C,B)
              | C = A ) ) ) ),
    inference(miniscoping,[status(esa)],[f52]) ).

fof(f54,plain,
    ( ! [A,B] :
        ( B != singleton(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | C = A )
          & ! [C] :
              ( in(C,B)
              | C != A ) ) )
    & ! [A,B] :
        ( B = singleton(A)
        | ( ( ~ in(sk0_0(B,A),B)
            | sk0_0(B,A) != A )
          & ( in(sk0_0(B,A),B)
            | sk0_0(B,A) = A ) ) ) ),
    inference(skolemization,[status(esa)],[f53]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( X0 != singleton(X1)
      | in(X2,X0)
      | X2 != X1 ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f59,plain,
    ! [A,B,C] :
      ( ( C != set_union2(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | in(D,A)
              | in(D,B) )
            & ( in(D,C)
              | ( ~ in(D,A)
                & ~ in(D,B) ) ) ) )
      & ( C = set_union2(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)],[f8]) ).

fof(f60,plain,
    ( ! [A,B,C] :
        ( C != set_union2(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_union2(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)],[f59]) ).

fof(f61,plain,
    ( ! [A,B,C] :
        ( C != set_union2(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_union2(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)],[f60]) ).

fof(f63,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_union2(X1,X2)
      | in(X3,X0)
      | ~ in(X3,X1) ),
    inference(cnf_transformation,[status(esa)],[f61]) ).

fof(f115,plain,
    ? [A] : ~ in(A,succ(A)),
    inference(pre_NNF_transformation,[status(esa)],[f33]) ).

fof(f116,plain,
    ~ in(sk0_12,succ(sk0_12)),
    inference(skolemization,[status(esa)],[f115]) ).

fof(f117,plain,
    ~ in(sk0_12,succ(sk0_12)),
    inference(cnf_transformation,[status(esa)],[f116]) ).

fof(f132,plain,
    ! [X0] : in(X0,singleton(X0)),
    inference(destructive_equality_resolution,[status(esa)],[f56]) ).

fof(f134,plain,
    ! [X0,X1,X2] :
      ( in(X0,set_union2(X1,X2))
      | ~ in(X0,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f63]) ).

fof(f229,plain,
    ! [X0,X1] : in(X0,set_union2(singleton(X0),X1)),
    inference(resolution,[status(thm)],[f134,f132]) ).

fof(f352,plain,
    ! [X0,X1] : in(X0,set_union2(X1,singleton(X0))),
    inference(paramodulation,[status(thm)],[f50,f229]) ).

fof(f369,plain,
    ! [X0] : in(X0,succ(X0)),
    inference(paramodulation,[status(thm)],[f51,f352]) ).

fof(f374,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f117,f369]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU230+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n029.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 09:23:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.20/0.39  % Refutation found
% 0.20/0.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.61  % Elapsed time: 0.045137 seconds
% 0.25/0.61  % CPU time: 0.027179 seconds
% 0.25/0.61  % Memory used: 5.622 MB
%------------------------------------------------------------------------------