TSTP Solution File: SEU125+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU125+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n031.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 20:41:05 EDT 2024

% Result   : Theorem 7.67s 1.39s
% Output   : CNFRefutation 7.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   39 (   6 unt;   0 def)
%            Number of atoms       :  133 (   8 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  147 (  53   ~;  58   |;  27   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   76 (  69   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [A,B,C] :
      ( C = set_union2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            | in(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f32,conjecture,
    ! [A,B,C] :
      ( ( subset(A,B)
        & subset(C,B) )
     => subset(set_union2(A,C),B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f33,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( subset(A,B)
          & subset(C,B) )
       => subset(set_union2(A,C),B) ),
    inference(negated_conjecture,[status(cth)],[f32]) ).

fof(f48,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)],[f6]) ).

fof(f49,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)],[f48]) ).

fof(f50,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)],[f49]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_union2(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X1)
      | in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f57,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f58,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)],[f57]) ).

fof(f59,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)],[f58]) ).

fof(f60,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_2(B,A),A)
          & ~ in(sk0_2(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f59]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ in(X2,X0)
      | in(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_2(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_2(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f123,plain,
    ? [A,B,C] :
      ( subset(A,B)
      & subset(C,B)
      & ~ subset(set_union2(A,C),B) ),
    inference(pre_NNF_transformation,[status(esa)],[f33]) ).

fof(f124,plain,
    ( subset(sk0_8,sk0_9)
    & subset(sk0_10,sk0_9)
    & ~ subset(set_union2(sk0_8,sk0_10),sk0_9) ),
    inference(skolemization,[status(esa)],[f123]) ).

fof(f125,plain,
    subset(sk0_8,sk0_9),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f126,plain,
    subset(sk0_10,sk0_9),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f127,plain,
    ~ subset(set_union2(sk0_8,sk0_10),sk0_9),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f131,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_union2(X1,X2))
      | in(X0,X1)
      | in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f51]) ).

fof(f165,plain,
    ! [X0] :
      ( ~ in(X0,sk0_10)
      | in(X0,sk0_9) ),
    inference(resolution,[status(thm)],[f61,f126]) ).

fof(f166,plain,
    ! [X0] :
      ( ~ in(X0,sk0_8)
      | in(X0,sk0_9) ),
    inference(resolution,[status(thm)],[f61,f125]) ).

fof(f621,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X1),X2)
      | in(sk0_2(X2,set_union2(X0,X1)),X0)
      | in(sk0_2(X2,set_union2(X0,X1)),X1) ),
    inference(resolution,[status(thm)],[f62,f131]) ).

fof(f625,plain,
    ! [X0] :
      ( subset(X0,sk0_9)
      | ~ in(sk0_2(sk0_9,X0),sk0_8) ),
    inference(resolution,[status(thm)],[f63,f166]) ).

fof(f2509,plain,
    ( spl0_80
  <=> in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f2510,plain,
    ( in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_8)
    | ~ spl0_80 ),
    inference(component_clause,[status(thm)],[f2509]) ).

fof(f2512,plain,
    ( spl0_81
  <=> in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_10) ),
    introduced(split_symbol_definition) ).

fof(f2513,plain,
    ( in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_10)
    | ~ spl0_81 ),
    inference(component_clause,[status(thm)],[f2512]) ).

fof(f2515,plain,
    ( in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_8)
    | in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_10) ),
    inference(resolution,[status(thm)],[f621,f127]) ).

fof(f2516,plain,
    ( spl0_80
    | spl0_81 ),
    inference(split_clause,[status(thm)],[f2515,f2509,f2512]) ).

fof(f3170,plain,
    ( subset(set_union2(sk0_8,sk0_10),sk0_9)
    | ~ spl0_80 ),
    inference(resolution,[status(thm)],[f625,f2510]) ).

fof(f3171,plain,
    ( $false
    | ~ spl0_80 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3170,f127]) ).

fof(f3172,plain,
    ~ spl0_80,
    inference(contradiction_clause,[status(thm)],[f3171]) ).

fof(f3479,plain,
    ( in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_9)
    | ~ spl0_81 ),
    inference(resolution,[status(thm)],[f2513,f165]) ).

fof(f4333,plain,
    ( subset(set_union2(sk0_8,sk0_10),sk0_9)
    | ~ spl0_81 ),
    inference(resolution,[status(thm)],[f3479,f63]) ).

fof(f4334,plain,
    ( $false
    | ~ spl0_81 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4333,f127]) ).

fof(f4335,plain,
    ~ spl0_81,
    inference(contradiction_clause,[status(thm)],[f4334]) ).

fof(f4336,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f2516,f3172,f4335]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU125+2 : 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 : n031.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 : Mon Apr 29 20:16:28 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 7.67/1.39  % Refutation found
% 7.67/1.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 7.67/1.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.32/1.42  % Elapsed time: 1.059961 seconds
% 8.32/1.42  % CPU time: 8.315668 seconds
% 8.32/1.42  % Total memory used: 128.942 MB
% 8.32/1.42  % Net memory used: 124.494 MB
%------------------------------------------------------------------------------